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Modern Analysis of Customer Surveys: with applications using R by Silvia Salini, Ron S. Kenett

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12

Log-linear model methods

Stephen E. Fienberg and Daniel Manrique-Vallier

The chapter introduces the structuring of categorical data in the form of contingency tables, and then turns to a brief introduction to log-linear models and methods for their analysis, followed by their application in the context of customer satisfaction surveys. The focus is on the adaption of methods designed primarily for nominal data to the type of ordinal data gathered in the ABC annual customer satisfaction survey (ACSS). The chapter outlines some basic methodology based on maximum likelihood methods and related model search strategies, and then puts these methodological tools to work in the context of data extracted from the ACSS.

12.1 Introduction

Categorical data are ubiquitous in virtually all branches of science, but especially in the social sciences and in marketing. A contingency table consists of counts of units of observation cross-classified according to the values of several categorical (nominal or ordinal) variables. Thus standard survey data, which are largely categorical in nature, are best thought of as forming a very large contingency table. If we have collected data from n individuals or respondents and there are p questions in the survey questionnaire, then the table is of dimension p and the counts total n.

Suppose there are p=16 questions with binary response categories on a questionnaire. Then the corresponding contingency table would contain 216=65 536 cells. With a sample ...

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