# Effect sizes from LMM

My question is, how to get effect sizes for a linear mixed model?

I am using the following model in SPSS:

MIXED
transfer  BY distance training rotation sequence  WITH pretest
/CRITERIA = CIN(95) MXITER(100) MXSTEP(5) SCORING(1) SINGULAR(0.000000000001)
HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED = pretest rotation sequence distance training distance*training  | SSTYPE(3)
/METHOD = REML
/REPEATED = distance | SUBJECT(ResponseID) COVTYPE(CS) .


I've also done it in R, where it looks like this:

library( nlme )
options(contrasts=c("contr.sum","contr.poly"))
lm1 <- lme(transfer ~ training * distance + rotation + sequence + pretest,
random=~1|ResponseID, method="REML", data=wide.data )
fit <- anova.lme(lm1,type='marginal')
print( fit )


The dv, transfer, measures pretest to posttest improvement for a given level of distance. Distance is a categorical within-subjects variable with either 2 or 3 levels depending on the dataset. Training is a categorical between-subjects variable with either 2 or 4 levels depending on the dataset. Rotation and sequence are binary categorical between-subjects variables. Pretest is a covariate with different values for each level of distance.

I've already submitted the results of the analysis for publication, and got a reviewer comment asking for odds ratios. Ideally I'd like to get odds ratios for each effect in the model. If I can't get odds ratios, some other measure of effect sizes might be OK. Most important, I need to get it for the training * distance interaction and the covariate (pretest) because these are the only significant effects.

Ideally I'd get it straight from SPSS but as far as I can see, SPSS can't do it. I couldn't figure out how to do it in R either. Second best would be to put the output of one of these into some other software that could calculate it for me. I found some free software that could compute eta-squared for regular mixed ANOVA but not for linear mixed model.

Other questions about effect sizes seem to relate to other models, not LMMs. I did see another similar question about LMMs which is currently unanswered.

Any ideas?

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Is your response variable (transfer) 0/1? Usually odds ratios are for a dichotomous response; I'm not sure I see how they would function in this situation. It's worth noting that model betas are a measure of effect size, just not a standardized one. Also, can you include a link to the other CV question that you think is related? –  gung Dec 15 '12 at 16:27