The Past, Present, and Future of Workplace Safety Research – A Review of Beus, McCord, & Zohar (2016)

Beus and colleagues (2016) introduce the integrative safety model to provide a much needed comprehensive and coherent narrative behind research on workplace safety.  This includes thinking which has been supported by research and that which is currently attracting the attention of researchers. The integrative safety model (see figure below) is not an attempt at providing an overarching theory but is simply a way of organizing the most current approaches to workplace safety. The conceptual frame combines the three most dominant theories in workplace safety literature: job performance theory (Campbell, McCloy, Oppler, & Sager, 1993), job demands-resources theory (Bakker & Demerouti, 2007), and organizational climate theory (Zohar, 1980).

Screen Shot 2018-02-24 at 12.39.26 AM.png

An important advance in safety research was to start thinking about safety as a performance behaviour. To perform well, a person requires knowledge, motivation, and skill, and these three are largely determined by individual differences (such as personality) and contextual factors (such as leadership and training). The theory also suggests that history and experience will also shape knowledge, motivation, and skills. Together, job performance theory suggests that individual and contextual factors influence the safety triad of knowledge, motivation, and skill, which in turn influence safety behaviour and outcomes. Outcomes are then said to loop back and have a role in further shaping this safety triad of knowledge, motivation, and skill.

The literature largely, albeit in a rather scattered fashion, supports the proposed links between individual and contextual factors on knowledge, motivation, and skill. These in turn are related to safety-related behaviour and outcomes. However, no actual path or mediation models were reviewed, so it is unclear whether the actual indirect effects have been supported. In addition, the authors repeatedly mention safety skills as a feature with knowledge and motivation, but has this actually been developed? What does safety skill actually look like? The authors acknowledge that the idea of safety skill requires more work, but even the article they cite as an example to have used safety skill (Eklöf & Törner, 2002) really only measured knowledge despite calling their measure knowledge and skill. As such, safety skill is something worth thinking about and potentially developing as a construct, even just to show that it has no effect on safety behaviour.

Another advancement in the workplace safety literature was the adoption of the job demands-resources theory. This theory has proven to be extremely useful because it focuses on an array of job characteristics and contextual factors that either contribute to a person’s ability to do their job (i.e., resources) or contribute to the pressure people face do their job (i.e., demands).  In other words, contextual and job-related demands and resources influence personal resources, which in turn are related to safe and unsafe behaviour.

Again, the literature largely supports this theory. As research on the job demands-resources theory has been fairly substantial, there is a fuller picture of the relationship. Not only do demands and resources rooted in job characteristics and contextual factors indirectly impact safety behaviour through personal resources, they also have a direct relationship with safety behaviour. However, generalizability of the job demands-resources theory is also its weakness. There is very little consensus on how demands and resources interact with each other and what the most important types of demands and resources are to safety behaviour and outcomes. This necessary theoretical contribution will, when it occurs, have important implications for workplace safety research and will have a considerable contribution to practice.

Finally, the most prominent theory in workplace safety research is the application of organizational climate theory in the form of safety climate.  The broader theory suggests that an organization’s collective expectations of how people behave will shape individual- and group-level safety related behaviours.  These expectations typically represent the belief that certain behaviours will be reinforced or punished, and in turn motivate people to behave accordingly. Then, in typical topic specific fashion, the appropriate adjective of safety gets tacked onto climate and we have shared perceptions about the value of safety in the workplace.

The literature on safety climate has turned out to be one of the most productive approaches to explaining and predicting safety-related behaviour.  This includes both levels of safety climate: individual and collective perceptions of safety. However, climate is not the only contextual factor shaping expectations about safety and safety-related behaviour. Other factors include transformational leadership, safety norms, and organizational goal-setting and feedback. While the evidence for these features toward safety-related behaviour is strong, there is disagreement about the intermediate behaviour-outcome expectancy of individuals and the nature of the consequential motivation. The authors argue that safety motivation and behaviour-outcome expectancy produce different types of motivation, the former is a matter of valence (i.e., there is value attached to safety), and the latter is a matter of instrumentality (i.e., the connection between behaviour and outcome is a strategy to achieve or retrieve desired outcomes). Theoretically this makes sense, but empirically I can imagine this would be difficult to separate and is something that will need to be solved to contribute to this argument.

Combining the three theories together, we get the natural tail end of the conceptual model linking individual- and group-level safety-related behaviour to accidents. These accidents in turn have consequences for contextual factors such as policy surrounding workplace safety and perceptions of safety climate. Unlike the previous set of variables, there is no theoretical narrative given to weave these variables together. However, this is arguably unnecessary as it is only one step removed from the previous three theories and can be argued to be a natural consequence of the causal sequence for all three theories.

Nonetheless, the presence of a theoretical explanation for the link between safety-related behaviour and accidents may be warranted.  As much as it is no surprise that safety-related behaviour is related to injuries and accidents, the actual effect size is smaller than would be expected, both at the individual and group level. The authors suggest that part of the story is missing, and other factors outside employee safety-related behaviour play an important role in determining the likelihood of accidents. Therefore, the introduction of a broader narrative encompassing employee safety-related behaviour and accidents will be necessary to fully appreciate the predictors of workplace accidents.

Overall, I found the integrative safety model to be a useful narrative for thinking about workplace safety from a distance. Beus and colleagues provide a good overview of what management and occupational health research has uncovered about workplace safety, what researchers are thinking now, and some speculation as to where we should focus our efforts next. Ultimately, I found this paper to be a helpful exercise to also speculate as to what the future of workplace safety research will look like.

References:

Bakker, A. B., & Demerouti, E. (2007). The job demands-resources model: State of the art. Journal of Managerial Psychology22(3), 309-328.

Beus, J. M., McCord, M. A., & Zohar, D. (2016). Workplace safety: A review and research synthesis. Organizational Psychology Review6(4), 352-381.

Campbell, J. P., McCloy, R. A., Oppler, S. H., & Sager, C. E. (1993). A theory of performance. Personnel Selection in Organizations3570, 35-70.

Eklöf, M. & Törner, M. (2002). Perception and control of occupational injury risks in fishery–a pilot study. Work & Stress16(1), 58-69.

Zohar, D. (1980). Safety climate in industrial organizations: theoretical and applied implications. Journal of Applied Psychology65(1), 96-102.

Chronic motivational state interacts with task reward structure in dynamic decision-making

This paper is about motivation. Cooper and colleagues (2015) claim that the definition of motivation (i.e., “a simple increase in effortful cognitive processing”) is due for a revision.  The authors suggest that motivation is instead better thought of as something more dynamic – an interacting multilevel variable if you will.  This is exemplified in the theoretical lens that they adopted.

The theoretical lens through which Cooper & co. approached motivation is called regulatory fit. This regulatory fit is “achieved when the individual’s global motivational state (chronic or situational) aligns with the local motivational task framing” (p. 41).  When there is “fit”, there should be an increase in effortful cognitive processing and a decreased reliance on habitual cognitive processing. When there is a misfit, the opposite occurs.

To clarify, the global motivational states that Cooper & co. are speaking of are called promotion-focused (i.e., these individuals are more sensitive to potential gains) and prevention-focused (i.e., these individuals are more sensitive to potential losses).

Without overcomplicating things, people who a chronically promotion-focused will engage in effortful cognitive processing if a task is framed as promotion-focused (i.e., they are asked to maximize gains), while individuals who are chronically prevention-focused will engage in effortful cognitive processing if a task is framed as prevention-focused (they are asked to minimize losses).  They call this effortful cognitive processing goal-directed or the model-based system.  Meanwhile, if there is a misfit (e.g., a chronically promotion-focused person is asked to complete a prevention-focused task), people will opt towards the less costly habitual reward-based or model-free system of cognitive processing.

To test this motivational regulatory fit model, the authors recruited participants who were either chronically promotion or prevention focused to repeatedly (250 times) choose between two rewarding options for extracting a valuable resource: one will always provide larger immediate reward but decrease future rewards (called the decreasing option) and the other will always provide lower immediate reward but causes future rewards to increase (called the increasing option).  Meanwhile, participants were randomly assigned to either a gain-maximization condition (the extraction procedures produce varying gains of the resource that needs to be maximized) or loss-minimization condition (the extraction procedures produce a varying output of a dangerous by-product that needs to be minimized). See figure below for how this was shown to participants (gain-maximization on the left, loss-minimization on the right).

Screen Shot 2017-10-29 at 15.11.26

What were the most important results?  In the gain-maximization condition, promotion-focused folks performed better than the prevention-focused folks, and in the loss-minimization condition, prevention-focused folks performed better than the promotion-focused folks.  Even within the regulatory focus groups, the alignment of regulatory focus proved beneficial.  Promotion-focused folk performed better in the gain-maximization condition and prevention-focused folk performed better (albeit non-significantly) in the loss-minimization condition.  The regulatory fit hypothesis of motivation was thus supported.  Additional regression analyses reinforced these findings by showing that that relatively promotion-focused folk performed better in gain-maximization and worse at loss-minimization.

Screen Shot 2017-10-29 at 15.20.13.png

References

Cooper, J. A. Worthy, D. A. & Maddox, W. T. (2015). Chronic motivational state interacts with task reward structure in dynamic decision-making. Cognitive Psychology, 83, 40-53.

Hand or foot?

homonculus

Photo via Dr. Joe Kiff

If you could only keep one, which would you choose: Hand or foot? Eyesight or hearing? Arm or leg? Choices like this luckily come to most of us in the form of morbid games of imagination we play with our friends. But for an unfortunate population, the choice is made for them at work.

In an article by Elsie Cheung and colleagues (2003), they drew on an observation of many clinicians: employees who experience severe injuries or amputations to their upper-extremity (i.e., fingers, hands, arms) at work seem to be particularly vulnerable to psychological maladjustment. While anecdotes may serve their purpose, Cheung and co. wanted to test whether those who experienced upper-extremity injuries were in fact psychologically worse-off than others who experienced severe injuries and amputations elsewhere. This clearly had implications for treatment and rehabilitation.

Diving into the library at the Workers Compensation Board of British Columbia, Cheung and colleagues pulled out files for individuals who 1) experienced upper extremity amputations or lower extremity amputations, 2) who were assessed by a clinical psychologist at the outpatient rehabilitation center, and 3) were psychologically healthy prior to the injury.

Statistical comparisons of the two groups revealed some interesting results in line with the observations of clinicians.  Workers who had injuries to their upper extremities had substantially more symptoms of posttraumatic stress disorder (e.g., distressing flashbacks, emotional numbness) and slightly elevated signs of depression. When considering pain, however, both groups experienced similar levels.

