Mplus
Tuesday
March 19, 2024
HOME ORDER CONTACT US CUSTOMER LOGIN MPLUS DISCUSSION
Mplus
Mplus at a Glance
General Description
Mplus Programs
Pricing
Version History
System Requirements
Platforms
Mplus Demo Version
Training
Mplus Web Talks
Short Courses
Short Course Videos
and Handouts
Web Training
Mplus YouTube Channel
Documentation
Mplus User's Guide
Mplus Diagrammer
Technical Appendices
Mplus Web Notes
FAQ
User's Guide Examples
Mplus Book
Mplus Book Examples
Mplus Book Errata
Analyses/Research
Mplus Examples
Papers
References
Special Mplus Topics
Bayesian SEM (BSEM)
Complex Survey Data
DSEM – MultiLevel Time Series Analysis
Exploratory SEM (ESEM)
Genetics
IRT
Measurement Invariance
and Alignment
Mediation Analysis
Missing Data
Mixture Modeling
Multilevel Modeling
Randomized Trials
RI-CLPM
RI-LTA
Structural Equation Modeling
Survival Analysis
How-To
Using Mplus via R
Mplus plotting using R
Chi-Square Difference
Test for MLM and MLR
Power Calculation
Monte Carlo Utility
Search
 
Mplus Website Updates
Mplus Privacy Policy
VPAT/508 Compliance

How To Calculate The Power To Detect That A Parameter Is Different From Zero

  1. Create a mean vector and covariance matrix for the hypothesized parameter values for the model of interest. This is done by specifying your model with all parameters fixed to the population values and asking for RESIDUAL. These population parameter values can come from past research or theory.
    TITLE:    Power calculation for a growth model
              Step 1: Computing the population means
              and covariance matrix
    
    DATA:     FILE IS artific.dat;
              TYPE IS MEANS COVARIANCE;
                  ! Below is the data in artific.dat. The first
                  ! row is the means.  The rest in the
                  ! covariance matrix.
                  !   0 0 0 0
                  !   1
                  !   0 1
                  !   0 0 1
                  !   0 0 0 1
    
              NOBSERVATIONS = 500;
                  ! This number is arbitrary but should be no
                  ! smaller than 500 to get sufficient
                  ! precision.
    
    VARIABLE: NAMES ARE y1-y4;
    
    ANALYSIS: TYPE=MEANSTRUCTURE;
    
    MODEL:    i BY y1-y4@1;
              s BY y2@1 y3@2 y4@3;
              [y1-y4@0];
              [i@0 s@.2];
    
              i@.5;
              s@.1;
              i WITH s@0;
              y1-y4@.5;
    
    OUTPUT:  STANDARDIZED RESIDUAL;
    
  2. Analyze the mean and covariance matrix obtained from the residuals in the first step to check that a mistake was not made. The parameter values will be recovered if the mean and covariance matrix were created correctly.
    TITLE:    Power calculation for a growth model
              Step 2: Analyzing the population means and
              Covariance matrix to check that parameters
              are recovered
    
    DATA:     FILE IS pop.dat;
              TYPE IS MEANS COVARIANCE;
              NOBSERVATIONS = 500;
                  ! Below is the data in pop.dat.
                  !  0 .2 .4 .6
                  !  1
                  !  .5 1.1
                  !  .5 .7 1.4
                  !  .5 .8 1.1 1.9
    
    
    VARIABLE: NAMES ARE y1-y4;
    
    ANALYSIS: TYPE=MEANSTRUCTURE;
    
    MODEL:    i BY y1-y4@1;
              s BY y2@1 y3@2 y4@3;
    
              [y1-y4@0];
    
              [i s];
    
    OUTPUT:   STANDARDIZED RESIDUAL;
    
  3. Analyze the mean and covariance matrix obtained from the first step with a model that misspecifies one parameter by fixing it to zero and specifies the number of observations for which power is wanted.
    TITLE:    Power calculation for a growth model
              Step 3: Analyzing the population means and
              Covariance matrix with a misspecified model
    
    DATA:     FILE IS pop.dat;
              TYPE IS MEANS COVARIANCE;
              NOBSERVATIONS = 50;
                ! sample size for power
    
    VARIABLE: NAMES ARE y1-y4;
    
    ANALYSIS: TYPE=MEANSTRUCTURE;
    
    MODEL:    i BY y1-y4@1;
              s BY y2@1 y3@2 y4@3;
    
              [y1-y4@0];
    
              [i s@0];
                 !  The mean of the slope growth factor
                 !  is fixed to zero.
    
    OUTPUT:   STANDARDIZED RESIDUAL;
    
  4. Use the chi-square value of 9.286 from the third step as an approximate noncentrality parameter. Calculate the power to detect the misspecification using the SAS program below where the degrees of freedom are equal to one, the critical chi-square value for p of .05 is 3.841459, and the approximate noncentrality parameter is 9.286.
    DATA POWER;
    DF=1; CRIT=3.841459;
    LAMBDA=9.286;
    POWER=(1-(PROBCHI(CRIT,DF,LAMBDA)));
    RUN;
    
    Chi-square values for other sample sizes can be calculated by using the fact that chi-square is equal to 2*sample size*F. Multiplying chi-square by the ratio of the new sample size to the sample size for the chi-square gives a chi-square for the new sample size that can be put into the SAS program above to obtain the power for that sample size. For example, the chi-square for sample size 100 is equal to 100/50*9.286 or 18.572. Following are the power results for this example.

    SAMPLE SIZEPOWER
    440.80
    500.85
    1000.98
    2000.99