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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.

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  • $\begingroup$ If the countries are exchangeable, or conditionally exchangeable you have (by de Finetti's theorem) an argument for using some random effects approach, regardless of how you sampled the data. Which random effects approach to use is a much more difficult question, however. $\endgroup$ – guest Feb 7 '12 at 6:46
  • $\begingroup$ In terms of exchange, what if I think those products comsumptions only happened on those who bought them, what will happen when other people never using before now start to consume? $\endgroup$ – Fred Feb 7 '12 at 21:29

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