Latent Class Models in Social Work

In recent years, methods of analyzing latent variables have become increasingly popular in social work research. Techniques such as structural equation modeling (SEM) and confirmatory factor analysis (CFA) have been introduced into the curriculum of social work doctoral programs (Gillespie, Alsup, & Rubio, 1995). Many social worker researchers are now familiar with these techniques. Another useful but less well known approach to analyzing latent variables is latent class (LC) modeling. LC models are person-centered methods. These approaches can be quite useful when investigating problems that affect diverse groups of people. LC models estimate a latent variable that explains an aspect of heterogeneity (or diversity) in a population. This is particularly important when the aspect of heterogeneity is elusive and difficult to capture with a single measure (for example, religiosity, attitudes about moral issues) (McCutcheon, 1987a). LC modeling is not a particularly new concept-techniques have been described for more than 50 years (Green, 1951, 1952). Early examples of LC modeling include the use of General Social Survey data from the 1970s to identify classes of racial prejudice and lack of racial prejudice among white respondents (Tuch, 1981) and to identify classes of respondents regarding sexual morality and values (McCutcheon, 1987b). The recent development of more efficient and useable statistical methods, described later in this article, has made the application of LC models to social science problems a more realistic possibility (Goodman, 2002). LC models are becoming increasingly popular as a method of analysis. A search for "latent class analysis" in PsycINFO reveals that LC modeling techniques have been used for examining subtypes of borderline personality disorder (Clifton & Pilkonis, 2007), bipolar disorder (Fagiolini et al., 2007), and attention-deficit/hyperactivity disorder (de Nijs, Ferdinand, & Verhulst, 2007). LC models have been used to examine patterns of juvenile offending (Odgers et al., 2007), couple violence (Simpson, Doss, Wheeler, & Christensen, 2007), and substance abuse (Agrawal, Lynskey, Madden, Bucholz, & Heath, 2007; Dierker, Vesel, Sledjeski, Costello, & Perrine, 2007). It is clear that LC models have important applications that are relevant to social work research, yet they are infrequently used by social work researchers. A keyword search of Social Work Abstracts (in April 2009, using the terms "latent AND [class OR cluster OR profile OR structure]") and a hand search of five social work journals (Journal of Social Service Research, Journal of Sociology and Social Welfare, Social Service Review, Social Work Research, and Research on Social Work Practice) revealed only six social work articles using LC models (Bowen, Lee, & Weller, 2007; Keller, Cusick, & Courtney, 2007; Neely-Barnes, Marcenko, & Weber, 2008; Pears, Kim, & Fisher, 2008; Travis & Combs-Orme, 2007; Vaughn, Shook, & McMillen, 2008). This research note is intended to extend the knowledge of social work researchers about LC models by explaining the basic concepts of and assumptions underlying LC models, the distinction between latent class analysis (LCA) and latent profile analysis (LPA), exploratory and confirmatory analysis, methods for model estimation, tests of model fit, and statistical software packages that are available for conducting LC modeling. Examples are used throughout to illustrate these concepts. BASIC CONCEPTS AND ASSUMPTIONS A latent variable is one that cannot be directly observed. Because it cannot be directly observed, the relationship between a set of measured variables is used to characterize the unobserved (latent) one (McCutcheon, 1987a). Social work researchers have frequently used the concept of latent variables to estimate measurement models (Gillespie et al., 1995). In CFA, the relationships between measured indicators are used to estimate the "true" value of one or more latent construct(s) (McCutcheon, 1987a) and the measurement error (Kline, 2005). …