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.