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Interpreting results of a mixed model
2 messages · Elizabeth Beck, Ben Bolker
Elizabeth Beck <elizabethbeck0 at ...> writes:
I have a question about the use of lme for hypothesis testing. I am interested in the effect of treatment on my response variables (potassium) in this case - I have about 50 blood variables total. My basic design is:
Like many questions that have been appearing on r-sig-mixed-models lately, this question isn't really specific to mixed models. It's more of a general question about interpreting the results of linear models. My general advice would be to read a really good, modern, R-centric book on statistical modeling -- I would recommend Frank Harrell's "Regression Modeling Strategies", but it might be a bit too advanced. (While it would be off-topic here, I would be interested in other opinions on this subject. I would also tentatively suggest Faraway's "Linear Models with R" and John Fox's "Companion to Applied Regression", but I have to admit that I don't have much first-hand experience with those books. (You might also look for examples/ reading on the specific issues of effect modification and confounding, e.g. biostat.mc.vanderbilt.edu/wiki/pub/Main/CourseBios312/effmod.pdf? -- this stuff is expressed in a slightly different set of vocabulary, but seems highly relevant.)
$ ID: Factor w/ 36 levels --> RANDOM EFFECT $ EXPOSURE : int -> FIXED FACTOR (REPEATED MEASURE) $ TREATMENT: Factor w/ 2 levels "Control","Experimental":
--> FIXED FACTOR
$ SEX : Factor w/ 2 levels "Female","Male": --> FIXED FACTOR $ K : num 2.2 2.3 2 3.5 ... --> RESPONSE VARIABLE I am unsure how to proceed to test for the effect of treatment on my response as I've had several opinions leading to different results. It was first suggested to me that my loaded model (in terms of fixed factors) should be the final step, and I should look at the p-values from the summary table which in this case yields a significant effect of exposure:treatment, as well as the treatment main effect. M2K.lme<-lme(K~ SEX*EXPOSURE*TREATMENT, random=~1|ID, method='REML', weights=varIdent(form=~1|EXPOSURE),data=biochem12)
summary(M2K.lme)
Although this makes sense, I am concerned that by over-fitting the model like this (the 3-way interaction especially) I am not getting an accurate result. I was told my another to continue with backwards selection of my fixed effects which, in the case of potassium means I remove every interaction and main effect leaving an empty model! While that may be true biologically speaking (if none of my factors impact potassium whatsoever) it makes for an awkward interpretation of my results. I also have the opposite problem with several variables whereby with backwards selection non significant terms becomes significant - which doesn't necessarily make the evidence much stronger in the biological sense.
In general I prefer the "keep the full model" approach, to avoid snooping, although then you have to be extremely careful to interpret the main effects appropriately (marginality, least-squares means, sum-to-zero-contrasts, blah blah blah ...). I don't object to mild simplification by removal of non-significant interactions, but the fact that the interpretation changes should concern you. My primary advice would be to create a meaningful plot of the data in order to understand what's actually going on. Ben Bolker