Random Effects Old and New: It Affects Your Simulation Design

• Activity Number: 408
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): James Hodges*+
• Companies: Univ of Minnesota
• Keywords: random effect ; smoothing ; shrinkage ; simulation experiment

Abstract

The term "random effect" is used more broadly than it was, say, 50 years ago. Then, a random effect had (in ANOVA jargon) levels that were draws from a population, which were not of interest in themselves but only as samples from the population. By contrast, new-style random effects have levels that are not draws from any population, or that are the entire population, or that may be a sample but a new draw of the random effect could not conceivably be drawn, and the levels themselves are usually of interest. Any new-style random effect can be understood as a formal device to implement smoothing or shrinkage, i.e., it is part of the model's mean, not its covariance, even though the random effect's specification includes a covariance matrix. This distinction has practical consequences for simulation experiments (among other things): In simulating data to evaluate a statistical method, you never need to make draws from the new-style random effect; in fact, simulating draws from a new-style random effect is usually incorrect and self-defeating. Instead, you should specify true values or functions that the method is intended to estimate or predict and add simulated errors.