[R-sig-ME] LMM diagnostics: conditional residuals correlated highly with fitted values

[Yizhou Ma]

Dear LMM experts:

I am pretty new to using LMM and I have found the following situation
bewildering as I was trying to do diagnostics with my fitted model: my
conditional residuals correlated highly with the fitted values.

I have a dataset with multiple families, each has 1-4 siblings. I am trying
to regress Y onto EVs include Drink, Gender, & Age, while using random
intercept for family. This is the model I used:
model<-lmer(Y~Drink*Gender+Age
                      +(1|Family_ID),data,REML=FALSE)

After fitting the model, I used
plot(model)
to see the relationship between conditional residuals and fitted values. I
expect them to be uncorrelated and I expect to see homoscedasticity.

Yet to my surprise there is a high correlation (~0.5) between the residuals
and the fitted values. (see here <http://imgur.com/pPsG4aR>). I know from
GLM that this usually suggest nonlinear relationships between the EVs and
the DV.

I read some online posts (post1
<http://stats.stackexchange.com/questions/43566/strange-pattern-in-residual-plot-from-mixed-effect-model>
post2
<http://stats.stackexchange.com/questions/168179/correlation-between-standardized-residuals-and-fitted-values-in-a-linear-mixed-e/168210#168210>)
that suggest this can result from a poor model fit. So I tried a few
different models, including: 1) log transform Drink, which is originally
positively skewed; 2) add random slopes for Drink, Age, etc. None of these
changes have led to a substantial difference for the residual & fitted
value correlation.

Some other info:
1) my overall model fit is not poor as indicated by the correlation between
fitted values & Y. It is around 0.8;
2) most variables in my model has a normal, or at least symmetrical,
distribution.
3) conditional residuals are normally distributed as shown in qqplots.
4) conditional residuals are not correlated with any fixed effects, such as
Drink or Age.

I have two guesses as to what is going on:
1) maybe the fact that each family is a different size actually violates
assumptions of the model?
2) or maybe there is something wrong with estimation of the random effect
(family intercept)?

I'd really appreciate your insights as to what is going on here and if
there is any problems with my model.

Thank you very much,
Cherry

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