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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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6.1 LCA Model

Traditionally, cluster analysis has been used to uncover homogeneous groups based on a set of observed variables. Different clustering methods can be used to identify relatively homogeneous groups of cases based on selected observed variables (Hartigan, 1975; Everitt, 1980; Aldenderfer and Blashfield, 1984). However, a major criticism of cluster analysis is that there are no statistical indices and tests, based upon which the number of clusters can be determined (Bergman and Magnusson, 1997; Steinley, 2003). As such, determination of the number of clusters is often done by examining tabular or graphical output, and researcher's subjectivity may bias the choice of a solution (Aldenderfer and Blashfield, 1984).

LCA is a model-based approach to cluster individuals/cases into distinctive groups (i.e., latent classes) based on their responses to a set of observed categorical variables (McCutcheon, 1987; Clogg, 1995; Muthén, 2001, 2002; Magidson and Vermunt, 2004; Collins and Lanza, 2010). LCA was initially introduced by Lazarsfeld (1950), and then further developed by Lazarsfeld and Henry (1968) and Goodman (1974). Due to the increasing availability of tremendous computing power and access to computer software for mixture models, LCA has been increasingly applied to various fields of social science studies.

Similar to the traditional cluster analysis techniques, the objective of LCA is to identify unobserved subgroups comprised of similar individuals. Unlike traditional ...

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