# Variance structure with multiple covariates in GLS

I am building a GLS model following protocol in "Zuur, 2009. Mixed effects models..." on p.90.

I have 5 continuous predictors. VarConstPower variance structure works best for me. At first the fixed part of the model includes all covariates. At that point I get the lowest AIC when variance part also includes all 5 covariates. But with model selection my fixed part shrinks to only 2 covariates. Can I still retain all 5 covariates in my variance part?

• Removing covariates in this way biases $\sigma^2$ towards zero, which will invalidate $P$-values and confidence limits. – Frank Harrell Feb 7 '14 at 13:24

You don't have to treat the variance structures like you would treat random effects in a non-gls model. With random effects you usually assume that they have zero mean, hence you include the corresponding fixed effect covariate to ensure this zero mean.