Screen Shot 2017-10-17 at 07.40.25.png

So, what is the take away? Why do severe injuries and amputations to our fingers, hands, and arms leave us more vulnerable to psychological maladjustment? Cheung and co. align with Grunert and colleagues (1988), who made the argument that it comes down to functional loss, self-image, and social acceptance. So much of what we do on a day-to-day basis depends on using our hands (like typing this very sentence). What we do is important in shaping who we are, and who we are is who people have come to accept. All of this comes crashing down when that choice is made for the unfortunate few.

References

Cheung, E., Alvaro, R., & Colotla, V. A. (2003). Psychological distress in workers with traumatic upper or lower limb amputations following industrial injuries. Rehabilitation Psychology, 48(2), 109-112.  

Grunert, B. K., Smith, C. J., Devine, C. A., Fehring, B. A., Matloub, H. S., Sanger, J. R., & Yousif, N. J. (1988). Early psychological aspects of severe hand injury. Journal of Hand Surgery, 13B, 177–180.

Get [M]oving in Mplus – part 5: Define subcommands

Despite having to import a dataset into Mplus from another stats program, you can conduct most of the variable manipulation you need in Mplus. This is good news as you’ll often find yourself in a position of having to transform exisiting variables (e.g., log transformations) or creating new variables (e.g., mean scores).

In any case, it can be very annoying having to go back to SPSS to do all of this stuff. Fret not, Mplus has your back with the DEFINE command.

There are a few notes to make before summarizing the most used operations under the DEFINE command.

  • Operations with the DEFINE command can be done on all observations or a selection of some based on conditional statements (e.g., IF(gender EQ 1) THEN…)
  • Transformations do not alter the original data (phew) but hold the alterations in memory only during analysis (unless you use the SAVEDATA command, then the transformed values are saved)
  • All statements in the DEFINE command are done in order (so if you create a mean score and want to transform it, it must be done in this order and not the opposite)
  • Any new variables you create for use in analysis must be listed after original variables being used in analysis within the USEVARIABLES subcommand.
  • The following logical operators, arithmetic operators, and functions can be used in the DEFINE command:

Screen Shot 2017-06-05 at 6.24.34 PM.png

And here are some of the common operations (although not an exhaustive list) you’ll likely find yourself using at one point or another:

Create mean score variables:

Love = Mean(intimate passion commit); 

or

Love = intimate+passion+commit/3;

Create summative score variables:

Love = Sum(intimate passion commit);

Create other variables (e.g., interaction terms or convert units such as kilos to pound)

Lust = intimate*passion;
Pounds = .454*kgs;

Grand- or group-mean center a variable or variables:

CENTER Love (GRANDMEAN);

or

CENTER Love (GROUPMEAN);

Standardize a variable or variables:

STANDARDIZE Love;

Transform variables:

Lovelog = log10(Love);
Lovesqrt = sqrt(Love);

Conditional statements:

IF (sex EQ 0 AND relstat EQ 1) THEN group = 1;
IF (sex EQ 0 AND relstat EQ 2) THEN group = 2;
IF (sex EQ 1 AND relstat EQ 1) THEN group = 3;
IF (sex EQ 1 AND relstat EQ 2) THEN group = 4;

If there are other operations that you need to do and are possible in the DEFINE command but I haven’t covered here, please let me know. If there are other operations I ever use along the way, I’ll be sure to update this post!

Rudi[M]entary Model Commands in Mplus – part 3: BY

The third rudimentary model command in Mplus is BY or factor. Although statistically more complicated than the previous two, a factor simply generates a latent or unobserved variable through its prediction of observed variables. In other words, you are telling Mplus you have a variable that exists but cannot be measured directly (what is called a latent variable) and that you have some measurements of behaviour proposed to be caused by this latent variable (what are called observed or measured variables).

This is important to understand, so how about an example?

Consider the personality trait extraversion. People who are extraverted are considered outgoing and gregarious (McCrae & Costa, 1987). However, we cannot put someone’s extraversion on a bathroom scale and weigh it — nor can we pour it out of people into a test tube. Extraversion is simply a way of organizing and thinking about a common pattern of behaviours. In other words, extraversion is a latent variable and we must measure it by gathering observed variables representative of our idea of what an extraverted person is, how they behave, and the thoughts they commonly have.

In psychology, asking people questions about themselves and their behaviour is the most common form of measurement. It is no surprise that people tend to understand themselves better than anyone else (especially when it comes internal behaviours such as beliefs, attitudes, and emotions). When measuring extraversion, we can, for instance, ask people to rate the degree to which they consider themselves as talkative.

There are also other ways of gathering observed variables aside from self-report. We can hire coders to observe someone’s behaviour (e.g., code how frequently a participant approaches strangers to strike up a conversation), recruit people who know our participant (e.g., have peers rate how gregarious our participant is in general), and so forth into the realms of creativity.

Essentially, our model of reality is that the personality trait of extraversion (our latent variable) is causing specific patterns of behaviour, such as talkativeness, sociability, and gregariousness (the observed variables).

Visually, this is what it looks like:

factor example

And here is a generic syntax that would run this factor analysis:

Screen Shot 2017-04-29 at 2.26.51 PM

Now, lets look at an example from a real dataset.

Here, participants were asked to think about themselves and rate the extent to which they agree with the following statements about their tendency to perspective-take (i.e., try to understand the world from another’s point of view):

  1. “I try to look at everybody’s side of a diagreement before I make a decision”
  2. “I sometimes try to understand my friends better by imagining how things look from their perspective”
  3. “I believe there are two sides to every question, and try to look at them both”
  4. “When I’m upset at someone, I usually try to put myself in his/her shoes for a while”
  5. “Before criticizing somebody, I try to imagine how I would feel if I were in their place”

Translating these items into Mplus and producing their factor results in the following syntax:


TITLE:
Simple Confirmatory Factor Analysis;

DATA:
File is PT5.dat;

VARIABLE:
Names are PT1 PT2 PT3 PT4 PT5;
Missing are all(-999);
Usevariables = PT1 PT2 PT3 PT4 PT5;

MODEL:
PT by PT1 PT2 PT3 PT4 PT5;
!Latent factor by observed factors

OUTPUT:
Standardized sampstat Modindices(all);

And produces the following output:


Mplus VERSION 7.4 (Mac)
MUTHEN & MUTHEN
05/28/2017  10:01 AM

INPUT INSTRUCTIONS

TITLE:
Simple Confirmatory Factor Analysis;

DATA:
File is PT5.dat;

VARIABLE:
Names are PT1 PT2 PT3 PT4 PT5;
Missing are all(-999);
Usevariables = PT1 PT2 PT3 PT4 PT5;

MODEL:
PT by PT1 PT2 PT3 PT4 PT5;
!Latent factor by observed factors

OUTPUT:
Standardized sampstat Modindices(all);

*** WARNING
Data set contains cases with missing on all variables.
These cases were not included in the analysis.
Number of cases with missing on all variables:  8
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS

Simple Confirmatory Factor Analysis;

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         982

Number of dependent variables                                    5
Number of independent variables                                  0
Number of continuous latent variables                            1

Observed dependent variables

Continuous
PT1         PT2         PT3         PT4         PT5

Continuous latent variables
PT

Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03

Input data file(s)
PT5.dat

Input data format  FREE

SUMMARY OF DATA

Number of missing data patterns             2

COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100

PROPORTION OF DATA PRESENT

Covariance Coverage
PT1           PT2           PT3           PT4           PT5
________      ________      ________      ________      ________
PT1            1.000
PT2            0.998         0.998
PT3            1.000         0.998         1.000
PT4            1.000         0.998         1.000         1.000
PT5            1.000         0.998         1.000         1.000         1.000

SAMPLE STATISTICS

ESTIMATED SAMPLE STATISTICS

Means
PT1           PT2           PT3           PT4           PT5
________      ________      ________      ________      ________
1         3.990         3.910         4.071         3.684         3.784

Covariances
PT1           PT2           PT3           PT4           PT5
________      ________      ________      ________      ________
PT1            0.829
PT2            0.559         0.881
PT3            0.496         0.520         0.734
PT4            0.539         0.633         0.481         1.051
PT5            0.574         0.607         0.512         0.671         0.996

Correlations
PT1           PT2           PT3           PT4           PT5
________      ________      ________      ________      ________
PT1            1.000
PT2            0.654         1.000
PT3            0.635         0.646         1.000
PT4            0.577         0.658         0.547         1.000
PT5            0.632         0.648         0.599         0.656         1.000

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -5337.842

UNIVARIATE SAMPLE STATISTICS

UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

PT1                   3.990      -0.935       1.000    1.43%       3.000      4.000      4.000
982.000       0.829       0.761       5.000   30.35%       4.000      5.000
PT2                   3.910      -0.797       1.000    1.63%       3.000      4.000      4.000
980.000       0.882       0.368       5.000   28.16%       4.000      5.000
PT3                   4.071      -0.953       1.000    1.22%       3.000      4.000      4.000
982.000       0.734       1.095       5.000   33.20%       4.000      5.000
PT4                   3.684      -0.746       1.000    4.07%       3.000      4.000      4.000
982.000       1.051       0.173       5.000   20.57%       4.000      5.000
PT5                   3.784      -0.664       1.000    2.44%       3.000      4.000      4.000
982.000       0.996       0.001       5.000   25.46%       4.000      5.000

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       15

Loglikelihood

H0 Value                       -5357.476
H1 Value                       -5337.842

Information Criteria

Akaike (AIC)                   10744.952
Bayesian (BIC)                 10818.296
Sample-Size Adjusted BIC       10770.656
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value                             39.268
Degrees of Freedom                     5
P-Value                           0.0000

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.084
90 Percent C.I.                    0.060  0.109
Probability RMSEA <= .05           0.010

CFI/TLI

CFI                                0.987
TLI                                0.974

Chi-Square Test of Model Fit for the Baseline Model

Value                           2686.639
Degrees of Freedom                    10
P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

Value                              0.017

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PT       BY
PT1                1.000      0.000    999.000    999.000
PT2                1.091      0.039     27.699      0.000
PT3                0.910      0.036     25.272      0.000
PT4                1.099      0.044     24.953      0.000
PT5                1.115      0.042     26.451      0.000

Intercepts
PT1                3.990      0.029    137.334      0.000
PT2                3.909      0.030    130.471      0.000
PT3                4.071      0.027    148.892      0.000
PT4                3.684      0.033    112.616      0.000
PT5                3.784      0.032    118.810      0.000

