The Coalescence of Statistical Models

Several statistical models have been described so far as distinct families of approaches that makes the flexible modeling of multimethod data possible. Although the distinctness helps us understand the peculiarities of each method, it conceals the close relationships between the methods. For example, IRT models can also be formulated as multilevel models for categorical variables (Rijmen, Tuer-lincks, de Boeck, & Kuppens, 2003). Moreover, an increasing endeavor by psychometric researchers has been observed to integrate the advantages of several methodological approaches. For example,

Rost and Walter (chap. 18, this volume) show how Rasch models can be integrated with latent class models to detect population heterogeneity. Most recently, SEM have also been combined with latent class models to achieve structural equation mixture modeling (Bauer & Curran, 2004; Jedidi, Jagpal, & de Sarbo, 1997). Latent class models have been extended to multilevel models (Vermunt, 2003), and this is also true for SEM (Muthen, 1994) and models of IRT (Adams, Wilson, & Wu, 1997). These extended models offer enormous possibilities for formulating multimethod models. However, not everything that is possible is theoretically meaningful. Both the choice and the formulation of an appropriate model have to be guided by theoretical assumptions about the measurement process and the type of methods considered.

The following chapters demonstrate how the modeling frameworks of loglinear modeling (Nuss-

beck, chap. 17, this volume), IRT (Rost & Walter, chap. 18, this volume), generalizability theory and multilevel modeling (Hox & Maas, chap. 19, this volume), and SEM (Eid et al., chap. 20, this volume) can be applied to define models for different purposes of multimethod research. Finally, Khoo et al. (chap. 21, this volume) show how different approaches such as SEM and multilevel modeling can be used for analyzing longitudinal data.

As previously mentioned, the aim of these chapters is not to present a complete list of multimethod models that have been discussed in these domains. Rather, it is intention of this handbook to provide a comprehensible introduction to the possibilities of these approaches to multimethod research, thus enabling readers to find or create the model that is most appropriate for their research question.

Chapter 17

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