We offer a new conceptualization and measurement models for constructs at the group-level of analysis in small group research. The conceptualization starts with classical notions of group behavior proposed by Tönnies, Simmel, and Weber and then draws upon plural subject theory by philosophers Gilbert and Tuomela to frame a new perspective…

Measurement invariance (MI) is a property of measurement that is often implicitly assumed, but in many cases, not tested. When the assumption of MI is tested, it generally involves determining if the measurement holds longitudinally or cross-culturally. A growing literature shows that other groupings can, and should, be considered as well.…

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

The authors show how structural equation modeling can be applied to analyze change in longitudinal multitrait-multimethod (MTMM) studies. For this purpose, an extension of latent difference models (McArdle, 1988; Steyer, Eid, & Schwenkmezger, 1997) to multiple constructs and multiple methods is presented. The model allows investigators to separate…

The question as to which structural equation model should be selected when multitrait-multimethod (MTMM) data are analyzed is of interest to many researchers. In the past, attempts to find a well-fitting model have often been data-driven and highly arbitrary. In the present article, the authors argue that the measurement design (type of methods…

An extension of latent state-trait (LST) theory to hierarchical LST models is presented. In hierarchical LST models, the covariances between 2 or more latent traits are explained by a general 3rd-order factor, and the covariances between latent state residuals pertaining to different traits measured on the same measurement occasion are explained…

A confirmatory factor analysis of 61 published data sets from multitrait-multimethod studies provides estimates of the trait, method, and error variances of measures used in the social and behavioral sciences. Traits accounted for less than 50 percent of the variance among construct measures overall. Implications for testing are discussed. (SLD)

The advantages of applying confirmatory factor analysis (CFA) to multitrait-multimethod (MTMM) data are widely recognized. However, because CFA as traditionally applied to MTMM data incorporates single indicators of each scale (i.e., each trait/method combination), important weaknesses are the failure to: (1) correct appropriately for measurement…