I have a couple of questions regarding random effects (or hierarchic models). I am doing some analysis of experiments where I measure a gene expression within three replicates and compare the results of a healthy and sick group. In order to propagate the measurement information, I understand I should include all replicates as random effects. In lme4 package the formula should look something like this.

glmer(sick ~ expression + (1|sample), family = logit())

Meaning there is a random effect for each sample. But if understood correctly this model will just adjust my interception for each sample. If so what is the difference to just include sample as a fixed effect? like this:

glm(sick ~ expression + sample, family = logit())

Can someone help me understand the logic behind?


Random effects models are effectively just statistically shrunken fixed effects models. This is to say that the estimates of the heterogeneous intercepts are shrunken towards zero. Doing so reduces the variability of the model, at the expense of some bias. If your sample strata were correlated with expression characteristics, then this shrinkage would bias your coefficient estimates on expression, because you are not "fully" projecting the effect of sample out of the regression -- information about sample would remain in the error term, and this would be correlated with expression, thereby biasing its coefficient.

This is why scientists dealing with multi-replicate experimental data usually use random effects, while economists dealing with repeated observations in non-experimental data use fixed effects.

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  • $\begingroup$ Great! If you're satisfied then please upvote and accept the answer! @andremrsantos $\endgroup$ – generic_user Nov 19 '17 at 20:59

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