Variances
PT                 0.515      0.036     14.217      0.000

Residual Variances
PT1                0.314      0.018     17.719      0.000
PT2                0.268      0.017     15.958      0.000
PT3                0.308      0.017     18.414      0.000
PT4                0.429      0.024     18.207      0.000
PT5                0.357      0.021     17.217      0.000

STANDARDIZED MODEL RESULTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PT       BY
PT1                0.788      0.015     54.078      0.000
PT2                0.834      0.013     66.497      0.000
PT3                0.762      0.016     48.446      0.000
PT4                0.770      0.015     49.858      0.000
PT5                0.801      0.014     57.054      0.000

Intercepts
PT1                4.383      0.104     42.175      0.000
PT2                4.165      0.099     41.945      0.000
PT3                4.751      0.112     42.475      0.000
PT4                3.594      0.087     41.239      0.000
PT5                3.791      0.091     41.522      0.000

Variances
PT                 1.000      0.000    999.000    999.000

Residual Variances
PT1                0.379      0.023     16.487      0.000
PT2                0.304      0.021     14.555      0.000
PT3                0.419      0.024     17.462      0.000
PT4                0.408      0.024     17.170      0.000
PT5                0.358      0.023     15.907      0.000

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PT       BY
PT1                0.788      0.015     54.078      0.000
PT2                0.834      0.013     66.497      0.000
PT3                0.762      0.016     48.446      0.000
PT4                0.770      0.015     49.858      0.000
PT5                0.801      0.014     57.054      0.000

Intercepts
PT1                4.383      0.104     42.175      0.000
PT2                4.165      0.099     41.945      0.000
PT3                4.751      0.112     42.475      0.000
PT4                3.594      0.087     41.239      0.000
PT5                3.791      0.091     41.522      0.000

Variances
PT                 1.000      0.000    999.000    999.000

Residual Variances
PT1                0.379      0.023     16.487      0.000
PT2                0.304      0.021     14.555      0.000
PT3                0.419      0.024     17.462      0.000
PT4                0.408      0.024     17.170      0.000
PT5                0.358      0.023     15.907      0.000

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PT       BY
PT1                0.718      0.025     28.434      0.000
PT2                0.783      0.025     30.927      0.000
PT3                0.653      0.024     27.098      0.000
PT4                0.789      0.029     27.454      0.000
PT5                0.800      0.027     29.100      0.000

Intercepts
PT1                3.990      0.029    137.334      0.000
PT2                3.909      0.030    130.471      0.000
PT3                4.071      0.027    148.892      0.000
PT4                3.684      0.033    112.616      0.000
PT5                3.784      0.032    118.810      0.000

Variances
PT                 1.000      0.000    999.000    999.000

Residual Variances
PT1                0.314      0.018     17.719      0.000
PT2                0.268      0.017     15.958      0.000
PT3                0.308      0.017     18.414      0.000
PT4                0.429      0.024     18.207      0.000
PT5                0.357      0.021     17.217      0.000

R-SQUARE

Observed                                        Two-Tailed
Variable        Estimate       S.E.  Est./S.E.    P-Value

PT1                0.621      0.023     27.039      0.000
PT2                0.696      0.021     33.249      0.000
PT3                0.581      0.024     24.223      0.000
PT4                0.592      0.024     24.929      0.000
PT5                0.642      0.023     28.527      0.000

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.150E-01
(ratio of smallest to largest eigenvalue)

MODEL MODIFICATION INDICES

Minimum M.I. value for printing the modification index    10.000

M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.

ON Statements

PT1      ON PT3                   13.131     0.156      0.156        0.147
PT1      ON PT4                   10.045    -0.117     -0.117       -0.131
PT3      ON PT1                   13.131     0.153      0.153        0.162
PT3      ON PT4                   14.998    -0.136     -0.136       -0.163
PT4      ON PT1                   10.045    -0.159     -0.159       -0.141
PT4      ON PT3                   14.998    -0.189     -0.189       -0.158
PT4      ON PT5                   19.784     0.215      0.215        0.209
PT5      ON PT4                   19.784     0.178      0.178        0.183

WITH Statements

PT3      WITH PT1                 13.131     0.048      0.048        0.154
PT4      WITH PT1                 10.045    -0.050     -0.050       -0.136
PT4      WITH PT3                 14.998    -0.058     -0.058       -0.160
PT5      WITH PT4                 19.784     0.077      0.077        0.196

DIAGRAM INFORMATION

Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
If running Mplus from the Mplus Diagrammer, the diagram opens automatically.

Diagram output
/Users/Granger/Google Drive/Website/Stats Resources/Mplus/Files for post/Rudimentary analyses in

Beginning Time:  10:01:14
Ending Time:  10:01:14
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2015 Muthen & Muthen

 

There are two highlighted regions in the output that we want to pay particular attention to. The first region pertains to the Model Fit of our perspective-taking scale (i.e., how well our scale captures reality). Most researchers report the following fit indices: Chi-square test of model fit, CFI, RMSEA, and SRMR. What these mean is a whole other post, but here are the general “rules of thumb” (Hu & Bentler, 1999):

  • Chi-square test of model fit: non-significant (or as small a value as possible — this fit index is unfortunately vulnerable to larger sample sizes, so people can often shrug off a signficant value with the right reference, e.g., Bentler, 1990)
  • Comparative Fit Index (CFI): Equal to or greater than .95
  • Root Mean Square Error of Approximation (RMSEA): Equal to or less than .06
  • Standardized Root Mean Square Residual (SRMR): Equal to or less than .08

In the sample output, you can see that some fit indices meet or surpass our rules of thumb (including the CFI and SRMR) and some fit indices are edging on problematic (including the chi-square test of model fit and RMSEA). Messiness like this is very common in research but the general take-away here is that the scale is satisfactory but not great.

The second region we need to pay attention to is the Standardized Model Results, STDYX Standardization.  Here we have what are called our factor loadings (or lambdas; under the Estimate column) which are kind of like correlations between the observed variables and the latent variable. In general, you want factor loadings no lower than .40, but higher is even better. In this example, our items are loading on the latent factor very well – which is a good sign!

Finally, if you happen to use Mplus Diagrammer instead of Mplus editor, Mplus will produce sweet diagrams such as this to help you visualize your factor analysis:

PT factor diagram

And that is about it for the basics of how to use and interpret the BY command! And now for some Mplus syntax humor: Good BY see you later;

References

Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238-246.

Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55.

McCrae, R. R., & Costa, P. T. (1987). Validation of the five-factor model of personality across instruments and observers. Journal of Personality and Social Psychology, 52(1), 81-90.

When I Flirted with Evolutionary Psychology: My Undergraduate Thesis on Mating Strategies and Power

11888974263_a015984662_h(photograph via Mike Boswell)

Intimate relationships are a fascinating phenomenon and have played an important role throughout human evolutionary history.  In fact, they are why we are here today.  Non-coincidentally, whom we choose as our romantic partner(s) is largely, consciously or unconsciously, strategic.  This can be seen in our mate preferences and our desire for short- or long-term relationships.  The reason for these deep-rooted desires is that they helped our ancestors solve adaptive problems (Buss & Schmitt, 1993).  Amazingly, we can make predictions about our current behaviour based on these underlying desires, better known as our evolutionary psychology.  This is exactly what I attempted to examine in my undergraduate thesis.

Specifically, I was interested in examining the factors that led people to use strategies related to short-term mating (i.e., brief affairs) and I predicted that power (i.e., the capacity to influence others) would be such a factor.

Previous research has shown that power has striking effects on our behaviour.  In particular, when we feel powerful, we tend to be less restrained, take more risks, and feel more optimistic about how others feel about us (Keltner, Gruenfeld, & Anderson, 2003).  On the other hand, when we feel powerless, we feel inhibited, anxious, and prudent about other peoples’ intentions.  It is important to keep in mind that power plays a role in our social context, and that mating strategies are context dependent.

The next question was, how can you momentarily and ethically alter peoples’ sense of power? At the time of my undergraduate thesis, there was a popular and influential study that claimed to have found that holding certain postures influences our feelings of power (Carney, Cuddy, & Yap, 2010).  Given I wanted to create a study that was fun for my participants (and entertaining for me), I joined the power pose replication party (of course, with hindsight, we now know that there is little-to-no evidence for the effect of power posing!; Ranehill, E., Dreber, Johannesson, Leiberg, Sul, & Weber, 2015).

I ran a study with participants in heterosexual dating relationships, some of which were assigned to hold high-power poses marked by open and expansive nonverbal behaviour – while others were assigned to hold low-power poses marked by closed and restricted nonverbal behaviour.  All participants were then asked to ostensibly rate photographs of attractive others of the opposite sex (while I measured how long they looked at the photographs) and complete a number of questions about their attitudes.

Unfortunately, the power posing did not have an effect on subjective sense of power (i.e., my manipulation check did not pass muster!). However both males and females in the high-power posing condition did look significantly longer at the attractive people.

I then further examined the subjective sense of power as measured through self-report questions.  On the whole, males felt significantly more powerful than females.  In addition, when participants felt a higher subjective sense of power, they paid greater attention towards attractive others.  That is, higher-power participants displayed approach-oriented behaviour toward attractive others.  This aligns nicely with previous research on power, and the subsequent approach-oriented behaviour that it has been found to produce (Keltner et al., 2003).

I was also interested in examining sex differences in terms of attention to attractice others.  Based on evolutionary theory, males should show a stronger preference for sexual variety, and therefore should exhibit greater attention to alternatives (Schmitt, Shackelford, & Buss, 2001).  In addition, females should exhibit less interest in allocating attention to alternative partners.  Both of these predictions were supported.

Furthermore, I predicted that attention to attractive others would be negatively associated with relationship quality.  That is, those who are satisfied and committed to their relationships should show less interest in paying attention to attractive others.  This prediction was also confirmed.

Overall, the results of the study for my undergraduate thesis aligned with several lines of research.  First, the findings for power support previous theoretical predictions based on the leading model of power (and added to the stockpile of unsuccessful power pose studies).  Second, the replication of sex differences provided further support to the mounting evidence for evolutionary psychology.  Finally, the connection between sex, power, and mating strategies provided further insight into how intimate relationships thrive or dissipate.

References

Buss, D. M., & Schmitt, D. P. (1993). Sexual strategies theory: An evolutionary perspective on human mating. Psychological Review, 100, 204-232. doi: 10.1037/0033-295X.100.2.204

Carney, D. R., Cuddy, A. J. C., & Yap, A. J. (2010). Power posing: Brief nonverbal displays affect neuroendocrine levels and risk tolerance. Psychological Science, 21, 1363-1368. doi: 10.1177/0956797610383437

Keltner, D., Gruenfeld, D. H., & Anderson, C. (2003). Power, approach, and inhibition. Psychological Review, 110, 265-284. doi: 10.1037/0033-295X.110.2.265

Ranehill, E., Dreber, A., Johannesson, M., Leiberg, S., Sul, S., & Weber, R. A. (2015). Assessing the robustness of power posing: No effect on hormones and risk tolerance in a large sample of men and women. Psychological Science, 26(5), 653-656.

