G-factor models such as the bifactor model and the hierarchical G-factor model are increasingly applied in psychology. Many applications of these models have produced anomalous and unexpected results that are often not in line with the theoretical assumptions on which these applications are based. Examples of such anomalous results are vanishing specific factors and irregular loading patterns. In this article, the authors show that from the perspective of stochastic measurement theory anomalous results have to be expected when G-factor models are applied to a single-level (rather than a 2-level) sampling process. The authors argue that the application of the bifactor model and related models require a 2-level sampling process that is usually not present in empirical studies. We demonstrate how alternative models with a G-factor and specific factors can be derived that are more well-defined for the actual single-level sampling design that underlies most empirical studies. It is shown in detail how 2 alternative models, the bifactor-(S - 1) model and the bifactor-(S·I - 1) model, can be defined. The properties of these models are described and illustrated with an empirical example. Finally, further alternatives for analyzing multidimensional models are discussed. (PsycINFO Database Record

We present a revision of latent state-trait (LST-R) theory with new definitions of states and traits. This theory applies whenever we study the consistency of behavior, its variability, and its change over time. States and traits are defined in terms of probability theory. This allows for a seamless transition from theory to statistical modeling of empirical data. LST-R theory not only gives insights into the nature of latent variables but it also takes into account four fundamental facts: Observations are fallible, they never happen in a situational vacuum, they are always made using a specific method of observations, and there is no person without a past. Although the first fact necessitates considering measurement error, the second fact requires allowances for situational fluctuations. The third fact implies that, in the first place, states and traits are method specific. Furthermore, compared to the previous version of LST theory (see, e.g., Steyer et al. 1992 , 1999 ), our revision is based on the notion of a person-at-time-t. The new definitions in LST-R theory have far-reaching implications that not only concern the properties of states, traits, and the associated concepts of measurement errors and state residuals, but also are related to the analysis of states and traits in longitudinal observational and intervention studies.

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 used) should guide the choice of the statistical model to analyze the data. In this respect, the authors distinguish between (a) interchangeable methods, (b) structurally different methods, and (c) the combination of both kinds of methods. The authors present an appropriate model for each type of method. All models allow separating measurement error from trait influences and trait-specific method effects. With respect to interchangeable methods, a multilevel confirmatory factor model is presented. For structurally different methods, the correlated trait-correlated (method-1) model is recommended. Finally, the authors demonstrate how to appropriately analyze data from MTMM designs that simultaneously use interchangeable and structurally different methods. All models are applied to empirical data to illustrate their proper use. Some implications and guidelines for modeling MTMM data are discussed.

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