Concepts of mixed effects in statistics and econometrics, how to cope with them?

Question

When I search for the definition about fixed-effects, random-effects or mixed-effects model here or elsewhere on the internet, there are a lot of discrepances. My first exposure to linear mixed-effects model was in longitudinal data analysis in Biostatistics. The definition is clear to me that the fixed-effect is the population-averaged effect, and random-effects is the subject-specific effect. Then the mixed-effects model is the model that contains both fixed-effects and random-effects. The mixed-effects model is usually the random effects model because it contains at least one fixed-effects parameters. Like time slope, you have one mean slope for all individuals in the data, and random-effects are those subject-specific slope deviating from the mean slope.

However in Econometrics, the deveoplments of fixed-effects and random-effects models have distinct definitions, which is whether heterogeneity correlates or not with the error term. Some statistical tests were developed to test whether fixed-effects or random-effects model should be used. There are lot of social science analyses adopting the Econometric approach as well. Therefore when I read the discussions about fixed-effects, random-effects or mixed-effects models posted by people from different areas, they always confuse me. Even though sometimes the mathematical defintions are similar, the modelling process and consideration behind it are quite different.

I hope there are some general discussions on Statistics and Econometrics about their discrepance in defintions or concepts rather than methodologies or algorithms used.

Answer 1

I think the problem is that you are focussing on properties of the random effects rather than the actual meaning of random effect. It is simply a term in the model where the observed effect is considered to be a particular realization of a random variable that is characterized by a variance in the model. When you look at the random effect in this general way rather than thinking in terms of specific cases such as subject-specific slopes you might see commonality in the examples in econometrics and statistics.

Having seen other answers and other idscussions there may be cases where random effect has a different meaning and it does not just seem to be econometricians versus statisticians. But I still think that the most common and appropriate definition is the one I gave above.