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