Schmitt, D. P., Shackelford, T. K., & Buss, D. M. (2001). Are men really more ‘oriented’ toward short-term mating than women? A critical review of theory and research. Psychology, Evolution & Gender, 3, 211-239. doi: 10.1080/14616660110119331

Rudi[M]entary Model Commands in Mplus – part 2: ON

The second rudimentary model command in Mplus is ON or regress. This is similar to correlation but now you are inferring direction (i.e., single-headed arrow).


TITLE:
Simple Regression Analysis;

DATA:
File is example.dat;

VARIABLE:
Names are VARx VARy;
Missing are all(-999);
Usevariables = VARx VARy;

ANALYSIS:
Estimator = ML;

MODEL:
VARy on VARx; !VARx is predicting VARy

OUTPUT:
Standardized sampstat;

Now the language used here can be a bit tricky, as Mplus uses traditional regression speak. But just try to remember that it’s backwards to the intuitive understanding: VARy on VARx means VARy is being regressed on our predictor VARx or VARx is predicting VARy.

If you’re anything like me, that takes a little while to warm up to, but it will happen. As you’re learning, I would recommend you always make notes after each line of command to remind yourself what your testing (like I did above), regression or otherwise, it’s good practice.

Now let’s look at an example of a simple regression using real data:

Screen Shot 2017-04-30 at 8.02.57 PM

In this example we have political knowledge (i.e., an employee’s collection of strategic and potentially sensitive information about his or her supervisor) predicting change-oriented organizational citizenship behaviour (i.e., an individual’s extra-role behaviour enacted to bring around change in the workplace). The idea here is that an individual’s knowledge about their supervisor will enable them to bring around change.

And here is the output created from running this syntax:


Mplus VERSION 7.4 (Mac)
MUTHEN & MUTHEN
04/30/2017   7:57 PM

INPUT INSTRUCTIONS

TITLE:
Simple Regression Analysis;

DATA:
File is PK4regression.dat;

VARIABLE:
Names are PK PW PS PT CHOCB LMX;
Missing are all(-999);
Usevariables = PK CHOCB;

ANALYSIS:
Estimator = ML;

MODEL:
CHOCB on PK; !PK is predicting CHOCB

OUTPUT:
Standardized sampstat;

*** WARNING
Data set contains cases with missing on all variables.
These cases were not included in the analysis.
Number of cases with missing on all variables:  1
*** WARNING
Data set contains cases with missing on x-variables.
These cases were not included in the analysis.
Number of cases with missing on x-variables:  1
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS

Simple Regression Analysis;

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         493

Number of dependent variables                                    1
Number of independent variables                                  1
Number of continuous latent variables                            0

Observed dependent variables

Continuous
CHOCB

Observed independent variables
PK

Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03

Input data file(s)
PK4regression.dat

Input data format  FREE

SUMMARY OF DATA

Number of missing data patterns             1

COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100

PROPORTION OF DATA PRESENT

Covariance Coverage
CHOCB         PK
________      ________
CHOCB          1.000
PK             1.000         1.000

SAMPLE STATISTICS

ESTIMATED SAMPLE STATISTICS

Means
CHOCB         PK
________      ________
1         3.640         3.458

Covariances
CHOCB         PK
________      ________
CHOCB          0.585
PK             0.238         0.547

Correlations
CHOCB         PK
________      ________
CHOCB          1.000
PK             0.421         1.000

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -1070.188

UNIVARIATE SAMPLE STATISTICS

UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

CHOCB                 3.640      -0.581       1.000    0.41%       3.000      3.500      3.750
493.000       0.585       0.443       5.000    5.48%       4.000      4.250
PK                    3.458      -0.433       1.040    0.20%       2.870      3.350      3.520
493.000       0.547       0.200       5.000    1.01%       3.700      4.090

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                        3

Loglikelihood

H0 Value                        -519.526
H1 Value                        -519.526

Information Criteria

Akaike (AIC)                    1045.053
Bayesian (BIC)                  1057.654
Sample-Size Adjusted BIC        1048.132
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value                              0.000
Degrees of Freedom                     0
P-Value                           0.0000

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.000
90 Percent C.I.                    0.000  0.000
Probability RMSEA <= .05           0.000

CFI/TLI

CFI                                1.000
TLI                                1.000

Chi-Square Test of Model Fit for the Baseline Model

Value                             96.004
Degrees of Freedom                     1
P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

Value                              0.000

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

CHOCB    ON
PK                 0.435      0.042     10.295      0.000

Intercepts
CHOCB              2.134      0.150     14.276      0.000

Residual Variances
CHOCB              0.482      0.031     15.700      0.000

STANDARDIZED MODEL RESULTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

CHOCB    ON
PK                 0.421      0.037     11.348      0.000

Intercepts
CHOCB              2.790      0.254     10.992      0.000

Residual Variances
CHOCB              0.823      0.031     26.392      0.000

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

CHOCB    ON
PK                 0.569      0.048     11.859      0.000

Intercepts
CHOCB              2.790      0.254     10.992      0.000

Residual Variances
CHOCB              0.823      0.031     26.392      0.000

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

CHOCB    ON
PK                 0.435      0.042     10.295      0.000

Intercepts
CHOCB              2.134      0.150     14.276      0.000

Residual Variances
CHOCB              0.482      0.031     15.700      0.000

R-SQUARE

Observed                                        Two-Tailed
Variable        Estimate       S.E.  Est./S.E.    P-Value

CHOCB              0.177      0.031      5.674      0.000

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.337E-02
(ratio of smallest to largest eigenvalue)

Beginning Time:  19:57:50
Ending Time:  19:57:50
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2015 Muthen & Muthen

Looking under the section STANDARDIZED MODEL RESULTS we can see that political knowledge predicting change-oriented organizational citizenship behaviour produces a standardized beta weight of .42, < .001. Looking under R-SQUARE we can see that PK accounts for close to 18% of the variance in predicting CHOCB  (R² = .18 [rounded up]). Although there is directionality inferred in regression analysis, study design determines whether causality can be inferred — and in this case it cannot because the study was a self-report survey which measured both variables.

Now, you would very rarily run just a single simple regression, but I wanted to keep it simple for show. If you wanted to run a multiple regression, you would just add more predictor variables on the right-hand side of the ON model command. Simple as that!

Rudi[M]entary Model Commands in Mplus – part 1: WITH

One of the beautiful things about Mplus is that there are only three rudimentary model commands. One of these is “WITH” which asks Mplus to correlate/covariate variables that fall on either side of it.

Here is an generic syntax applying the WITH model command:

TITLE:
Simple correlation analysis;

DATA:
File is FILENAME.dat;

VARIABLE:
Names are VARx VARy;

Missing are all(-999);

Usevariables = VARx VARy;

MODEL:
VARx with VARy;

OUTPUT:
Standardized Sampstat;

Visually the above is asking, what is the relationship between VARx and VARy (i.e., no causation is inferred):

correlation

Imagine you have a bunch of variables you want to correlate, how would you write the syntax so that you can create a correlation matrix? Below is an applied example using real data to answer this question.

Screen Shot 2017-04-29 at 12.45.15 AM

Here we are looking at the correlations between political knowledge (i.e., an employee’s collection of strategic and potentially sensitive information about his or her supervisor), political will (i.e., an individual’s motivation to engage in political behaviour), political skill (i.e., an individual’s interpersonal effectiveness), and change-oriented organizational citizenship behaviour (i.e., an individual’s extra-role behaviour enacted to bring around change in the workplace).

The above syntax produces the output below. There are actually two places where standardized correlations are provided because I also asked for the sample statistics (sampstat) under the output command: one under SAMPLE STATISTICS and one under STANDARDIZED MODEL RESULTS (see highlighted areas):


Mplus VERSION 7.4 (Mac)
MUTHEN & MUTHEN
04/29/2017  12:32 AM

INPUT INSTRUCTIONS

TITLE:
Simple Correlation Analysis;

DATA:
File is PK4correlations.dat;

VARIABLE:
Names are PK PW PS PT CHOCB LMX;
Missing are all(-999);
Usevariables = PK PW PS CHOCB;

ANALYSIS:
Estimator = ML;

MODEL:
PK PW PS CHOCB with PK PW PS CHOCB;

OUTPUT:
Standardized sampstat;

*** WARNING
Data set contains cases with missing on all variables.
These cases were not included in the analysis.
Number of cases with missing on all variables:  1
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS

Simple Correlation Analysis;

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         494

Number of dependent variables                                    4
Number of independent variables                                  0
Number of continuous latent variables                            0

Observed dependent variables

Continuous
PK          PW          PS          CHOCB

Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03

Input data file(s)
PK4correlations.dat

Input data format  FREE

SUMMARY OF DATA

Number of missing data patterns             3

COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100

PROPORTION OF DATA PRESENT

Covariance Coverage
PK            PW            PS            CHOCB
________      ________      ________      ________
PK             0.998
PW             0.996         0.996
PS             0.996         0.996         0.996
CHOCB          0.998         0.996         0.996         1.000

SAMPLE STATISTICS

ESTIMATED SAMPLE STATISTICS

Means
PK            PW            PS            CHOCB
________      ________      ________      ________
1         3.459         4.130         5.100         3.642

Covariances
PK            PW            PS            CHOCB
________      ________      ________      ________
PK             0.547
PW             0.215         1.640
PS             0.360         0.347         1.042
CHOCB          0.238         0.232         0.384         0.586

Correlations
PK            PW            PS            CHOCB
________      ________      ________      ________
PK             1.000
PW             0.227         1.000
PS             0.476         0.265         1.000
CHOCB          0.421         0.237         0.492         1.000

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -2477.074

UNIVARIATE SAMPLE STATISTICS

UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

PK                    3.458      -0.433       1.040    0.20%       2.870      3.350      3.520
493.000       0.547       0.200       5.000    1.01%       3.700      4.090
PW                    4.130      -0.403       1.000    2.24%       3.130      3.880      4.250
492.000       1.640      -0.338       7.000    0.20%       4.500      5.250
PS                    5.100      -0.581       1.220    0.20%       4.280      4.940      5.220
492.000       1.043       0.542       7.000    2.03%       5.440      5.940
CHOCB                 3.642      -0.583       1.000    0.40%       3.000      3.500      3.750
494.000       0.586       0.441       5.000    5.47%       4.000      4.250

