A New Framework for Random Effects Models

TL;DR

The paper introduces Full Randomness, a new framework for random effects models that treats many fixed quantities as random, enabling richer analysis and computational benefits.

Contribution

It proposes the Full Randomness approach, which reduces fixed effects to random effects, providing a novel perspective and methodology for random effects models.

Findings

FR enables richer, more probing analyses.

FR offers computational advantages.

FR produces correct results even with fixed factors.

Abstract

A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR applied to a repeated measures model, even the number of repetitions would be modeled as random. It is argued that in many applications such quantities really are random, and that recognizing this enables the construction of much richer, more probing analyses. Methodology for this approach will be developed here, and suggestions will be made for the broader use of the approach. It is argued that even in settings in which some factors are fixed by the experimental design, FR still "gives the right answers." In addition, computational advantages to such methods will be shown.