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?