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Mplus Discussion > Growth Modeling of Longitudinal Data >
 Anonymous posted on Tuesday, May 04, 2004 - 10:16 am
I'm modeling a binary growth model with time-varying covariates (TVC's). Some of my TVC's are binary and some our continuous. I'd like to be able to determine the percent of variance explained (or some other measure of effect size) for each of my TVC's so that I can determine which TVC's are most important. Can you point me in the direction of a paper that would help me...or can you offer me some advice on how to proceed. Thank you!
 Linda K. Muthen posted on Tuesday, May 04, 2004 - 10:37 am
I don't know what to look at apart from the standardized solution. Any comments from others?
 Bill Dudley posted on Tuesday, January 13, 2009 - 9:28 am
I hope to use Monte Carlo simulations to estimate power for mediation in a longitudinal study in which the predictor (X), outcome (Y) and mediator (M) are all measured at four time points. In this model the slopes (Sx Sm and Sy) are the focus - that is the change in the predictor leads to change in the mediator which in turn leads to the change in the outcome. Mackinnon diagrams this as figure 8.4 in his new book.

I have been able to run models such as the MacKinnon model using some old data I had lying around and now I am working through some of the challenges in setting up the Monte Carlo but need a bit of advice re effect size. Mackinnon provides several forms for effect size including: a*b/SdY. Y in this case would be the slope of the outcome (Sy).

QUESTION - What would be the easiest way to model the Standard dDeviation of of Sy within the Monte Carlo. Would this just be an "Sy*XXX" line Where XXX would be the residual variance of Sy??. And then a*b would just be the product of Sm on Sx (=a) and the Sm coefficient from SY on SM SX (=b).
 Bengt O. Muthen posted on Tuesday, January 13, 2009 - 5:23 pm
I assume you are planning on computing the effect size using Model Constraint. You want to use the SD, not the residual SD, so you have to use Model Constraint to compute that since it isn't a model parameter. And, I don't think using the slope SD is as transparent as using the SD for the outcome at some key time point. The outcome variance is calculated in line with our growth handouts.
 Bill Dudley posted on Wednesday, January 14, 2009 - 3:30 am
Dr Muthen
Thank you for the direction and food for thought.
 Hanno Petras posted on Thursday, October 14, 2010 - 10:57 am
Dear Linda & Bengt,

when conducting a power analysis for the effect of a binary covariate on the slope of a conventional growth model with binary indicators, do you follow the same steps as outlined in Muthen & Muthen (2002)? Thank you.
 Linda K. Muthen posted on Friday, October 15, 2010 - 9:09 am
The principles are the same for any model.
 Hanno Petras posted on Friday, October 15, 2010 - 9:19 am
Dear Linda,

thank you for your response. My question was a little bit more specific than your response. Would you use the same parts of the model (the slope of the covariate effect, the variance of x and the residual variance of the slope) to compute an effect size, independently if the change is on Y as compared to Y*? Thank you.
 Linda K. Muthen posted on Friday, October 15, 2010 - 9:31 am
 Hanno Petras posted on Friday, October 15, 2010 - 9:41 am
Dear Linda,

thank you for confirming this.


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