I am fitting a linear mixed effect model in R with
nlmer, using the approach described in Zuur et al. "Mixed Effects Models and Extensions in Ecology with R".
As a first step, I use
gls to fit a linear model and look for evidence of heterogeneity, starting with a full model.
require(nlme) M0 <- gls(ptltcued ~ facesex*emo*agegroup, data=data, na.action = na.exclude) plot(M0)
I find no (?) evidence of heterogeneity.
Next, I use AIC and REML fits to choose between models with no random effect, a random intercept, or random intercept and slope. I have 2 fixed between-subject factors (agegroup, emo), 1 fixed within-subject factor (facesex), and one random subject factor (numsubj).
M1 <- gls(ptltcued ~ facesex*emo*agegroup, method="REML", na.action= na.exclude, data=data) M2 <- lme(ptltcued ~ facesex*emo*agegroup, random=~1|numsubj,method="REML", na.action= na.exclude, data=data) M3 <- lme(ptltcued ~ facesex*emo*agegroup, random=~1+facesex|numsubj, method="REML", na.action= na.exclude, data=data) AIC(M1,M2,M3)
AIC gives the following result:
- M1 df 13 AIC -215.2172
- M2 df 14 AIC -213.2172
- M3 df 16 AIC -221.1735
Based on AIC, I decide for a model with random intercept and slope. Next, I validate M3 before going on to select fixed effects.
Normality checks look good (?).
Heterogeneity check looks... well, hum. I have never seen this kind of pattern in a plot of standardized residuals versus fitted values. There is no change in spread along the fitted values, but there is an obvious correlation between residuals and fitted values.
plot(fitted(M3),resid(M3)) abline(h=0,col="grey") lines(lowess(fitted(M3)[is.finite(fitted(M3))],resid(M3)[is.finite(fitted(M3))]),col="red")
The pattern is absent in M1 and M2. For example, here is the plot for M2:
I don't understand the reason behind this. It seems to me that I should abandon M3 and go for M1, the next best in terms of AIC. However, I have a feeling that this kind of obvious relationship probably has an obvious cause such as a formula mistake or something else which I am unaware of.
So: What should be the course of action here? Is there an obvious reason for this pattern?