One of the most vexing challenges facing developmental researchers today is the statistical modeling of two or more behaviors as they unfold jointly over time. Although quantitative methodologists have studied these issues for more than half a century, no widely agreed-upon principled strategy exists to empirically analyze codevelopmental…

Structured means analysis is a very useful approach for testing hypotheses about population means on latent constructs. In such models, a z test is most commonly used for testing the statistical significance of the relevant parameter estimates or of the differences between parameter estimates, where a z value is computed based on the asymptotic…

Longitudinal models provide researchers with a framework for investigating key aspects of change over time, but rarely is "time" itself modeled as a focal parameter of interest. Rather than treat time as purely an index of measurement occasions, the proposed Time to Criterion (T2C) growth model allows for modeling individual variability…

In this ITEMS module, we frame the topic of scale reliability within a "confirmatory factor analysis" and "structural equation modeling" (SEM) context and address some of the limitations of Cronbach's a. This modeling approach has two major advantages: (1) it allows researchers to make explicit the relation between their items…

Although differences in goodness-of-fit indices (?GOFs) have been advocated for assessing measurement invariance, studies that advanced recommended differential cutoffs for adjudicating invariance actually utilized a very limited range of values representing the quality of indicator variables (i.e., magnitude of loadings). Because quality of…

Latent interaction models have motivated a great deal of methodological research, mainly in the area of estimating such models. Product-indicator methods have been shown to be competitive with other methods of estimation in terms of parameter bias and standard error accuracy, and their continued popularity in empirical studies is due, in part, to…

We present types of constructs, individual- and cluster-level, and their confirmatory factor analytic validation models when data are from individuals nested within clusters. When a construct is theoretically individual level, spurious construct-irrelevant dependency in the data may appear to signal cluster-level dependency; in such cases,…

Although classical statistical techniques have been a valuable tool in second language (L2) research, L2 research questions have started to grow beyond those techniques' capabilities, and indeed are often limited by them. Questions about how complex constructs relate to each other or to constituent subskills, about longitudinal development in…

Growth mixture modeling has gained much attention in applied and methodological social science research recently, but the selection of the number of latent classes for such models remains a challenging issue, especially when the assumption of proper model specification is violated. The current simulation study compared the performance of a linear…

Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…

A two-step process is commonly used to evaluate data-model fit of latent variable path models, the first step addressing the measurement portion of the model and the second addressing the structural portion of the model. Unfortunately, even if the fit of the measurement portion of the model is perfect, the ability to assess the fit within the…

Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following…

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust…

Valuable methods have been developed for incorporating ordinal variables into structural equation models using a latent response variable formulation. However, some model parameters, such as the means and variances of latent factors, can be quite difficult to interpret because the latent response variables have an arbitrary metric. This limitation…

As Rupp and Templin (2008) stated directly, diagnostic classification methods "are confirmatory in nature." Methods, though, are neither inherently confirmatory nor exploratory. Diagnostic classification modeling, with its analytical and computational obstacles eventually yielding as a comprehensive and potent discipline emerges, will…