Conditional logistic regression vs GLMM in R I have paired data (GWAS case/control study) and I have heard using conditional logistic regression or generalized linear mixed models (GLMM) is appropriate. Which should I use in this case? Why would you use one over the other. More importantly can you guys point me towards resources for doing these methods in R? I'm finding a lot of material for SAS, which I do not prefer. I can provide more details if necessary.  
 A: *

*The conditional logistic regression applies fixed effects (in the
context of econometrics),
$$ logit(p_{ij})=\boldsymbol x_{ij}^{'}\boldsymbol\beta+u_i.$$
where each pair of subjects has an individual intercept ($u_i$). It can be implemented  with clogit() of package survival or clogistic() of package Epi.

*Generalized linear mixed models (GLMM) for binary data can adopt link
functions like logit, probit and cloglog. The mixed logistic
regression is as,
$$ logit(p_{ij})=\boldsymbol x_{ij}^{'}\boldsymbol\beta+\boldsymbol
   z_{ij}^{'}\boldsymbol u_i$$
where $\boldsymbol u_i$ are random variables and can have the distribution assumption (e.g. normal distribution). Of course you can use a random intercept model, i.e. $\boldsymbol z_{ij}^{'}=1$ and $\boldsymbol u_i$ is a scalar. You can estimate GLMM using glmer() of package lme4.

*As to the choice between conditional logistic regression and GLMM for binary data,
some people are in favor of conditonal (fixed-effects) logistic regression and GLMM with probit link, but against fixed-effects probit or GLMM with logit link. The reason may be that some of the consistency properties break down, especially with small within-cluster sample size ($n_i=2$ for your case).
You can find the clarification of fixed effects and random effects (and marginal models) in
different contexts here.
