Stats

Jargon

 * Identification:
 * In econometrics you specify a model for how data comes to exist. The model has some random variable(s) in it so doesn't tell you exactly what data will exist but it might tell you something about the relative likelihood of different hypothetically possible data sets. The model typically has some unknown parameters which you intend to estimate. An identification problem exists if the mathematical nature of the model is such that changing the value of some parameter(s) does not alter the relative likelihood of different potential data sets. It's a problem because you then can't use the data that you actually do have as a basis for estimating the values of those parameters.
 * Imagine a country where everybody always wears a hat. You have a randomly selected sample of heights (hats included) and want to estimate the population average height of a person (hat not included). You can't do it because a population of short people with tall hats can lead to the same data as would a population of tall people with short hats."
 * Random, fixed, mixed effects:
 * Fixed effects are constant across individuals, and random effects vary; effects are fixed if they are interesting in themselves or random if there is interest in the underlying population
 * When a sample exhausts the population, the corresponding variable is fixed
 * When the sample is a small (i.e., negligible) part of the population the corresponding variable is random
 * If an effect is assumed to be a realized value of a random variable, it is called a random effect
 * Fixed effects are estimated using least squares (or, more generally, maximum likelihood) and random effects are estimated with shrinkage (“linear unbiased prediction”)
 * Random effects are estimated with partial pooling, while fixed effects are not
 * Mixed: model has both fixed and random effects, so let's focus on the difference between fixed and random

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