# Mixed-effect for Dichotomy/binomial variables?

For normal-distributed interval/ratio data, we can apply linear mixed effect model for analysing longitudinal data, where each subject is measured multiple times. How about dichotomy (binomial) data?

My experiment is as follows:

There are two conditions A and B, and M is an interaction technique that will be used by the users for a task in the experiment on a VOLUNTARY base. (it means the task can be accomplished with or without M, and we are interested to know whether or not they use it). The experiment lasts for 4 weeks. Each week we experimented only ONCE for each participant. The task in each week is the same for each participant, but is different across different weeks. So in total each participant were tested on the same set of 4 tasks.

In the first 2 weeks, all 5 subjects were exposed to condition A, we observe if a subject has used M or not. So M is a dichotomy or binary variable which is either YES or NO. In the last 2 weeks, all 5 subjects were exposed to condition B, we again observe if a subject has used M or not.

The data is something like follows

subject   week   condition   useTechnique
1       1         A           YES
2       1         A           NO
3       1         A           YES
.........................................
.........................................
.........................................
3       4         B           NO
4       4         B           YES
5       4         B           YES


The research question is the following:

Does the change of condition has an effect on whether or not a user used the interaction technique M?

Normally we use chi-square test or mcnemar test for dichotomy data. The former one deals with unpaired and unmatched groups and the latter one deals with paired groups. McNemar's test is often used when we asked whether the participants liked/used a device before and after the experiment. This is essentially what I want to test, but unfortunately my experiment introduced random effect factors, because each subject is tested two twice under each condition.Furthermore, the task used in each week was different.

What test I should use for my research question for such data and how? I am using R, can anyone give some suggestions?