Defining and Testing Models: Concepts and Examples

Abstract

This chapter introduces the general notation and framework for modeling and testing discrete multivariate data. Through a series of examples we introduce the concept of a null model for the parameters of the sampling distribution in Section 2.1, and motivate the use of goodness-of-fit test statistics to check the null model in Section 2.2. A detailed example is given in Section 2.3, which illustrates how the magnitudes of the cell frequencies cause the traditional goodness-of-fit statistics to behave differently. An explanation of these differences is provided by studying the power-divergence statistic (introduced in Section 2.4) and is developed throughout this book. Section 2.5 considers an application from the area of visual perception.