I'm working on a project looking at cross-national public opinion across two different observational "waves". Many countries were surveyed in both waves, though some were surveyed in the first wave and not the other (and vice-versa). With predictors at both the level of the individual and the level of the country, a mixed effects model is appropriate.
My question involves specifying the random effects, or the groupings. I think there are two: the country and the wave. That is, individuals in certain countries are going to be more like each other than individuals in other countries. Further, observations in the first wave are going to be more similar than with observations in the second wave, but it is not entirely a repeated measures design. Thus, I'm inclined to believe I should model the random effect component in lmer as
(1 | country/wave) [alternatively:
(1|country:wave) + (1|country)], where the country is nested within the wave. The results are a little sensitive to changes in the random effects structure. Nesting waves within countries and excluding the wave grouping altogether produce different results on key independent variables.
I was wanting to know if you think that's right. I could also be inviting trouble by treating wave as a random effect when there are only two waves.
Thanks for any input.