UCLA

Respondents in social and behavioral studies often belong to two or more non-nestedhigher-level groups of aggregation simultaneously, yielding the so-called cross-classified data structure. For example, in education, students belong to the schools they attend and the neighborhoods they live in, and there exists no exact nesting between the schools and neighborhoods. The cross-classified multilevel model (CCMM; Goldstein, 1994; Rasbash & Goldstein, 1994) was introduced as an extension of the standard multilevel model to accommodate the prevalent cross-classified data. The CCMM has been mainly applied in education to study the impacts of various contexts on certain outcomes, such as the influence of schools and neighborhoods on smoking behaviors among adolescents (Dunn, Richmond, Milliren, & Subramanian, 2015). However, applications of the CCMM in other fields are relatively scant and little-known. One potential reason for this lack of applications could be the limited availability of software programs that allow the easy fit of the CCMM.

To advocate more applications of the CCMM in a broader spectrum, in this article, wefirst show the connections between the CCMM and several widely used psychometric models, including the random effect item response theory (IRT) model (Van den Noortgate, De Boeck, & Meulders, 2003), the model for rater effects (e.g., Murphy & Beretvas, 2015), the multitrait-multimethod (MTMM) model (Campbell & Fiske, 1959), and the generalizability theory (G-theory) model (Shavelson & Webb, 1991). Then we review a few modern applications of the CCMM, such as its applications to meta-analyses and social network analysis (SNA).

To address the issue of software programs, we introduce a flexible and efficient Rpackage PLmixed (Jeon & Rockwood, 2017), and show how the above-mentioned related models and applications of the CCMM can be estimated with PLmixed and other existing R packages. Finally, we conclude that the CCMM would be applied more broadly with the support of computer software such as PLmixed.