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.
