Common Errors in Statistics (and How to Avoid Them), 4th Edition

FIXED- AND RANDOM-EFFECTS MODELS

Most textbooks introduce fixed- and random-effects ANOVA models through a series of examples. Cases are presented wherein multiple observations are collected for each farm animal, or multiple observations are collected for each farm. The basic issue in deciding whether to utilize a fixed- or random-effects model is whether the sampling units (for which multiple observations are collected) represent the collection of most or all of the entities for which inference will be drawn. If so, the fixed-effects estimator is to be preferred. On the other hand, if those same sampling units represent a random sample from a larger population for which we wish to make inferences, then the random-effects estimator is more appropriate.

Fixed- and random-effects models address unobserved heterogeneity. The random-effects model assumes that the panel-level effects are randomly distributed. The fixed-effects model assumes a constant disturbance that is a special case of the random-effects model. If the random-effects assumption is correct, then the random-effects estimator is more efficient than the fixed-effects estimator. If the random-effects assumption does not hold (that is, if we specify the wrong distribution for the random-effects), then the random effects model is not consistent. To help decide whether the fixed- or random-effects models is more appropriate, use the Durbin–Wu–Hausman³ test comparing coefficients from each model.

The fixed-effects approach ...