Categories
Stats Work

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

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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.

Categories
Stats Work

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.

Categories
Stats Work

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!

 

Categories
Stats Work

Get [M]oving with Mplus – part 2: A Serving of Commands with a Side of Syntax

You know the saying, “it’s not on the outside that matters, it what’s on the inside that counts”? Well, that’s certainly the case with Mplus. It’s time to get a taste of what Mplus really has to offer with it’s very simple and intuitive syntax.

A good place to start is a blank slate. When you open up a new syntax window, that’s what you get. Oftentimes I’ll copy an old syntax and just replace the details, but it’s typically a wise decision to get a sense of the required syntax and how it works so that you can quickly troubleshoot when the time comes when Mplus refuses to run.

Screen Shot 2017-04-25 at 23.32.42

Let’s get started with a few general notes (albeit very important notes – details matter in Mplus!):

  • All command headings/lines must be followed by a colon (:) and will turn blue
  • Subcommands and syntax lines must be followed by a semicolon (;)
  • Use an exclamation point (!) to make short notes that will turn green and Mplus does not read (note: if your note is not green, this means you forgot the exclamation point!)

Next, I’ll go through the command lines and their respective subcommands.

TITLE: ! command allows you to name or label what you are testing

Simply the best title ever;  ! This is an example title

! Helpful for keeping track of multiple analyses, although I often forget to change this!

DATA: ! command provides info about the dataset to be analyzed

! I will have a detailed post on getting your data into Mplus, but here are a couple helpful notes:

! Two types of data can be entered: individual data and summary data (see type subcommand below)

! Store data in the same folder as the Mplus syntax (for ease, otherwise must specify full path to file)

! Data Subcommands:

File is FILENAME.dat; ! Tells Mplus where the data file is stored

Type = !means stdeviations correlation; !can import individual or summary data, default is individual

Nobservations = !___; !this command tells MPlus # of observations when type = summary data

VARIABLE: ! command provides info about the variables in the dataset to be analyzed

!Names of variables MUST NOT exceed 8 characters

! Variable subcommands:

names are ! list your variables here; !this tells MPlus which variables are in the whole data set – you could also use the subcommand “Names=”

categorical are ! X1; ! describes type of variable, Mplus assumes variables are continuous unless told otherwise, can specify categorical, nominal, count, etc.

missing are all(-999); ! Must replace missing data with identifier (e.g., -999) before importing data

usevariables = ! list variables you want to use in analysis here;

!If variables are sequential you can simply place a hyphen between the first and last variables (e.g., for X1, X2, X3, X4 you can put X1-X4)

!If variables are created in define command below, add them to END of usevariables list

DEFINE: ! command used to transform existing variables and create new variables

! Define subcommands: you can…

! create new variables, “X12 = (X1 + X2)/2;” OR “X12 = mean(X1 X2);”

! create interaction terms, “int = X1*X2;”

! provide conditional statements, “IF (X1 EQ 1) THEN group = 1;” “IF (X1 EQ 2) THEN group = 2;” Mplus creates variable “group”

! make transformations,

! create parcels, X = mean(X1 X2 X3)

! center variables, “Center X1 X2 X3 (grandmean);”

ANALYSIS: ! command used to describe the nature of the analysis

! Analysis subcommands:

! Type = twolevel; ! nature of the model, default is general for typically don’t have to specify unless doing multilevel analysis (for SEM, regression)

! Estimator = ML; ! Tells Mplus which estimator you want to use, such as ML or Bayes

! Bootstrap = 10000; !Tells Mplus the number of bootstrap samples you want

MODEL: ! command used to describe the model to be estimated

!Three Fundamental commands:

! “ON”

! used to specify regression path (B matrix)

! Y on X1 X2; !regress Y on X1 and X1 or X1 and X2 predict Y

! “WITH”

! Used to specify covariance/correlation *double-headed arrow

! X1 with X2 !can be covariance between observed or latent variables

! “BY”

! Used to specify factor loadings

! X by X1 X2 X3;

! By default, first loading is fixed to 1.0 (similar to other programs)

!Some other things you can do under the model command:

!Constrain a parameter

! Y on X1@.25; ! Fixes regression weight of X1 to .25

! [X1@0]; ! Constrains X1 intercept to 0

! Label or name parameters/paths:

! M on X (a);

! Y on M (b);

! Y on X (c);

!These paths can then be used later for fun things in the model constrain command

!Constrain effects of IVs on DV to be equal:

!Y on X M (a);

MODEL CONSTRAINT: ! Command used for applying your labelled parameters

! Example: mediation using labelled parameters above

new (med total);

med = a*b; 

total = a*b+c;

MODEL INDIRECT: ! Command designed for testing mediation effects

! Mplus provides total and indirect effects (similar to PROCESS macro in SPSS)

! Combine with bootstrap option in analysis to get bootstrapped indirect effects

! If using Bayes estimator, do not use this, but rather use model constraint above

OUTPUT: ! Command used to request additional info not included in default

! Put all desired commands into a single line of syntax

! Popular output subcommand examples:

