In mixed models (GLMMs), random effects are often used to account for non-independence between observations e.g. of the same patient, or of animals from the same farm. I sometimes see multiple random effects being included just because there might be an effect. What are the consequences of including multiple random effects if they don't explain additional variance?
- I suspect it will affect the degrees of freedom and make the test overly conservative. At least in p-value based hypothesis testing.
- If several models are compared in an AIC framework but all have the same random effect structure will there be any effect on which fixed effect structure is identified as best?
- Will the estimates of fixed and/or random effects be biased or their standard errors increased?
- Will model convergence be impeded? And hence is the inference from a bayesian/MCMC model such as MCMCglmm (in R) likely compromised?