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       14

Loglikelihood

H0 Value                       -2477.074
H1 Value                       -2477.074

Information Criteria

Akaike (AIC)                    4982.147
Bayesian (BIC)                  5040.983
Sample-Size Adjusted BIC        4996.546
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value                              0.000
Degrees of Freedom                     0
P-Value                           0.0000

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.000
90 Percent C.I.                    0.000  0.000
Probability RMSEA <= .05           0.000

CFI/TLI

CFI                                1.000
TLI                                1.000

Chi-Square Test of Model Fit for the Baseline Model

Value                            341.302
Degrees of Freedom                     6
P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

Value                              0.000

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PK       WITH
PW                 0.215      0.044      4.910      0.000
PS                 0.360      0.038      9.548      0.000
CHOCB              0.238      0.028      8.612      0.000

PW       WITH
PS                 0.347      0.061      5.687      0.000
CHOCB              0.232      0.045      5.111      0.000

PS       WITH
CHOCB              0.384      0.039      9.796      0.000

Means
PK                 3.459      0.033    103.886      0.000
PW                 4.130      0.058     71.548      0.000
PS                 5.100      0.046    110.878      0.000
CHOCB              3.642      0.034    105.760      0.000

Variances
PK                 0.547      0.035     15.700      0.000
PW                 1.640      0.105     15.686      0.000
PS                 1.042      0.066     15.692      0.000
CHOCB              0.586      0.037     15.716      0.000

STANDARDIZED MODEL RESULTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PK       WITH
PW                 0.227      0.043      5.307      0.000
PS                 0.476      0.035     13.677      0.000
CHOCB              0.421      0.037     11.350      0.000

PW       WITH
PS                 0.265      0.042      6.328      0.000
CHOCB              0.237      0.043      5.563      0.000

PS       WITH
CHOCB              0.492      0.034     14.385      0.000

Means
PK                 4.678      0.156     30.066      0.000
PW                 3.225      0.112     28.738      0.000
PS                 4.996      0.165     30.206      0.000
CHOCB              4.758      0.158     30.130      0.000

Variances
PK                 1.000      0.000    999.000    999.000
PW                 1.000      0.000    999.000    999.000
PS                 1.000      0.000    999.000    999.000
CHOCB              1.000      0.000    999.000    999.000

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PK       WITH
PW                 0.227      0.043      5.307      0.000
PS                 0.476      0.035     13.677      0.000
CHOCB              0.421      0.037     11.350      0.000

PW       WITH
PS                 0.265      0.042      6.328      0.000
CHOCB              0.237      0.043      5.563      0.000

PS       WITH
CHOCB              0.492      0.034     14.385      0.000

Means
PK                 4.678      0.156     30.066      0.000
PW                 3.225      0.112     28.738      0.000
PS                 4.996      0.165     30.206      0.000
CHOCB              4.758      0.158     30.130      0.000

Variances
PK                 1.000      0.000    999.000    999.000
PW                 1.000      0.000    999.000    999.000
PS                 1.000      0.000    999.000    999.000
CHOCB              1.000      0.000    999.000    999.000

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

PK       WITH
PW                 0.215      0.044      4.910      0.000
PS                 0.360      0.038      9.548      0.000
CHOCB              0.238      0.028      8.612      0.000

PW       WITH
PS                 0.347      0.061      5.687      0.000
CHOCB              0.232      0.045      5.111      0.000

PS       WITH
CHOCB              0.384      0.039      9.796      0.000

Means
PK                 3.459      0.033    103.886      0.000
PW                 4.130      0.058     71.548      0.000
PS                 5.100      0.046    110.878      0.000
CHOCB              3.642      0.034    105.760      0.000

Variances
PK                 0.547      0.035     15.700      0.000
PW                 1.640      0.105     15.686      0.000
PS                 1.042      0.066     15.692      0.000
CHOCB              0.586      0.037     15.716      0.000

R-SQUARE

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.130E-01
(ratio of smallest to largest eigenvalue)

Beginning Time:  00:32:46
Ending Time:  00:32:46
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2015 Muthen & Muthen

We can conclude that all of the variables are correlated significantly (ps < .001) but that there are stronger correlations between political knowledge, political skill, and change-oriented organizational citizenship behaviour. So individuals who have a deep understanding of their supervisor are also more socially astute and also try to bring around more change in the workplace. However, as any lesson on correlation goes, causation cannot be inferred! All we can tell from this analysis is that these variables go hand-in-hand in the same direction (i.e., as one goes up, so does the other and vice versa).

Finally, you can take the correlations in the output and create a beautiful table:

Screen Shot 2017-04-29 at 1.53.01 PM

Okay, maybe not beautiful, but informative at least! And that’s about sums up basic correlation analysis.

Get [M]oving with Mplus – part 4: Individual versus Summary Data

One of the many cool things about Mplus is that you have the option to run individual and summary data. And what does that mean exactly? Well, in addition to the typical individual data where each tab separated colum is a variable (like you’d see in a typical dataset), like this:

Screen Shot 2017-04-27 at 11.46.46 PM

…you can take a correlation table (along with the means, standard deviations, and sample size) like this:

Screen Shot 2017-04-27 at 11.42.57 PM

…and run analyses like you normally would. Now, that’s pretty cool.

What you see in the summary data file is

first line: means

second line: standard deviations

third line onwards: lower diagonal of your correlation/covariance matrix

and all else you would need to do is specify a few more things under the DATA command line to run analysis like normal:

Type = means stdeviations correlations;

Nobservations = # of observations in dataset;

and this would look like the following:

Screen Shot 2017-04-28 at 12.24.19 AM

On another note, if you have a full correlation or covariance matrix instead of only the bottom diagonal, you would replace correlation in the Type subcommand with FULLCORR or FULLCOV

Otherwise have at it the same way you would typically run analyses with individual level data — but now you also have a tool to check the integrity of published analyses!

Hofmann & Morgeson (1999) example

When I heard about the ability to use summary data, I thought it was incredibly cool but never actually tried it out for myself (beyond using a dataset that was already prepared with summary data). So I went and tried it out for myself and here are the steps I took:

Step 1:

Locate an article that has a correlation table, means, standard deviations and sample size available. In my case, I just picked a random article on support and employee safety from a top journal in my field (Hofmann & Morgeson, 1999).

Screen Shot 2017-04-28 at 2.34.42 PM

Step 2:

Record data into a .dat file (at least 2 easy options)

  • [Easiest] On Mac, open TextEdit (for Windows, it is probably similar with Notepad) and make sure it is in Plain text (to check, go to Format and look for “Make Plain Text”, if it is already in this format, you will see Make Rich Text)
    • Enter the means on the top row: start tight to top left corner, enter a number, press tab, enter next number, etc.
    • Enter standard deviations on second row: press enter once all means are in, and repeat the same thing with standard deviations making sure they are separated by pressing tab
    • Enter correlation/covariance table the same way you entered the means and standard deviations
    • Save file with the extension: .dat

Screen Shot 2017-04-28 at 2.47.01 PM

  • [Second easiest] Do the same thing in SPSS
    • Save as Fixed ASCII (*.dat)

Screen Shot 2017-04-28 at 2.51.41 PM

Step 3:

Write your syntax and save it in the same folder as the data file. Below is an example of the syntax as a screenshot and a copy-and-paste ready code

Screen Shot 2017-04-28 at 2.57.58 PM

TITLE:
Sample summary data analysis on Hofmann & Morgeson 1999;
DATA:
File is H&M1999.dat;
Type is MEANS STDEVIATIONS CORRELATION;
Nobservations = 49;
!they have uneven observations by variable, but we'll stick with 49

VARIABLE:
names are POS LMX SCMU SCMI ACC AGE ORGT JOBT;
!POS = perceived org support
!LMX = leader-member exchange
!SCMU = safety communication
!SCMI = safety commitment
!ACC = accidents
!ORGT = org tenure
!JOBT = job tenure
usevariables = POS LMX SCMU SCMI ACC;

!H1&2: POS & LMX +r w/ SCMU
!H3&4: POS & LMX +r w/ SCMI
!H5: SCMU +r w/ SCMI
!H6&7: SCMU & SCMI -r w/ ACC

ANALYSIS:
Estimator = ML;
MODEL:
SCMU on POS LMX; !H1&2
SCMI on POS LMX; !H3&4
SCMU with SCMI; !H5
ACC on SCMU SCMI; !H6&7

OUTPUT:
Standardized sampstat TECH1;

Step 4:

Press run and see if it works! Below is the output that was produced when I ran the above syntax. The results of interest can be found under STANDARDIZED MODEL RESULTS. We can see that we replicate the basic findings for hypotheses 1-5 (a non-finding in the case of hypothesis 3), but we actually do not find that safety communication and safety commitment have a significant negative association with accidents (likely due to power issues in how I ran the analyses – they only looked at the correlation coefficients, while I ran a multiple regression which takes into account overlapping variance):

Mplus VERSION 7.4 (Mac)
MUTHEN & MUTHEN
04/28/2017   2:43 PM

INPUT INSTRUCTIONS

TITLE:
Sample summary data analysis on Hofmann & Morgeson 1999;
DATA:
File is H&M1999.dat;
Type is MEANS STDEVIATIONS CORRELATION;
Nobservations = 49;
!they have uneven observations by variable, but we'll stick with 49

VARIABLE:
names are POS LMX SCMU SCMI ACC AGE ORGT JOBT;
!POS = perceived org support
!LMX = leader-member exchange
!SCMU = safety communication
!SCMI = safety commitment
!ACC = accidents
!ORGT = org tenure
!JOBT = job tenure
usevariables = POS LMX SCMU SCMI ACC;

!H1&2: POS & LMX +r w/ SCMU
!H3&4: POS & LMX +r w/ SCMI
!H5: SCMU +r w/ SCMI
!H6&7: SCMU & SCMI -r w/ ACC

ANALYSIS:
Estimator = ML;
MODEL:
SCMU on POS LMX; !H1&2
SCMI on POS LMX; !H3&4
SCMU with SCMI; !H5
ACC on SCMU SCMI; !H6&7

OUTPUT:
Standardized sampstat TECH1;

INPUT READING TERMINATED NORMALLY

Sample summary data analysis on Hofmann & Morgeson 1999;

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                          49

Number of dependent variables                                    3
Number of independent variables                                  2
Number of continuous latent variables                            0

Observed dependent variables

Continuous
SCMU        SCMI        ACC

Observed independent variables
POS         LMX

Estimator                                                       ML
Information matrix                                        EXPECTED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20

