Introduction to Mixed Modelling: Beyond Regression and Analysis of Variance, 2nd Edition

Preface

This book is intended for research workers and students who have made some use of the statistical techniques of regression analysis and analysis of variance (anova), but who are unfamiliar with mixed models and the criterion for fitting them called REsidual Maximum Likelihood (REML, also known as REstricted Maximum Likelihood). Such readers will know that, broadly speaking, regression analysis seeks to account for the variation in a response variable by relating it to one or more explanatory variables, whereas anova seeks to detect variation among the mean values of groups of observations. In regression analysis, the statistical significance of each explanatory variable is tested using the same estimate of residual variance, namely the residual mean square, and this estimate is also used to calculate the standard error of the effect of each explanatory variable. However, this choice is not always appropriate. Sometimes, one or more of the terms in the regression model (in addition to the residual term) represents random variation, and such a term will contribute to the observed variation in other terms. It should therefore contribute to the significance tests and standard errors of these terms: but in an ordinary regression analysis, it does not do so. Anova, on the other hand, does allow the construction of models with additional random-effect terms, known as block terms. However, it does so only in the limited context of balanced experimental designs.

The capabilities ...