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?
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$\begingroup$ Since mixed-effects models are a superset of fixed-effects models, it seems like this could only make the problem worse. $\endgroup$– eric_kernfeldSep 26, 2017 at 16:07
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4$\begingroup$ Are you asking whether this could ameliorate the bias discussed in the linked paper? Or are you assuming that such bias is not an issue, and asking whether using a mixed effect model in the first step introduces a separate set of problems? I suspect the answers are 'no' to the first, and 'maybe' to the second. $\endgroup$– Jacob SocolarSep 27, 2017 at 1:25
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$\begingroup$ the second question $\endgroup$– Andrew MardersteinSep 27, 2017 at 13:41
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1$\begingroup$ The linked Demissie paper is pretty explicit that Multiple Regression is always to be preferred. Is there a reason that doesn't work for you? $\endgroup$– Jacob SocolarOct 2, 2017 at 18:09
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$\begingroup$ some applications that I perform require a two step approach $\endgroup$– Andrew MardersteinOct 2, 2017 at 21:54
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