There are various definitions of fixed and random effects in linear mixed-effects models in the statistics literature, and even in the fixed-effects models from econometrics. The data I have now represent the entire consumption of some products in a country. I aggregated them to annual level for 6 years by each state. A longitudinal analysis was planned.
The primary question here is for the population data by every state in the country, whether fixed-effects models (N states fixed-parameters) or mixed-effects models (1 fixed-effect parameter, N states random-effects) should be used?
Personally, I prefer the definition by Fitzmaurice et al. (Applied Longitudinal Analysis), where a fixed-effect represents the population-average, while random-effects represent subject/state-specific effects. Therefore even the data is based on a fixed number of states in a country, each state will have its own growing trajectories over time, which is regarded as random-effects.
Some authors argue that for individual patient or small unit data, where an individual or unit was drawn from a large population, mixed-effects models or random-effects models are appropriate. But state-level data for a country can hardly be considered as a subset, then fixed-effects models is more appropriated.
Please correct me if any of the statements above is wrong. I wish to hear more opinions on this.