Effect sizes
Message/Author
 Daniel Rodriguez posted on Thursday, November 13, 2003 - 8:31 am
I am pursuing publication in a journal that now requires reporting of effect sizes. I conducted a study with general growth mixture modeling. With the multinomial logistic regressions applicable both to the covariates and the distal outcome, how would you approach this issue of effect size?
 bmuthen posted on Thursday, November 13, 2003 - 8:36 am
I don't know that there are common, established effect size measures for binary outcomes such as distals, but here is how I would reason. Assuming that you have say a binary covariate that influences a binary distal outcome, you can consider the log odds change in the distal as a function of changing covariate status. See the 2002 Biostatistics paper by Muthen et al on the home page of Mplus.
 Anonymous posted on Tuesday, September 20, 2005 - 12:06 pm
Suppose a Mixture Model generates k-classes for a continuous outcome. Then based on known statistics (e.g., -2*L, BIC, AIC, Entropy, and Lo-Mendell–Rubin Adjusted LRT Test) i decide that k-classes are acceptable. How can i estimate an effect size for the number of classes found. I found some artciles that suggest using 1-Wilks'lambda (Tatsuoka, 1988) and then use Cohen's (1988) approach. Then the effect size would [(1-WilksL full model)-(1-WilksL reduced)]/(1-WilksL full model).
Is there any other way to estimate the effect size. Do you have any comments regarding this way of estimating effects sizes?
 BMuthen posted on Wednesday, September 21, 2005 - 3:28 pm
I am not sure what you mean by effect size for the number of classes found. I am not familiar with the article you mention as it relates to mixture modeling. Are these articles related to k-means clustering.
 Juned Siddique posted on Friday, September 30, 2011 - 11:10 am
Hi. I fit the following GMM:

i s q| y0@0 y1@1 y2@2 ... y12@12;
q@0;
c ON x1 x2;
s ON i ;

I used KNOWNCLASS to specify three treatment groups. And found a two-class solution.

I estimated the difference (at months 6 and 12) in means between two treatment groups within the same class and used the delta method to calculate the std error of the difference.

I now need to report the difference in terms of an effect size. Hence I need the standard deviation of my outcome at months 6 and 12 within latent class. Is this value: Var(I) + t^2*Var(S) + 2t*Cov(I,S) + Residual Variance at month t? Where I and S are latent intercepts and slopes indexed by class.

Where can I get the residual variance? Thank you.
 Bengt O. Muthen posted on Friday, September 30, 2011 - 8:08 pm
Right. The residual variance is what is labelled y6/y12 under Residual variances.

And you can do all these calculations in Model Constraint, which will then give you the Delta method SEs.
 Juned Siddique posted on Monday, October 03, 2011 - 1:36 pm
Thanks Bengt. One more question. My slope term also has residual variance. Has this already been incorporated into the slope variance that is reported in the Tech 4 output?
 Bengt O. Muthen posted on Monday, October 03, 2011 - 8:17 pm
Yes.
 Joseph E. Glass posted on Saturday, June 29, 2013 - 6:58 am
I have a mixture model with complex survey data. I would like to determine the effect size for a mean difference across classes. Could you recommend a method to calculate the effect size for the mean difference in y? (see below). Thank you!

%OVERALL%
%c#1%
[y];
%c#2%
[y];
 Linda K. Muthen posted on Monday, July 01, 2013 - 7:45 am
%OVERALL%
y (v);
%c#1%
[y](p1);
%c#2%
[y] (p2);

MODEL CONSTRAINT:
NEW (effect);
effect = (p1 - p2) / sqrt (v);
 Katherine Cotter posted on Tuesday, March 13, 2018 - 10:36 am
Hello,

I am running a LCA with 2 classes and want to compare class differences on both binary and continuous distal outcomes. I've used the AUXILIARY option with the DCATEGORICAL and BCH options for these outcomes.

Are there specific effect size statistics that can be used to accompany the significance tests reported? Would it be similar to Cohen's d for t-tests and phi for chi-square tests?

Thank you
 Bengt O. Muthen posted on Tuesday, March 13, 2018 - 11:23 am
Relating mean differences across groups (or latent classes) to the variable's SD would seem to be always relevant.
 Sarah Dermody posted on Monday, August 19, 2019 - 3:10 pm
I'd like to follow-up to Katherine Cotter's question. If the LCA has more than 2 classes, would one use the total sample SD or pooled SD for the two groups to be compared? Also, as the SDs are sample characteristics, should one rely on the sample mean differences as opposed to estimated mean differences?
 Bengt O. Muthen posted on Monday, August 19, 2019 - 5:16 pm

I would use model-estimated means and model-estimated SDs (square root of model-estimated variances).

For continuous DVs, I would use the above Model Constraint formula:

effect = (p1 - p2) / sqrt (v);

I am not familiar with the effect size metric of phi for chi-square tests. Simply reporting the 2 estimated probabilities would seem to be a very down-to-earth approach.