The topic of fixed versus random effects is one that causes much difficulty and debate. I have been thinking about it for some time now and the following represent my latest ideas on the topic.
Comments are welcome.
It is traditional to talk about complete versus incomplete samples and random selection versus something else as a basis for deciding random versus fixed effects. However, this seems to me to be missing the point. Afterall, what is really being done is deciding which sort of model is best for the population. I believe effects can be regarded as random if the population set of effects can be regarded as best characterised by a regular distribution whose variance is a reasonable parameter for representing the effects. If this is not the case, we are left with parameterizing in terms of mean values that differ arbitrarily, or perhaps in some systematic way.