Analysis of Linear Models with One Factor Having Both Fixed and Random Levels

Abstract

A general theory for a case where a factor has both fixed and random effect levels is developed under one-way treatment structure model. Estimation procedures for the fixed effects and variance components are consider for the model. The testing of fixed effects is considered when the variance-covariance matrix is known and unknown. Confidence intervals for estimable functions and prediction intervals for predictable functions are constructed. The computational procedures are illustrated using data from an on-farm trial.

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

“…The simplest case occurs when we fail to reject all the four hypotheses. Njuho and Milliken (2005) demonstrated using Graybill (1976, Theorem 6.8.1) how the weighted least squares estimator,ˆ = X V −1 X −1 X V −1 y equals to an ordinary least squares estimatorˆ OLS , a vector of fixed effects for a balanced model. Thus, the solutions to the fixed effects' part of (3) arê…”

“…A general theory for a case where a factor has both fixed and random effect levels exists (Njuho and Milliken, 2005). An extension to two or more factors with each having fixed and random effect levels is provided.…”

“…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.…”

A modified nested-error regression model for small area estimation

“…A general theory for a case where a factor has both fixed-and random-effect level was developed under a one-way ANOVA model by Njuho and Milliken [6]. In this paper, their model is extended to a linear regression model with an intercept being fixed in a part of the domains and being random in the rest of the domains.…”

Monte Carlo simulation study of regression models used to estimate the credit banking risk in home equity loans

“…This method consists of estimating by one side the variance components and by the other side the fixed effects [13][14][15]. REML estimates of σ = (σ 2 0 , σ 2 1 ) t can be obtained by maximizing the log-likelihood function…”