Assessing Multimethod Association With Categorical Variables

Fridtjof W Nussbeck

This chapter provides an introduction to methods for analyzing the associations between categorical variables. The focus is on the analysis of nonordered categorical data, also referred to as nominal data or nominal variables (for the analysis of ordered categorical data, see Rost & Walter, chap. 18, this volume). First, general association indices such as the proportion (or percentage) agreement index, the occurrence (nonoccurrence) agreement index, the chi-square value, and coefficient kappa are presented. Their advantages and disadvantages are discussed. The second section shows how loglinear modeling can be used to analyze associations between categorical variables.

Nominal variables are variables whose values only serve to identify categories without any quantitative meaning. Clinical disorders, for example, are often assessed using nominal variables. The assignment of "1" to "paranoid schizophrenia disorder" and "2" to "major depressive disorder" is equally admissible as the reverse. The assignment of numbers to the categories has no impact on the further analysis of the data, because nominal variables are not ordered in a specific manner. Nominal variables can be obtained using a wide array of measurement methods such as self-ratings, peer ratings, and medical and psychological diagnoses (see Neyer, chap. 4, this volume; Bakeman & Gnisci, chap. 10, this volume). It is important to note that every subject has to be categorized and that he or she can only be classified into one category. In other words, the categories must be exhaustive and mutually exclusive. In most cases, however, categories are not defined very accurately, and not all the information needed for a perfect diagnosis is available. Therefore, multimethod assessment can be used to verify the correct categorization by raters.

To analyze the convergence of different methods, nominal variables are usually presented in cross tables, in which the rows and columns represent the different categories of the manifest variables measured by the different methods. Two cross-classified variables are shown in Table 17.1a. This table demonstrates the simplest case consisting of two variables with two categories, where the variables are the ratings of two educational psychologists who assessed hyperactivity in a total of 500 pupils. Associations between both raters (Educational Psychologists A and B) are apparently evident. In the data set, for example, both tend to judge most pupils as "not hyperactive" and only a few (55 by A, 60 by B) as "hyperactive." Moreover, both raters agree in their ratings of the same 40 pupils as "hyperactive" and 425 pupils as "not hyperactive." They disagree in 35 cases. Both ratings converge in the majority of cases. The last column presents the marginal distribution for A, and the last row presents the marginal distribution for B.

When subjects are simultaneously rated by two or more observers, the ratings are associated when some combinations of categories are chosen more often than expected, given their marginal distributions—on the other hand, agreement only occurs when both observers assign the same categories to

Cross-Classification of Hyperactivity Ratings by Two Educational Psychologists (Artificial Data)

Educational Marginal

Psychologist B distribution of A

hyperactive Normal au

Educational Marginal

Psychologist B distribution of A

hyperactive Normal au

Educational

Hyperactive

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