Input data file(s)
H&M1999.dat

Input data format  FREE

SAMPLE STATISTICS

SAMPLE STATISTICS

Means/Intercepts/Thresholds
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         3.930         3.740         0.920         2.500         3.000

Covariances/Correlations/Residual Correlations
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.449
SCMI           0.183         0.608
ACC           -0.274        -0.296         2.132
POS            0.311         0.074        -0.113         0.740
LMX            0.246         0.176        -0.364         0.322         0.608

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       13

Loglikelihood

H0 Value                        -176.104
H1 Value                        -174.654

Information Criteria

Akaike (AIC)                     378.207
Bayesian (BIC)                   402.801
Sample-Size Adjusted BIC         362.006
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value                              2.900
Degrees of Freedom                     2
P-Value                           0.2346

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.096
90 Percent C.I.                    0.000  0.316
Probability RMSEA <= .05           0.276

CFI/TLI

CFI                                0.969
TLI                                0.862

Chi-Square Test of Model Fit for the Baseline Model

Value                             38.320
Degrees of Freedom                     9
P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

Value                              0.038

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.318      0.102      3.110      0.002
LMX                0.235      0.113      2.085      0.037

SCMI     ON
POS               -0.034      0.141     -0.244      0.808
LMX                0.308      0.156      1.979      0.048

ACC      ON
SCMU              -0.469      0.314     -1.496      0.135
SCMI              -0.346      0.270     -1.282      0.200

SCMU     WITH
SCMI               0.116      0.059      1.965      0.049

Intercepts
SCMU               2.428      0.321      7.577      0.000
SCMI               2.901      0.442      6.558      0.000
ACC                4.057      1.306      3.107      0.002

Residual Variances
SCMU               0.286      0.058      4.950      0.000
SCMI               0.545      0.110      4.950      0.000
ACC                1.862      0.376      4.950      0.000

STANDARDIZED MODEL RESULTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.409      0.123      3.310      0.001
LMX                0.274      0.128      2.135      0.033

SCMI     ON
POS               -0.038      0.156     -0.244      0.807
LMX                0.308      0.150      2.055      0.040

ACC      ON
SCMU              -0.215      0.141     -1.526      0.127
SCMI              -0.185      0.142     -1.301      0.193

SCMU     WITH
SCMI               0.292      0.131      2.239      0.025

Intercepts
SCMU               3.662      0.769      4.765      0.000
SCMI               3.758      0.791      4.754      0.000
ACC                2.808      0.822      3.417      0.001

Residual Variances
SCMU               0.651      0.110      5.922      0.000
SCMI               0.915      0.076     11.990      0.000
ACC                0.892      0.084     10.635      0.000

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.480      0.142      3.390      0.001
LMX                0.355      0.164      2.164      0.030

SCMI     ON
POS               -0.045      0.183     -0.244      0.807
LMX                0.399      0.191      2.093      0.036

ACC      ON
SCMU              -0.215      0.141     -1.526      0.127
SCMI              -0.185      0.142     -1.301      0.193

SCMU     WITH
SCMI               0.292      0.131      2.239      0.025

Intercepts
SCMU               3.662      0.769      4.765      0.000
SCMI               3.758      0.791      4.754      0.000
ACC                2.808      0.822      3.417      0.001

Residual Variances
SCMU               0.651      0.110      5.922      0.000
SCMI               0.915      0.076     11.990      0.000
ACC                0.892      0.084     10.635      0.000

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.318      0.102      3.110      0.002
LMX                0.235      0.113      2.085      0.037

SCMI     ON
POS               -0.034      0.141     -0.244      0.808
LMX                0.308      0.156      1.979      0.048

ACC      ON
SCMU              -0.469      0.314     -1.496      0.135
SCMI              -0.346      0.270     -1.282      0.200

SCMU     WITH
SCMI               0.116      0.059      1.965      0.049

Intercepts
SCMU               2.428      0.321      7.577      0.000
SCMI               2.901      0.442      6.558      0.000
ACC                4.057      1.306      3.107      0.002

Residual Variances
SCMU               0.286      0.058      4.950      0.000
SCMI               0.545      0.110      4.950      0.000
ACC                1.862      0.376      4.950      0.000

R-SQUARE

Observed                                        Two-Tailed
Variable        Estimate       S.E.  Est./S.E.    P-Value

SCMU               0.349      0.110      3.179      0.001
SCMI               0.085      0.076      1.117      0.264
ACC                0.108      0.084      1.292      0.196

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.589E-03
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1           0             0             0             0             0

LAMBDA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0             0             0             0             0
SCMI               0             0             0             0             0
ACC                0             0             0             0             0
POS                0             0             0             0             0
LMX                0             0             0             0             0

THETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0
SCMI               0             0
ACC                0             0             0
POS                0             0             0             0
LMX                0             0             0             0             0

ALPHA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1           1             2             3             0             0

BETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0             0             0             4             5
SCMI               0             0             0             6             7
ACC                8             9             0             0             0
POS                0             0             0             0             0
LMX                0             0             0             0             0

PSI
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU              10
SCMI              11            12
ACC                0             0            13
POS                0             0             0             0
LMX                0             0             0             0             0

STARTING VALUES

NU
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         0.000         0.000         0.000         0.000         0.000

LAMBDA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           1.000         0.000         0.000         0.000         0.000
SCMI           0.000         1.000         0.000         0.000         0.000
ACC            0.000         0.000         1.000         0.000         0.000
POS            0.000         0.000         0.000         1.000         0.000
LMX            0.000         0.000         0.000         0.000         1.000

THETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.000
SCMI           0.000         0.000
ACC            0.000         0.000         0.000
POS            0.000         0.000         0.000         0.000
LMX            0.000         0.000         0.000         0.000         0.000

ALPHA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         3.930         3.740         0.920         2.500         3.000

BETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.000         0.000         0.000         0.000         0.000
SCMI           0.000         0.000         0.000         0.000         0.000
ACC            0.000         0.000         0.000         0.000         0.000
POS            0.000         0.000         0.000         0.000         0.000
LMX            0.000         0.000         0.000         0.000         0.000

PSI
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.224
SCMI           0.000         0.304
ACC            0.000         0.000         1.066
POS            0.000         0.000         0.000         0.725
LMX            0.000         0.000         0.000         0.315         0.596

Beginning Time:  14:43:04
Ending Time:  14:43:04
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2015 Muthen & Muthen

I also ran their structural model over again with indirect affects for anyone who is interested. Because I did not correct for their small sample size (and to be frank, I’m not entirely familiar with the strategy they took), the model fit is rather less than satisfactory (χ²(5) = 7.43, = .19, CFI = .92, TLI = .85, RMSEA = .10, and SRMR = .08) and the path coefficients are somewhat smaller (click to expand and view output):

Mplus VERSION 7.4 (Mac)
MUTHEN & MUTHEN
04/28/2017   6:56 PM

INPUT INSTRUCTIONS

TITLE:
Sample summary data analysis on Hofmann & Morgeson 1999;
DATA:
File is H&M1999.dat;
Type is MEANS STDEVIATIONS CORRELATION;
Nobservations = 49;
!they have uneven observations by variable, but we'll stick with 49

VARIABLE:
names are POS LMX SCMU SCMI ACC AGE ORGT JOBT;
!POS = perceived org support
!LMX = leader-member exchange
!SCMU = safety communication
!SCMI = safety commitment
!ACC = accidents
!ORGT = org tenure
!JOBT = job tenure
usevariables = POS LMX SCMU SCMI ACC;

!H1&2: POS & LMX +r w/ SCMU
!H3&4: POS & LMX +r w/ SCMI
!H5: SCMU +r w/ SCMI
!H6&7: SCMU & SCMI -r w/ ACC

ANALYSIS:
Estimator = ML;
MODEL: !Now testing their structural model
SCMU on POS;
SCMU on LMX;
SCMI on SCMU;
ACC on SCMI;
POS with LMX;

MODEL INDIRECT:
SCMI IND POS;
SCMI IND LMX;

OUTPUT:
Standardized sampstat TECH1;

INPUT READING TERMINATED NORMALLY

Sample summary data analysis on Hofmann & Morgeson 1999;

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                          49

Number of dependent variables                                    3
Number of independent variables                                  2
Number of continuous latent variables                            0

Observed dependent variables

Continuous
SCMU        SCMI        ACC

Observed independent variables
POS         LMX

Estimator                                                       ML
Information matrix                                        EXPECTED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20

Input data file(s)
H&M1999.dat

Input data format  FREE

SAMPLE STATISTICS

SAMPLE STATISTICS

Means/Intercepts/Thresholds
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         3.930         3.740         0.920         2.500         3.000

Covariances/Correlations/Residual Correlations
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.449
SCMI           0.183         0.608
ACC           -0.274        -0.296         2.132
POS            0.311         0.074        -0.113         0.740
LMX            0.246         0.176        -0.364         0.322         0.608

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       15

Loglikelihood

H0 Value                        -290.433
H1 Value                        -286.718

Information Criteria

Akaike (AIC)                     610.865
Bayesian (BIC)                   639.242
Sample-Size Adjusted BIC         592.172
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value                              7.429
Degrees of Freedom                     5
P-Value                           0.1907

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.100
90 Percent C.I.                    0.000  0.239
Probability RMSEA <= .05           0.251

CFI/TLI

CFI                                0.917
TLI                                0.851

Chi-Square Test of Model Fit for the Baseline Model

Value                             38.320
Degrees of Freedom                     9
P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

Value                              0.083

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.318      0.102      3.110      0.002
LMX                0.235      0.113      2.085      0.037

SCMI     ON
SCMU               0.407      0.156      2.615      0.009

ACC      ON
SCMI              -0.487      0.258     -1.885      0.059

POS      WITH
LMX                0.315      0.104      3.029      0.002

Means
POS                2.500      0.122     20.560      0.000
LMX                3.000      0.110     27.202      0.000

Intercepts
SCMU               2.428      0.321      7.577      0.000
SCMI               2.139      0.621      3.444      0.001
ACC                2.740      0.986      2.779      0.005

Variances
POS                0.725      0.146      4.950      0.000
LMX                0.596      0.120      4.950      0.000

Residual Variances
SCMU               0.286      0.058      4.950      0.000
SCMI               0.523      0.106      4.950      0.000
ACC                1.947      0.393      4.950      0.000

STANDARDIZED MODEL RESULTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.409      0.123      3.310      0.001
LMX                0.274      0.128      2.135      0.033

SCMI     ON
SCMU               0.350      0.125      2.792      0.005

ACC      ON
SCMI              -0.260      0.133     -1.952      0.051

POS      WITH
LMX                0.480      0.110      4.366      0.000

Means
POS                2.937      0.329      8.919      0.000
LMX                3.886      0.418      9.303      0.000

