Rudi[M]entary Model Commands in Mplus – part 2: ON

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:

Screen Shot 2017-04-30 at 8.02.57 PM

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, < .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!

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