Mixed effects models - which are the random parts? I have data on family care for elderly people. Data stem from 6 EU counries. People were asked at baseline and followed-up one year later. Now I'd like to find predictors that explain why people stopped caring for their elder relatives (or continued caring), or in short: to find barriers and facilitators that keep care-at-home settings stable (in 6 country comparison).
My idea was to use mixed effects models with country as random intercept. But how would I include the time comparison (i.e. all people were caring at baseline, but a certain percentage stopped caring one year later).
Would this be another random intercept? Or a random slope? Or would I include this predictor as interaction?
I'm planning to analyse my data with R and the lme4 package.
 A: IMPORTANT EDIT: I think I've misread your question. As described, you're not interested at all in the effect of time, but rather in what other factors predictors predict if people will stop being carers (assuming that everyone at time $A$ is a carer at the time). Your independent variable in this case is just whether or not a given person is still a carer at time $B$. Time shouldn't be in your model.

Original answer
As described, time would be a fixed effect (i.e. a predictor), although if you believe that countries might differ in this regard (the effect of time varies from country to country) you might also include a random slope, which allows for this variation.
In lme4, the first model (random intercepts per country) would be, roughly
glmer(is_caring ~ time + (1|country), data=your.data, family=binomial)
while the second (allowing by-country variation in the effect of time) would be
glmer(is_caring ~ time + (time|country), data=your.data, family=binomial)
Obviously, you'll want to include your other predictors alongside time here, and consider 
You might want to take a look at some of Andrew Gelman's publications (i.e. this, or this excellent book) on the topic for a good primer.
