Sections 4.3 and 4.4 introduced the basics of linear regression and analysis of covariance. This chapter begins with a recapitulation of the central concepts and ideas introduced in Chapter 4. It then broadens the horizon on linear regression in several ways. Section 6.2 discusses multiple linear regression and various analytical strategies for dealing with multiple predictors simultaneously. Section 6.3 introduces the generalized linear model, which extends the linear modeling approach to binary dependent variables (successes versus failures, correct versus incorrect responses, np or pp realizations of the dative, etc.) and factors with ordered levels (e.g. low, mid, and high education level). (The varbrul program used widely in sociolinguistics implements the general linear model for binary variables.) Finally, section 6.4 outlines a method for dealing with breakpoints, and section 6.5 discusses the special care required for dealing with word frequency distributions.

Introduction

Consider again the ratings data set that we studied in Chapter 4. We are interested in whether the rated size (averaged over subjects) of the referents of 81 English nouns can be predicted from the subjective estimates of these words' familiarity and from the class of their referents (plant versus animal). We begin by fitting a model of covariance with meanFamiliarity as nonlinear numeric predictor and Class as factorial predictor.