ABSTRACT
Generalized structured component analysis typically estimates parameters under the implicit assumption that all observations are drawn from a single homogenous population, unless it is known in advance that they belong to different groups. This leads to obtaining a single set of parameter estimates by pooling the data across observations. It is called an aggregate sample analysis. However, in some situations it may be more reasonable to assume that observations come from heterogeneous subgroups in the population, which display distinctive characteristics or response patterns, for example, different behaviors, choices, or preferences. This so-called group-or clusterlevel heterogeneity has been considered to be important substantively and studied actively in various disciplines. For example, in developmental psychology, two different longitudinal trends in the development of antisocial behavior, such as life-course persistent and adolescent-limited, were discussed (Moftt 1993). Moreover, six distinctive pathways in the evolution of adolescent delinquency over age have been identied, including rare offenders, moderate late peakers, high late peakers, decreasers, moderate-level chronics, and high-level chronics (Wiesner and Windle 2004). In marketing, consumer belief structures have been considered to diverge across market segments (Bagozzi 1982). Furthermore, from theoretical perspectives, in the situations where cluster-level heterogeneity is present, an aggregate sample analysis that disregards the heterogeneity is likely to result in biased parameter estimates (e.g., DeSarbo and Cron 1988; Jedidi, Jagpal, and DeSarbo 1997; Muthén 1989).