Intercepts
SCMU               3.662      0.769      4.765      0.000
SCMI               2.770      0.965      2.871      0.004
ACC                1.896      0.641      2.956      0.003

Variances
POS                1.000      0.000    999.000    999.000
LMX                1.000      0.000    999.000    999.000

Residual Variances
SCMU               0.651      0.110      5.922      0.000
SCMI               0.877      0.088     10.000      0.000
ACC                0.932      0.069     13.462      0.000

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.409      0.123      3.310      0.001
LMX                0.274      0.128      2.135      0.033

SCMI     ON
SCMU               0.350      0.125      2.792      0.005

ACC      ON
SCMI              -0.260      0.133     -1.952      0.051

POS      WITH
LMX                0.480      0.110      4.366      0.000

Means
POS                2.937      0.329      8.919      0.000
LMX                3.886      0.418      9.303      0.000

Intercepts
SCMU               3.662      0.769      4.765      0.000
SCMI               2.770      0.965      2.871      0.004
ACC                1.896      0.641      2.956      0.003

Variances
POS                1.000      0.000    999.000    999.000
LMX                1.000      0.000    999.000    999.000

Residual Variances
SCMU               0.651      0.110      5.922      0.000
SCMI               0.877      0.088     10.000      0.000
ACC                0.932      0.069     13.462      0.000

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.318      0.102      3.110      0.002
LMX                0.235      0.113      2.085      0.037

SCMI     ON
SCMU               0.407      0.156      2.615      0.009

ACC      ON
SCMI              -0.487      0.258     -1.885      0.059

POS      WITH
LMX                0.315      0.104      3.029      0.002

Means
POS                2.500      0.122     20.560      0.000
LMX                3.000      0.110     27.202      0.000

Intercepts
SCMU               2.428      0.321      7.577      0.000
SCMI               2.139      0.621      3.444      0.001
ACC                2.740      0.986      2.779      0.005

Variances
POS                0.725      0.146      4.950      0.000
LMX                0.596      0.120      4.950      0.000

Residual Variances
SCMU               0.286      0.058      4.950      0.000
SCMI               0.523      0.106      4.950      0.000
ACC                1.947      0.393      4.950      0.000

R-SQUARE

Observed                                        Two-Tailed
Variable        Estimate       S.E.  Est./S.E.    P-Value

SCMU               0.349      0.110      3.179      0.001
SCMI               0.122      0.088      1.396      0.163
ACC                0.068      0.069      0.976      0.329

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.570E-03
(ratio of smallest to largest eigenvalue)

TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.130      0.065      2.002      0.045
Total indirect       0.130      0.065      2.002      0.045

Specific indirect

SCMI
SCMU
POS                0.130      0.065      2.002      0.045

Effects from LMX to SCMI

Total                0.096      0.059      1.630      0.103
Total indirect       0.096      0.059      1.630      0.103

Specific indirect

SCMI
SCMU
LMX                0.096      0.059      1.630      0.103

STANDARDIZED TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.143      0.069      2.084      0.037
Total indirect       0.143      0.069      2.084      0.037

Specific indirect

SCMI
SCMU
POS                0.143      0.069      2.084      0.037

Effects from LMX to SCMI

Total                0.096      0.057      1.674      0.094
Total indirect       0.096      0.057      1.674      0.094

Specific indirect

SCMI
SCMU
LMX                0.096      0.057      1.674      0.094

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.143      0.069      2.084      0.037
Total indirect       0.143      0.069      2.084      0.037

Specific indirect

SCMI
SCMU
POS                0.143      0.069      2.084      0.037

Effects from LMX to SCMI

Total                0.096      0.057      1.674      0.094
Total indirect       0.096      0.057      1.674      0.094

Specific indirect

SCMI
SCMU
LMX                0.096      0.057      1.674      0.094

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.130      0.065      2.002      0.045
Total indirect       0.130      0.065      2.002      0.045

Specific indirect

SCMI
SCMU
POS                0.130      0.065      2.002      0.045

Effects from LMX to SCMI

Total                0.096      0.059      1.630      0.103
Total indirect       0.096      0.059      1.630      0.103

Specific indirect

SCMI
SCMU
LMX                0.096      0.059      1.630      0.103

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1           0             0             0             0             0

LAMBDA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0             0             0             0             0
SCMI               0             0             0             0             0
ACC                0             0             0             0             0
POS                0             0             0             0             0
LMX                0             0             0             0             0

THETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0
SCMI               0             0
ACC                0             0             0
POS                0             0             0             0
LMX                0             0             0             0             0

ALPHA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1           1             2             3             4             5

BETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0             0             0             6             7
SCMI               8             0             0             0             0
ACC                0             9             0             0             0
POS                0             0             0             0             0
LMX                0             0             0             0             0

PSI
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU              10
SCMI               0            11
ACC                0             0            12
POS                0             0             0            13
LMX                0             0             0            14            15

STARTING VALUES

NU
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         0.000         0.000         0.000         0.000         0.000

LAMBDA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           1.000         0.000         0.000         0.000         0.000
SCMI           0.000         1.000         0.000         0.000         0.000
ACC            0.000         0.000         1.000         0.000         0.000
POS            0.000         0.000         0.000         1.000         0.000
LMX            0.000         0.000         0.000         0.000         1.000

THETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.000
SCMI           0.000         0.000
ACC            0.000         0.000         0.000
POS            0.000         0.000         0.000         0.000
LMX            0.000         0.000         0.000         0.000         0.000

ALPHA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         3.930         3.740         0.920         2.500         3.000

BETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.000         0.000         0.000         0.000         0.000
SCMI           0.000         0.000         0.000         0.000         0.000
ACC            0.000         0.000         0.000         0.000         0.000
POS            0.000         0.000         0.000         0.000         0.000
LMX            0.000         0.000         0.000         0.000         0.000

PSI
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.224
SCMI           0.000         0.304
ACC            0.000         0.000         1.066
POS            0.000         0.000         0.000         0.370
LMX            0.000         0.000         0.000         0.000         0.304

Beginning Time:  18:56:59
Ending Time:  18:56:59
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2015 Muthen & Muthen

However, if you run the additional analyses they ran (controlling for organizational tenure), the model fit improves substantially (χ²(5) = 10.02, = .35, CFI = .97, TLI = .96, RMSEA = .05, and SRMR = .09) but the relationship between safety commitment and accidents is no longer significant (again, likely an issue with power due to small sample size):


Mplus VERSION 7.4 (Mac)
MUTHEN & MUTHEN
04/28/2017   7:20 PM

INPUT INSTRUCTIONS

TITLE:
Sample summary data analysis on Hofmann & Morgeson 1999;
DATA:
File is H&M1999.dat;
Type is MEANS STDEVIATIONS CORRELATION;
Nobservations = 49;
!they have uneven observations by variable, but we'll stick with 49

VARIABLE:
names are POS LMX SCMU SCMI ACC AGE ORGT JOBT;
!POS = perceived org support
!LMX = leader-member exchange
!SCMU = safety communication
!SCMI = safety commitment
!ACC = accidents
!ORGT = org tenure
!JOBT = job tenure
usevariables = POS LMX SCMU SCMI ACC
ORGT;

!H1&2: POS & LMX +r w/ SCMU
!H3&4: POS & LMX +r w/ SCMI
!H5: SCMU +r w/ SCMI
!H6&7: SCMU & SCMI -r w/ ACC

ANALYSIS:
Estimator = ML;
MODEL: !Now testing their structural model
SCMU on POS;
SCMU on LMX;
SCMI on SCMU;
ACC on SCMI;
POS with LMX;
ACC on ORGT;

MODEL INDIRECT:
SCMI IND POS;
SCMI IND LMX;

OUTPUT:
Standardized sampstat TECH1;

INPUT READING TERMINATED NORMALLY

Sample summary data analysis on Hofmann & Morgeson 1999;

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                          49

Number of dependent variables                                    3
Number of independent variables                                  3
Number of continuous latent variables                            0

Observed dependent variables

Continuous
SCMU        SCMI        ACC

Observed independent variables
POS         LMX         ORGT

Estimator                                                       ML
Information matrix                                        EXPECTED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20

Input data file(s)
H&M1999.dat

Input data format  FREE

SAMPLE STATISTICS

SAMPLE STATISTICS

Means/Intercepts/Thresholds
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         3.930         3.740         0.920         2.500         3.000

Means/Intercepts/Thresholds
ORGT
________
1        26.230

Covariances/Correlations/Residual Correlations
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.449
SCMI           0.183         0.608
ACC           -0.274        -0.296         2.132
POS            0.311         0.074        -0.113         0.740
LMX            0.246         0.176        -0.364         0.322         0.608
ORGT           0.127         0.963        -4.022         0.327         1.556

Covariances/Correlations/Residual Correlations
ORGT
________
ORGT          90.250

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       16

Loglikelihood

H0 Value                        -288.612
H1 Value                        -283.605

Information Criteria

Akaike (AIC)                     609.224
Bayesian (BIC)                   639.494
Sample-Size Adjusted BIC         589.285
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value                             10.015
Degrees of Freedom                     9
P-Value                           0.3493

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.048
90 Percent C.I.                    0.000  0.172
Probability RMSEA <= .05           0.445

CFI/TLI

CFI                                0.966
TLI                                0.955

Chi-Square Test of Model Fit for the Baseline Model

Value                             42.090
Degrees of Freedom                    12
P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

Value                              0.088

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.318      0.102      3.110      0.002
LMX                0.235      0.113      2.085      0.037

SCMI     ON
SCMU               0.407      0.156      2.615      0.009

ACC      ON
SCMI              -0.423      0.249     -1.701      0.089
ORGT              -0.040      0.020     -1.961      0.050

POS      WITH
LMX                0.315      0.104      3.029      0.002

Means
POS                2.500      0.122     20.560      0.000
LMX                3.000      0.110     27.202      0.000

Intercepts
SCMU               2.429      0.321      7.577      0.000
SCMI               2.139      0.621      3.444      0.001
ACC                3.553      1.091      3.258      0.001

Variances
POS                0.725      0.146      4.950      0.000
LMX                0.596      0.120      4.950      0.000

Residual Variances
SCMU               0.286      0.058      4.950      0.000
SCMI               0.523      0.106      4.950      0.000
ACC                1.808      0.365      4.950      0.000

STANDARDIZED MODEL RESULTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.409      0.123      3.310      0.001
LMX                0.274      0.128      2.135      0.033

