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.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s