Categorical Data Analysis with SAS and SPSS Applications

Categorical Data Analysis with SAS and SPSS Applications

Categorical Data Analysis with SAS and SPSS Applications

Categorical Data Analysis with SAS and SPSS Applications


This new book covers the fundamental aspects of categorical data analysis with an emphasis on how to implement the models used in the book using SAS and SPSS. This is accomplished through the frequent use of examples, with relevant codes and instructions, that are closely related to the problems in the text. Concepts are explained in detail so that students can reproduce similar results on their own. Beginning with chapter two, exercises at the end of each chapter further strengthen students' understanding of the concepts by requiring them to apply some of the ideas expressed in the text in a more advanced capacity. Most of these exercises require intensive use of PC-based statistical software. Numerous tables with results of analyses, including interpretations of the results, further strengthen students' understanding of the material. Categorical Data Analysis With SAS(r) and SPSS Applications features: detailed programs and outputs of all examples illustrated in the book using SAS 8.02(r) and SPSS on the book's CD; detailed coverage of topics often ignored in other books, such as oneway classification (ch. 3), the analysis of doubly classified data (ch. 11), and generalized estimating equations (ch. 12); and coverage of SAS(r) PROC FREQ, GENMOD, LOGISTIC, PROBIT, and CATMOD, as well as SPSS PROC CROSSTABS, GENLOG, LOG-LINEAR, PROBIT, LOGISTIC, NUMREG, and PLUM. This book is ideal for upper-level undergraduate or graduate-level courses on categorical data analysis taught in departments of biostatistics, statistics, epidemiology, psychology, sociology, political science, and education. A prerequisite of one year of calculus and statistics is recommended. The book has been class tested by graduate students in the department of biometry and epidemiology at the Medical University of South Carolina.


In this text, we will be dealing with categorical data, which consist of counts rather than measurements. A variable is often denned as the characteristic of objects or subjects that varies from one object or subject to another. Gender, for instance, is a variable as it varies from one person to another. In this chapter, because variables consist of different types, we describe the variable classification that has been adopted over the years in the following section.

1.1 Variable Classification

Stevens (1946) developed the measurement scale hierachy into four categories, namely, nominal, ordinal, interval and ratio scales. Stevens (1951) further prescribed statistical analyses that are appropriate and/or inappropriate for data that are classified according to one of the four scales above. The nominal scale is the lowest while the ratio scale variables are the highest.

However, this scale typology has seen a lot of critisisms from, namely, Lord (1953), Guttman (1968), Tukey (1961,) and Velleman and Wilkinson (1993). Most of the critisisms tend to focus on the prescription of scale types to justify statistical methods. Consequently, Velleman and Wilkinson (1993) give examples of situations where Steven's categorization failed and where statistical procedures can often not be classified by Steveen's measurement theory.

Alternative scale taxonomies have therefore been suggested. One of such was presented in Mosteller and Tukey (1977, chap. 5). The hierachy under their classification consists of grades, ranks, counted fractions, counts, amounts, and balances.

A categorical variable is one for which the measurement scale consists of a set of categories that is non-numerical. There are two kinds of categorical variables: nominal and ordinal variables. The first kind, nominal variables, have a set of unordered mutually exclusive categories, which according to Velleman and Wilkinson (1993) “may not even require the assignment of numerical values, but only of unique identifiers (numerals, letters, color)”. This kind classifies individuals or objects into variables such as gender (male or female), marital status (married, single, widowed, divorced), and party affiliation (Republican, Democrat, Independent). Other variables of this kind are race, religious affiliation, etc. The number of occurrences . . .

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