! standardized(all); !provides standardized estimates and standard errors

! sampstat; !provides sample statistics (e.g., sample means, (co)variances, correlations)

! modindices(all); !for SEM analyses, provides modification indices for model fit

! residual; !requests residuals for the observed variables in the model

! CInterval; request confidence (bootstrap)/credibility(HPD) intervals

! Tech1-16; Requests a variety of additional info on analysis

! Tech1; parameter specification and starting values

! Tech3; request estimated covariance and correlation matrices

! Tech4; means, covariances, correlations for latent variables

! Tech8; requests the optimization history in estimating the model (shows how long the analysis takes)

! See p.713+ of Mplus manual for other output subcommands

SAVEDATA: ! Command saves sample correlation and covariance matrices in separate ASCII file

! Savedata subcommands:

FILE IS output.sav;

! SAMPLE is output.sav; !speficies file name for sample statistics to be saved

! RESULTS ARE output.sav; !specifies name of file in which results of an analysis will be saved

!See p.744+ of manual for all save subcommands

PLOT: ! Command used to request graphical displays of observed data and results

! Plot subcommands:

! Type=PLOT1-3; used to specify types of plots (3 settings)

! PLOT1; see p. 763 in manual

! PLOT2; see p. 764

! PLOT3; see p. 765

!plot command does not work on Macs yet unfortunately, but I do have a how to guide for plotting Mplus outputs in R

So those are essentially the basic commands, subcommands, and a little bit of syntax. It may seem like a lot, but rarely will you need very much to run a single analysis. Here is an example of plausible input with a factor loading and a latent factor predicting an observed factor and a copy-and-paste basic template:

Screen Shot 2017-04-25 at 23.31.59

TITLE:
ENTER TITLE HERE;

DATA:
File is ENTERFILENAMEHERE.dat;

VARIABLE:
names are ENTER VARIABLE NAMES HERE;

missing are all(-999); !or whatever your missing value ID value is

usevariables = ENTER VARIABLES TO BE USED;

ANALYSIS:
estimator = ML;

MODEL:
ENTER YOUR DESIRED ANALYSIS HERE
! ON for regression
! BY for factor analyses
! WITH for correlation

OUTPUT:
Standardized Sampstat;

Seems pretty straight forward, eh?

Categories
Stats Work

Get [M]oving with Mplus – part 1: The Painful Basics

When you open Mplus for the first time (see below), it kind of looks like something you would retrieve from a floppy disk. I wasn’t kidding when I said on the Mplus home page that it leaves a lot to the imagination! But paraphrasing the Canadian icon Steve Smith (aka Red Green), “If they don’t find you handsome, they should at least find you handy.” And well, Mplus sure is handy.

Screen Shot 2017-04-25 at 09.41.12

To get started, I’ll quickly review the plethora of icons on the screen above.  As you’ll notice, it’s all quite intuitive.

Screen Shot 2017-04-25 at 09.52.27New: Opens up a blank syntax window (you’ll see what this looks like shortly)

Screen Shot 2017-04-25 at 09.53.05Open: You can open inputs, outputs, and your data files with this

Screen Shot 2017-04-25 at 09.53.17Save: Mplus requires you to save your syntax before running analysis, so you use this quite a bit

Screen Shot 2017-04-25 at 10.01.01Cut: removes syntax but makes a copy of it (makes it easy to move things around)

Screen Shot 2017-04-25 at 09.53.28Copy: copies syntax (e.g., if you want to make a copy of your syntax in a new window)

Screen Shot 2017-04-25 at 09.53.36Paste: Pastes stuff that you cut or copied

Screen Shot 2017-04-25 at 09.53.46Print: I’ve never printed anything, but I assume it prints your selected syntax window

Screen Shot 2017-04-25 at 09.53.54Run: The mission launch button – selecting this runs your syntax

And that’s basically it for the button options. There is only one more useful thing I’d like to show you for the real basics. When running several analyses with separate syntax windows, the working space in Mplus can get pretty crowded quickly. Fortunately, there are some handy view options.

Now imagine you had the following workspace (imagine these syntax windows were full of beautiful syntax and lovely results because you’re a stellar researcher):

Screen Shot 2017-04-25 at 10.35.50

Messy, isn’t it? And that’s just four windows. On a laptop that could be all it takes to get you a little overwhelmed. The first step to getting your life back on track is selecting the View option in the command list.

Screen Shot 2017-04-25 at 10.36.14

Selecting Cascade Frames does the following:

Screen Shot 2017-04-25 at 10.36.54

Selecting Tile Frames Vertically

Screen Shot 2017-04-25 at 10.37.12

Selecting Tile Frames Horizontally

Screen Shot 2017-04-25 at 10.37.31

 

And that’s about it for the real basics. All quite straightforward and intuitive – fortunately a trend in Mplus that goes right into the next topics of writing syntax and running analyses.

Categories
Stats Work

Getting Sta[R]ted with R!

First things, first

Install R & Rstudio!

Rstudio runs R while providing the user with a much more friendly environment to work with. Besides, most people who use R, use Rstudio.

Second things… second?

