Analysis of Linear Models with Two Factors Having Both Fixed and Random Levels

Abstract

A general theory for a case where some factors have both fixed and random effect levels is developed under a two-way treatment structure model. This is an extension of a one factor with both fixed and random levels (Njuho and Milliken, 2005). We consider several alternative approaches for estimating the fixed effects and the variance components using mixed models. We propose conducting the analysis in stages depending on the hypothesis being tested. The computational procedures are illustrated using two numerical examples.

Inference in nonorthogonal mixed models

“…A new estimator by combining ideas underlying the mixed and the ridge regression estimators when there are stochastic linear restrictions on the parameter vector is introduced in Ozkale 7 . A development of a general theory for a case where some factors have both fixed and random effect levels, under a two‐way treatment structure model may be seen in Njuho and Milliken 8 . There, the authors considered several alternative approaches for estimating the fixed effects and the variance components using mixed models and proposed conducting the analysis in stages depending on the hypothesis being tested.…”

Chisquared and related inducing pivot variables: an application to orthogonal mixed models

“…As a promising field of work we considered mixed models, since this type of model is widely used, see for example Hubert and Wijekoon (2006), Njuho and Milliken (2009), Ozkale (2009), Yang and Wu (2011) or Yang and Wu (2012).…”