SCMI     ON
SCMU               0.350      0.125      2.792      0.005

ACC      ON
SCMI              -0.228      0.131     -1.744      0.081
ORGT              -0.263      0.130     -2.028      0.043

POS      WITH
LMX                0.480      0.110      4.366      0.000

Means
POS                2.937      0.329      8.919      0.000
LMX                3.886      0.418      9.303      0.000

Intercepts
SCMU               3.662      0.769      4.765      0.000
SCMI               2.770      0.965      2.871      0.004
ACC                2.478      0.691      3.586      0.000

Variances
POS                1.000      0.000    999.000    999.000
LMX                1.000      0.000    999.000    999.000

Residual Variances
SCMU               0.651      0.110      5.922      0.000
SCMI               0.878      0.088     10.000      0.000
ACC                0.879      0.086     10.219      0.000

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.409      0.123      3.310      0.001
LMX                0.274      0.128      2.135      0.033

SCMI     ON
SCMU               0.350      0.125      2.792      0.005

ACC      ON
SCMI              -0.228      0.131     -1.744      0.081
ORGT              -0.028      0.014     -2.066      0.039

POS      WITH
LMX                0.480      0.110      4.366      0.000

Means
POS                2.937      0.329      8.919      0.000
LMX                3.886      0.418      9.303      0.000

Intercepts
SCMU               3.662      0.769      4.765      0.000
SCMI               2.770      0.965      2.871      0.004
ACC                2.478      0.691      3.586      0.000

Variances
POS                1.000      0.000    999.000    999.000
LMX                1.000      0.000    999.000    999.000

Residual Variances
SCMU               0.651      0.110      5.922      0.000
SCMI               0.878      0.088     10.000      0.000
ACC                0.879      0.086     10.219      0.000

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

SCMU     ON
POS                0.318      0.102      3.110      0.002
LMX                0.235      0.113      2.085      0.037

SCMI     ON
SCMU               0.407      0.156      2.615      0.009

ACC      ON
SCMI              -0.423      0.249     -1.701      0.089
ORGT              -0.040      0.020     -1.961      0.050

POS      WITH
LMX                0.315      0.104      3.029      0.002

Means
POS                2.500      0.122     20.560      0.000
LMX                3.000      0.110     27.202      0.000

Intercepts
SCMU               2.429      0.321      7.577      0.000
SCMI               2.139      0.621      3.444      0.001
ACC                3.553      1.091      3.258      0.001

Variances
POS                0.725      0.146      4.950      0.000
LMX                0.596      0.120      4.950      0.000

Residual Variances
SCMU               0.286      0.058      4.950      0.000
SCMI               0.523      0.106      4.950      0.000
ACC                1.808      0.365      4.950      0.000

R-SQUARE

Observed                                        Two-Tailed
Variable        Estimate       S.E.  Est./S.E.    P-Value

SCMU               0.349      0.110      3.179      0.001
SCMI               0.122      0.088      1.396      0.163
ACC                0.121      0.086      1.405      0.160

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.110E-03
(ratio of smallest to largest eigenvalue)

TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.130      0.065      2.002      0.045
Total indirect       0.130      0.065      2.002      0.045

Specific indirect

SCMI
SCMU
POS                0.130      0.065      2.002      0.045

Effects from LMX to SCMI

Total                0.096      0.059      1.630      0.103
Total indirect       0.096      0.059      1.630      0.103

Specific indirect

SCMI
SCMU
LMX                0.096      0.059      1.630      0.103

STANDARDIZED TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.143      0.069      2.084      0.037
Total indirect       0.143      0.069      2.084      0.037

Specific indirect

SCMI
SCMU
POS                0.143      0.069      2.084      0.037

Effects from LMX to SCMI

Total                0.096      0.057      1.674      0.094
Total indirect       0.096      0.057      1.674      0.094

Specific indirect

SCMI
SCMU
LMX                0.096      0.057      1.674      0.094

STDY Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.143      0.069      2.084      0.037
Total indirect       0.143      0.069      2.084      0.037

Specific indirect

SCMI
SCMU
POS                0.143      0.069      2.084      0.037

Effects from LMX to SCMI

Total                0.096      0.057      1.674      0.094
Total indirect       0.096      0.057      1.674      0.094

Specific indirect

SCMI
SCMU
LMX                0.096      0.057      1.674      0.094

STD Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Effects from POS to SCMI

Total                0.130      0.065      2.002      0.045
Total indirect       0.130      0.065      2.002      0.045

Specific indirect

SCMI
SCMU
POS                0.130      0.065      2.002      0.045

Effects from LMX to SCMI

Total                0.096      0.059      1.630      0.103
Total indirect       0.096      0.059      1.630      0.103

Specific indirect

SCMI
SCMU
LMX                0.096      0.059      1.630      0.103

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1           0             0             0             0             0

NU
ORGT
________
1           0

LAMBDA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0             0             0             0             0
SCMI               0             0             0             0             0
ACC                0             0             0             0             0
POS                0             0             0             0             0
LMX                0             0             0             0             0
ORGT               0             0             0             0             0

LAMBDA
ORGT
________
SCMU               0
SCMI               0
ACC                0
POS                0
LMX                0
ORGT               0

THETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0
SCMI               0             0
ACC                0             0             0
POS                0             0             0             0
LMX                0             0             0             0             0
ORGT               0             0             0             0             0

THETA
ORGT
________
ORGT               0

ALPHA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1           1             2             3             4             5

ALPHA
ORGT
________
1           0

BETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU               0             0             0             6             7
SCMI               8             0             0             0             0
ACC                0             9             0             0             0
POS                0             0             0             0             0
LMX                0             0             0             0             0
ORGT               0             0             0             0             0

BETA
ORGT
________
SCMU               0
SCMI               0
ACC               10
POS                0
LMX                0
ORGT               0

PSI
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU              11
SCMI               0            12
ACC                0             0            13
POS                0             0             0            14
LMX                0             0             0            15            16
ORGT               0             0             0             0             0

PSI
ORGT
________
ORGT               0

STARTING VALUES

NU
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         0.000         0.000         0.000         0.000         0.000

NU
ORGT
________
1         0.000

LAMBDA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           1.000         0.000         0.000         0.000         0.000
SCMI           0.000         1.000         0.000         0.000         0.000
ACC            0.000         0.000         1.000         0.000         0.000
POS            0.000         0.000         0.000         1.000         0.000
LMX            0.000         0.000         0.000         0.000         1.000
ORGT           0.000         0.000         0.000         0.000         0.000

LAMBDA
ORGT
________
SCMU           0.000
SCMI           0.000
ACC            0.000
POS            0.000
LMX            0.000
ORGT           1.000

THETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.000
SCMI           0.000         0.000
ACC            0.000         0.000         0.000
POS            0.000         0.000         0.000         0.000
LMX            0.000         0.000         0.000         0.000         0.000
ORGT           0.000         0.000         0.000         0.000         0.000

THETA
ORGT
________
ORGT           0.000

ALPHA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
1         3.930         3.740         0.920         2.500         3.000

ALPHA
ORGT
________
1        26.230

BETA
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.000         0.000         0.000         0.000         0.000
SCMI           0.000         0.000         0.000         0.000         0.000
ACC            0.000         0.000         0.000         0.000         0.000
POS            0.000         0.000         0.000         0.000         0.000
LMX            0.000         0.000         0.000         0.000         0.000
ORGT           0.000         0.000         0.000         0.000         0.000

BETA
ORGT
________
SCMU           0.000
SCMI           0.000
ACC            0.000
POS            0.000
LMX            0.000
ORGT           0.000

PSI
SCMU          SCMI          ACC           POS           LMX
________      ________      ________      ________      ________
SCMU           0.224
SCMI           0.000         0.304
ACC            0.000         0.000         1.066
POS            0.000         0.000         0.000         0.370
LMX            0.000         0.000         0.000         0.000         0.304
ORGT           0.000         0.000         0.000         0.000         0.000

PSI
ORGT
________
ORGT          88.408

Beginning Time:  19:20:15
Ending Time:  19:20:15
Elapsed Time:  00:00:00

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2015 Muthen & Muthen

In any case, this is the kind of stuff you can do with Mplus! Enjoy!

References

Hofmann, D. A., & Morgeson, F. P. (1999). Safety-related behavior as a social exchange: The role of perceived organizational support and leader–member exchange. Journal of applied psychology, 84(2), 286-296.

Get [M]oving with Mplus – part 3: Get Your Data On

Unlike other programs like SPSS or Stata, data entry is done externally with Mplus. In other words, you will need to use another spreadsheet or stats program to transfer your data into Mplus. Typically I use SPSS because 1) it’s how I learned it and 2) it’s also the program I am most familiar with. But this can also be done, to the extent of my knowledge, from Stata and SAS (and probably others as well). In any case, I will review how to do it from SPSS (and others in the future!).


From SPSS:

  1. Acquire and open SPSS dataset you want to analyze in Mplus
  2. Transform missing data into a numeric indicator
  • Select Transform in the menu bar
  • Scroll down to and select Recode into same variable 
  • Select all your variables, move them into the numeric variables box
  • Select Old and New Values…
  • In the Old Value box select System-missing
  • In the New value box enter -999 (or any missing value identifier you prefer)
  • Press Add
  • Select Continue and then OK
  1. Double check format of columns (i.e., width, decimals, alignment)
  • Width = 8
  • Decimals = 2
  • Align = right
  • Short variable names (shoot for 5 characters or less, but definitely no more than 8)
  1. Save as Fixed ASCII (*.dat)
  • If there are variables in dataset you do not want to transfer, select pick variables button and select the variables you wish to save
  • REMEMBER ORDER OF VARIABLES! This is important because Mplus doesn’t know which line of numbers respresents what, so you need to tell it in the syntax.
  • Double check the .dat file in a text editor to make sure there are no issues with it
    • Some common issues:
      • 1) there are funky symbols in the top left corner of the .dat file that need to be removed
      • 2) there is no coherent spacing of numbers in the .dat (i.e., when you open the data file there is no discernable patterns and it’s a chaotic mess of numbers, letters, and symbols – there should be no letters or symbols! or variable names for that matter)
        • checking these can save you hours of troubleshooting
  • Save file in the same folder as your Mplus syntax (otherwise you would have to specify the full file path – by why not just store it in the same folder so you can just use the file name).
  1. Want to know a quick way to get your variable labels into Mplus?
  • To copy and paste variable names from SPSS, go to Utilities, select Variables…
  • Highlight the variables in your dataset for Mplus (if there were variables you didn’t transfer over, don’t forget to drop these) and press paste to have the variables sent to syntax.
  • Copy and paste into your Mplus syntax.

 

Transferring from other programs to come!