Be aware that there are a lot of resources available online. Given that this software is open-source, R has a thriving community of keeners. In addition, I was told that Andy Field’s book, Discovering Statistics using R is very good! Here are a few other helpful examples:

More to come…!

Examining the interface of R and R studio and other basics to get you started!

Categories
Research Work

Leadership is tied to employee well-being through this subjective experience

blog-5-pic

(Photo via http://geracaodevalor.com/)

In a study by Arnold, Turner, Barling, Kelloway & McKee (2005), they examined the link between the most sought after form of leadership, called transformational leadership, and employee well-being. Transformational leadership is somewhat complex, but essentially consists of four key features:

A transformational leader is someone who has the ability to…

(1) …provide individual consideration to her or his employees

(2) …inspire and motivate her or his employees to challenge themselves

(3) …encourage employees to seek out their own answers by challenging the status quo

(4) …model ethical behaviour by doing “the right thing” when the occasion calls

Arnold and colleagues reasoned that the link between transformational leadership and employee well-being would be the ability of leaders to enhance an employee’s subjective experience that their work has meaning and purpose.

This is how they proposed it would work:

blog5-entry-pic

And that is exactly what they found.  Which is great news because transformational leadership is something that can be improved through training.

More recent research has also boosted confidence in these findings by overcoming many of the limitations in this study.

  • Directionality: A longitudinal study (i.e., research that involves measurements that occur over time) has found evidence for the direction of the findings (i.e., leadership leads to meaningfulness which leads to well-being, rather than well-being to meaningfulness to leadership).
  • Single source & other factors: A review of the literature helps overcome the fact that the data in this study were collected from a single source and that several other potential factors were not measured, such as personality.

Take home message: Leader/manager/supervisor/boss/etc (albeit, not always synonymous) behaviour has important consequences on their employees’ well-being (among other things!). It is important for leaders to recognize this and take an honest self-evaluation. To do this effectively, the transformational framework provides an ideal checklist.

Categories
Life Misc

Saving little Tommy and his three-legged dog, Scout, and other potential realities

Blog 4 pic

(Photo via Steve Granger)

I recently listened to the thought and action provoking conversation between the philosopher, William MacAskill, and author, Sam Harris, on the Waking Up podcast, which I highly recommend (unless, as I ruefully learned, you’re about to go do some back-to-school clothes shopping – you’ll get why shortly).  They discussed arguments for what is called effective altruism.  Effective altruism is the idea that we should apply reason and evidence to maximize our attempts at making the world a better place.

For most of us, we are in the advantageous position to do a great deal of good.  We can save a life right now.  Seriously.  Imagine the story you would have if you were out for a night-on-the-town and you pulled someone away from getting hit by a distracted driver – or the tale you would recite if you ran into a burning building and saved a little child and his three-legged dog.  As MacAskill and Harris conclude, we are in a position to reach out or run in whenever we want!

But then the questions start to roll in.  Who or what organization should we give to?  How much should we give?  How can I truly maximize the good I do?  Luckily the effective altruism movement has answers for these and many more questions: http://www.givewell.org/

The key takeaway for me is this: Giving shouldn’t necessarily be seen as an obligation, but an opportunity.  It’s easy to get overwhelmed by the “maximize the common good” mindset – where luxury is a sin and being a hypocrite is unavoidable (e.g., getting new clothes when your old ones are perfectly fine!).  Many get paralyzed by this approach.  They turn inward by putting up a wall of distrust and self-preservation.  They lash outward by reproaching those who express benevolent inclinations and dismiss them as virtue signals.  Ultimately, they give less than they would have in hindsight.

Yet it has never been so easy to reach out.  If we simply change how we think and reason about giving, we could do so much more.  That’s why I wanted to share this conversation between MacAskill and Harris, and the idea of effective altruism.  As Harris points out in his postscript, it is not so often that we can share ideas that have such immediate consequences.

Categories
Life Misc

An Open Love Letter to Winnipeg

Blog3 via unbekannt270_Edit(Photograph via unbekannt270)

I have seen you grow. I have wallowed in fields of grass and snow that are now schools and stores. I have watched a city revel in self-deprecating humor – to then vigorously defend itself with pride. I have witnessed the warm embrace of a community welcoming their fellow human beings; individuals similarly devoted to making a better life for future generations. I have observed time and again a collective upholding its values yet opening its mind outwardly and inwardly.

It is true that you have stumbled and fallen; that your hardened character from the bitter cold has been mistaken for meanness; that you have seen turmoil resulting from our nature to create out-groups. But it is also true that you have clung on to what matters. That most of you are there to help each other up; that you made it a place where people are free to make mistakes. That you are willing to acknowledge these mistakes and work hard to learn from them; where each day you put every ounce of effort into building up your confidence.

This sense of growth, the self-checking balance of humility and pride, the welcoming of diversity, and the awareness of the wisdom that lies in values is much of what makes you wonderful. The scars and the bruises, the shared hardness of your life in a frigid-to-sweltering swamp, and the mistakes that are made as you develop are what make you real. Your progeny engrain these features; when they depart, they only leave in the physical sense – but like dandelion seeds blowing in the gentle breeze, they will always be a part of you.