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:
…you can take a correlation table (along with the means, standard deviations, and sample size) like this:
…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:
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).
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
- [Second easiest] Do the same thing in SPSS
- Save as Fixed ASCII (*.dat)
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
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, p = .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, p = .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.
Let's Get You Back Out There 