New Developments in Categorical Data Analysis for the Social & Behavioral Science by L. Andries Van Der Ark, Marcel A. Croon, Klaas Sijtsma (Quantitative Methodology Series: Lawrence Erlbaum Associates) Almost all research in the social and behavioral sciences, economics, marketing, criminology, and medicine deals with the analysis of categorical data. Categorical data are quantified as either nominal variables-distinguishing different groups, for example, based on socio-economic status, education, and political persuasion-or ordinal variables-distinguishing levels of interest, such as the preferred politician for President or the preferred type of punishment for committing burglary. New Developments in Categorical Data Analysis for the Social and Behavioral Sciences is a collection of up-to-date studies on modern categorical data analysis methods, emphasizing their application to relevant and interesting data sets. A prominent breakthrough in categorical data analysis are latent variable models. This volume concentrates on two such classes of models-latent class analysis and item response theory. These methods use latent variables to explain the relationships among observed categorical variables. Latent class analysis yields the classification of a group of respondents according to their pattern of scores on the categorical variables. This provides insight into the mechanisms producing the data and allows the estimation of factor structures and regression models conditional on the latent class structure. Item response theory leads to the identification of one or more ordinal or interval scales. In psychological and educational testing these scales are used for individual measurement of abilities and personality traits. Item response theory has been extended to also deal with, for example, hierarchical data structures and cognitive theories explaining performance on tests.

Excerpt: The focus of this volume is applied. After a method is explained, the potential of the method for analyzing categorical data is illustrated by means of a real data example to show how it can be used effectively for solving a real data problem. These methods are accessible to researchers not trained explicitly in applied statistics. This volume appeals to researchers and advanced students in the social and behavioral sciences, including social, developmental, organizational, clinical and health psychologists, sociologists, educational and marketing researchers, and political scientists. In addition, it is of interest to those who collect data on categorical variables and are faced with the problem of how to analyze such variables-among themselves or in relation to metric variables.

Almost all research in the social and behavioral sciences, and also in economic and marketing research, criminological research, and social medical research deals with the analysis of categorical data. Categorical data are quantified as either nominal or ordinal variables. This volume is a collection of up-to-date studies on modern categorical data analysis methods, emphasizing their application to relevant and interesting data sets.

Different scores on nominal variables distinguish groups. Examples known to everyone are gender, socioeconomic status, education, religion, and political persuasion. Other examples, perhaps less well known, are the type of solution strategy used by a child to solve a mental problem in an intelligence test and different educational training programs used to teach language skills to eight-year old pupils. Because nominal scores only identify groups, calculations must use this information but no more; thus, addition and multiplication of such scores lead to meaningless results.

Different scores on ordinal variables distinguish levels of interest, but differences between such numbers hold no additional information. Such scores are rank numbers or transformations of rank numbers. Examples are the ordering of types of education according to level of sophistication, the choice of most preferred politician to run for president, the preference for type of punishment in response to burglary without using violence, and the degree in which someone who recently underwent surgery rates his or her daily quality of life as expressed on an ordered rating scale.

Originally, the analysis of categorical data was restricted to counting frequencies, collecting them in cross tables, and determining the strength of the relationship between variables. Nowadays, a powerful collection of statistical methods is available that enables the researcher to exhaust his or her categorical data in ways that seemed illusory only one or two decades ago.

A prominent breakthrough in categorical data analysis is the development and use of latent variable models. This volume concentrates on two such classes of models, latent class analysis and item response theory. These methods assume latent variables to explain the relationships among observed categorical variables. Roughly, if the latent variable is also cate¬gorical the method is called latent class analysis and if it is continuous the method is called item response theory.

Latent class analysis basically yields the classification of a group of re¬spondents according to their most likely pattern of scores on the categorical variables. Not only does this provide insight into the mechanisms producing the data, but modern latent class analysis also allows for the estimation of, for example, factor structures and regression models conditional on the la-tent class structure. Item response theory leads to the identification of one or more ordinal or interval scales. In psychological and educational testing these scales are used for individual measurement of abilities and person¬ality traits. Item response theory has been extended to also deal with, for example, hierarchical data structures and cognitive theories explaining performance on tests.

These developments are truly exiting because they enable us to get so much more out of our data than was ever dreamt of before. In fact, when realizing the potential of modern days statistical machinery one is tempted to dig up all those data sets collected not-so-long ago and re-analyze them with the latent class analysis and item response theory methods we now have at our disposal. To give the reader some flavor of these methods, the focus of most contributions in this volume has been kept applied; that is, after a method is explained, the potential of the method for analyzing categorical data is illustrated by means of a real data example. The purpose is to explain methods at a level that is accessible to researchers not trained explicitly in applied statistics and then show how it can be used effectively for solving a real data problem.