In some statistical analyses (ie genetics), it may makes sense to perform a two-step regression analysis. In this analysis, the dependent variable is regressed against several independent variables. The residuals are taken from this first regression, and modeled against a final independent variable (ie. a SNP in a genetic association study). Demissie et al. discusses possible bias under this two-stage design, but this bias is only if the final independent variable is correlated with one of the independent variables from the first models. However, what if the first model is a mixed effect model and the residuals from the mixed effect model are then regressed against the final covariate? Would there be an issue with incorporating random effects first, and then regressing a remaining fixed effect variable on the resulting residuals?