Introduction

Growth data and longitudinal data in general are often of an ordinal nature. For example, developmental stages may be classified into ordinal categories and behavioural variables repeatedly measured by discrete ordinal scales. Consider the data set presented in Table 15.1. This table contains information on marijuana use taken from five annual waves (1976–80) of the National Youth Survey (Elliot et al., 1989; Lang et al., 1999). The 237 respondents were 13 years old in 1976. The variable of interest is a trichotomous ordinal variable ‘Marijuana use in the past year’ measured during five consecutive years. There is also information on the gender of the respondents.

Ordinal data like this is often analysed as if it were continuous interval level data, that is, by means of methods that imply linear relationships and normally distributed errors. However, the data in Table 15.1 is essentially categorical and measured at ordinal, and not at interval level. Consequently, a much better way to deal with such an ordinal response variable is to treat it as a categorical variable coming from a multinomial distribution; the ordinal nature of the categories is then taken into account by imposing particular constraints on the odds of responding, i.e. of choosing one category rather than another. As will be further explained below, an ordinal analysis can be based on cumulative, adjacent-categories, or continuation-ratio odds (Agresti, 2002). The constraints are in the form of equality or inequality constraints on one of these types of odds.

In the past several years, a number of programs that estimate latent class models have appeared. These programs, based on maximum-likelihood estimation, have clearly superceded the earliest programs for latent class analysis: MLLSA (maximum likelihood latent structure analysis) by Clifford Clogg, LCAG (latent classes according to Goodman) by Jacques Hagenaars and Ruud Luijkx, and LAT and Newton by Shelby Haberman. The programs listed herein are a selection of some of the better-known programs that are currently available for solving a variety of latent class models.

WINMIRA

WINMIRA is a Windows-based program that estimates and tests a wide variety of discrete mixture models for categorical variables, including models with both nominal and continuous latent variables. In addition to latent class models, this program can be used to estimate Rasch models and mixed Rasch models with dichotomous and polytomous data.

PANMARK

PANMARK estimates and tests a range of latent class models, although as its name – a combination of panel Markov models – implies, this program was developed to estimate longitudinal latent class models. PANMARK also has a number of features such as its ability to generate multiple sets of starting values, which may be useful in avoiding local maxima, its reporting of asymptotic standard errors for model parameter estimates, and its use of bootstrapping methods for comparing models with different numbers of latent classes.

LATENTGOLD

LatentGOLD is a Windows-based latent class analysis program that is compatible with SPSS.

INTRODUCTION

The founding fathers of Latent Class Analysis (LCA) have explained LCA mainly as a categorical latent structure model, that is, as a particular scaling model (Lazarsfeld, 1950; Lazarsfeld and Henry, 1969; Goodman, 1974a, 1974b; Haberman, 1974, 1979; Clogg, 1981a, 1995). LCA is used to measure the true scores on underlying, not directly observed, categorical variables by means of a set of observed categorical variables that function as the indicators of these underlying, latent variables. The indicators are not perfect measures of the latent variables, but they are subjected to “random,” nonsystematic errors that lead to probabilistic relationships between the latent variables and the indicators. The standard LCA assumption of local independence specifies that the errors are conditionally independent of each other, when one controls for the latent variables. Throughout this chapter, the local independence assumption will be denoted as the independent classification error (ICE) assumption. Interpreting particular conditional response probabilities in terms of probabilities of classification errors (also termed misclassifications) is most appropriate when the scores on an indicator directly depend on just one latent variable and when there is a one-to-one correspondence between the categories of the indicator and the latent variable (Sutcliffe, 1965a, 1965b; Hagenaars, 1990; Kuha and Skinner, 1997). (For LCA models in which the latent variable has just a few categories and the indicators have many more, see Clogg, 1981b; also see Chapter 4 in this volume).

This appendix lists a number of books, chapters, and articles that may prove useful to those who wish to learn more about latent class analysis. Although the listing is by no means exhaustive, an effort has been made to include many of the most widely known sources. We have selected a set of general headings with which to separate the various works. Because several of the works can be classified under multiple topics, however, the reader is advised to consider works listed under headings other than that of his or her immediate interest. The bibliographies of the individual contributions are also an excellent source of additional readings on specific topics related to the latent class model.

In two very important overviews of latent class modeling, Clifford Clogg discussed the advances made in the area of latent class analysis during the past two decades (Clogg, 1981, 1995). From a formal, statistical point of view, great progress has been made regarding the estimation and testing of latent class models. It also has become clear that particular developments in econometrics, biometrics, and mathematical statistics concerning (finite) mixture models, unobserved heterogeneity, frailty models, and random coefficient models are identical or at least have very close ties to latent class modeling, thus enhancing our insight into the potentialities of latent class analysis. Furthermore, in the social and behavioral sciences, close relationships between latent class and loglinear models and between latent class and latent trait (item response) models have been discovered, leading latent class analysis to be viewed as a very general latent variable model for categorical data. Finally, and perhaps most importantly, it has been shown that latent class analysis provides a very useful tool for answering many substantive questions in the social and behavioral sciences.

Nevertheless, and despite the present availability of user-friendly software with which latent class models can be easily and routinely applied, practicing social and behavioral researchers do not always consider latent class analysis a serious alternative for better-known techniques, such as factor analysis or linear structural equation modeling, even where it would be a more appropriate means to address their questions.