ABSTRACT
The main effect and interaction structure of the variables that span a cross-classification can be described in terms of log-linear models (a brief introduction into the method of log-linear modeling is provided in Appendix A). The general log-linear model is https://www.w3.org/1998/Math/MathML"> log E = X λ , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781410606570/406bed72-6d1a-40cf-a7a1-adfbef1e4dce/content/eqn1_6_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where E is an array of model frequencies, X is the design matrix, also called indicator matrix, and λ is a parameter vector (Christensen, 1997; Evers & Namboodiri, 1978; von Eye, Kreppner, & Weβels, 1994). The design matrix contains column vectors that express the main effects and interactions specified for a model. There exist several ways to express the main effects and interactions. Most popular are dummy coding and effect coding. Dummy coding uses only the values of 0 and 1. Effect coding typically uses the values of −1, 0, and 1. However, for purposes of weighting, other values are occasionally used also. Dummy coding and effect coding are equivalent. In this book, we use effect coding because a design matrix specified in effect coding terms is easier for many researchers to interpret than a matrix specified using dummy coding.
