The second rudimentary model command in Mplus is ON or regress. This is similar to correlation but now you are inferring direction (i.e., single-headed arrow).

TITLE: Simple Regression Analysis; DATA: File is example.dat; VARIABLE: Names are VARx VARy; Missing are all(-999); Usevariables = VARx VARy; ANALYSIS: Estimator = ML; MODEL: VARy on VARx; !VARx is predicting VARy OUTPUT: Standardized sampstat;

Now the language used here can be a bit tricky, as Mplus uses traditional regression speak. But just try to remember that it’s backwards to the intuitive understanding: VARy on VARx means VARy is being regressed on our predictor VARx or VARx is predicting VARy.

If you’re anything like me, that takes a little while to warm up to, but it will happen. As you’re learning, I would recommend you always make notes after each line of command to remind yourself what your testing (like I did above), regression or otherwise, it’s good practice.

Now let’s look at an example of a simple regression using real data:

In this example we have political knowledge (*i.e., an employee’s collection of strategic and potentially sensitive information about his or her supervisor) *predicting change-oriented organizational citizenship behaviour (*i.e., an individual’s extra-role behaviour enacted to bring around change in the workplace*). The idea here is that an individual’s knowledge about their supervisor will enable them to bring around change.

And here is the output created from running this syntax:

Mplus VERSION 7.4 (Mac) MUTHEN & MUTHEN 04/30/2017 7:57 PM INPUT INSTRUCTIONS TITLE: Simple Regression Analysis; DATA: File is PK4regression.dat; VARIABLE: Names are PK PW PS PT CHOCB LMX; Missing are all(-999); Usevariables = PK CHOCB; ANALYSIS: Estimator = ML; MODEL: CHOCB on PK; !PK is predicting CHOCB OUTPUT: Standardized sampstat; *** WARNING Data set contains cases with missing on all variables. These cases were not included in the analysis. Number of cases with missing on all variables: 1 *** WARNING Data set contains cases with missing on x-variables. These cases were not included in the analysis. Number of cases with missing on x-variables: 1 2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS Simple Regression Analysis; SUMMARY OF ANALYSIS Number of groups 1 Number of observations 493 Number of dependent variables 1 Number of independent variables 1 Number of continuous latent variables 0 Observed dependent variables Continuous CHOCB Observed independent variables PK Estimator ML Information matrix OBSERVED Maximum number of iterations 1000 Convergence criterion 0.500D-04 Maximum number of steepest descent iterations 20 Maximum number of iterations for H1 2000 Convergence criterion for H1 0.100D-03 Input data file(s) PK4regression.dat Input data format FREE SUMMARY OF DATA Number of missing data patterns 1 COVARIANCE COVERAGE OF DATA Minimum covariance coverage value 0.100 PROPORTION OF DATA PRESENT Covariance Coverage CHOCB PK ________ ________ CHOCB 1.000 PK 1.000 1.000 SAMPLE STATISTICS ESTIMATED SAMPLE STATISTICS Means CHOCB PK ________ ________ 1 3.640 3.458 Covariances CHOCB PK ________ ________ CHOCB 0.585 PK 0.238 0.547 Correlations CHOCB PK ________ ________ CHOCB 1.000 PK 0.421 1.000 MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -1070.188 UNIVARIATE SAMPLE STATISTICS UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS Variable/ Mean/ Skewness/ Minimum/ % with Percentiles Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median CHOCB 3.640 -0.581 1.000 0.41% 3.000 3.500 3.750 493.000 0.585 0.443 5.000 5.48% 4.000 4.250 PK 3.458 -0.433 1.040 0.20% 2.870 3.350 3.520 493.000 0.547 0.200 5.000 1.01% 3.700 4.090 THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Number of Free Parameters 3 Loglikelihood H0 Value -519.526 H1 Value -519.526 Information Criteria Akaike (AIC) 1045.053 Bayesian (BIC) 1057.654 Sample-Size Adjusted BIC 1048.132 (n* = (n + 2) / 24) Chi-Square Test of Model Fit Value 0.000 Degrees of Freedom 0 P-Value 0.0000 RMSEA (Root Mean Square Error Of Approximation) Estimate 0.000 90 Percent C.I. 0.000 0.000 Probability RMSEA <= .05 0.000 CFI/TLI CFI 1.000 TLI 1.000 Chi-Square Test of Model Fit for the Baseline Model Value 96.004 Degrees of Freedom 1 P-Value 0.0000 SRMR (Standardized Root Mean Square Residual) Value 0.000 MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value CHOCB ON PK 0.435 0.042 10.295 0.000 Intercepts CHOCB 2.134 0.150 14.276 0.000 Residual Variances CHOCB 0.482 0.031 15.700 0.000 STANDARDIZED MODEL RESULTS STDYX Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value CHOCB ON PK 0.421 0.037 11.348 0.000 Intercepts CHOCB 2.790 0.254 10.992 0.000 Residual Variances CHOCB 0.823 0.031 26.392 0.000 STDY Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value CHOCB ON PK 0.569 0.048 11.859 0.000 Intercepts CHOCB 2.790 0.254 10.992 0.000 Residual Variances CHOCB 0.823 0.031 26.392 0.000 STD Standardization Two-Tailed Estimate S.E. Est./S.E. P-Value CHOCB ON PK 0.435 0.042 10.295 0.000 Intercepts CHOCB 2.134 0.150 14.276 0.000 Residual Variances CHOCB 0.482 0.031 15.700 0.000 R-SQUARE Observed Two-Tailed Variable Estimate S.E. Est./S.E. P-Value CHOCB 0.177 0.031 5.674 0.000 QUALITY OF NUMERICAL RESULTS Condition Number for the Information Matrix 0.337E-02 (ratio of smallest to largest eigenvalue) Beginning Time: 19:57:50 Ending Time: 19:57:50 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

Looking under the section STANDARDIZED MODEL RESULTS we can see that political knowledge predicting change-oriented organizational citizenship behaviour produces a standardized beta weight of .42, *p *< .001. Looking under R-SQUARE we can see that PK accounts for close to 18% of the variance in predicting CHOCB (R² = .18 [rounded up]). Although there is directionality inferred in regression analysis, study design determines whether causality can be inferred — and in this case it cannot because the study was a self-report survey which measured both variables.

Now, you would very rarily run just a single simple regression, but I wanted to keep it simple for show. If you wanted to run a multiple regression, you would just add more predictor variables on the right-hand side of the ON model command. Simple as that!