In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

This article derives the power curves for a Wald test that can be applied to randomized response models when small prevalence rates must be assessed (e.g., detecting doping behavior among elite athletes). These curves enable the assessment of the statistical power that is associated with each model (e.g., Warner's model, crosswise model, unrelated…

Statistical analyses investigating latent structure can be divided into those that estimate structural model parameters and those that detect the structural model type. The most basic distinction among structure types is between categorical (discrete) and dimensional (continuous) models. It is a common, and potentially misleading, practice to…

The statistical analysis of mediation effects has become an indispensable tool for helping scientists investigate processes thought to be causal. Yet, in spite of many recent advances in the estimation and testing of mediation effects, little attention has been given to methods for communicating effect size and the practical importance of those…

When using existing technology, it can be hard or impossible to determine whether two structural equation models that are being considered may be nested. There is also no routine technology for evaluating whether two very different structural models may be equivalent. A simple nesting and equivalence testing (NET) procedure is proposed that uses…

The social relations model (SRM) is a conceptual, methodological, and analytical approach that is widely used to examine dyadic behaviors and interpersonal perception within groups. This article introduces a general and flexible approach to estimating the parameters of the SRM that is based on Bayesian methods using Markov chain Monte Carlo…

This article uses a general latent variable framework to study a series of models for nonignorable missingness due to dropout. Nonignorable missing data modeling acknowledges that missingness may depend not only on covariates and observed outcomes at previous time points as with the standard missing at random assumption, but also on latent…

Panel studies, in which the same subjects are repeatedly observed at multiple time points, are among the most popular longitudinal designs in psychology. Meanwhile, there exists a wide range of different methods to analyze such data, with autoregressive and cross-lagged models being 2 of the most well known representatives. Unfortunately, in these…

MacCallum, Browne, and Cai (2006) proposed a new framework for evaluation and power analysis of small differences between nested structural equation models (SEMs). In their framework, the null and alternative hypotheses for testing a small difference in fit and its related power analyses were defined by some chosen root-mean-square error of…

In the last 2 decades attention to causal (and formative) indicators has grown. Accompanying this growth has been the belief that one can classify indicators into 2 categories: effect (reflective) indicators and causal (formative) indicators. We argue that the dichotomous view is too simple. Instead, there are effect indicators and 3 types of…

I discuss the recommendations and cautions in Steinley and Brusco's (2011) article on the use of finite models to cluster a data set. In their article, much use is made of comparison with the "K"-means procedure. As noted by researchers for over 30 years, the "K"-means procedure can be viewed as a special case of finite mixture modeling in which…

This article provides a large-scale investigation into several of the properties of mixture-model clustering techniques (also referred to as latent class cluster analysis, latent profile analysis, model-based clustering, probabilistic clustering, Bayesian classification, unsupervised learning, and finite mixture models; see Vermunt & Magdison,…

Random coefficient and latent growth curve modeling are currently the dominant approaches to the analysis of longitudinal data in psychology. The application of these models to longitudinal data assumes that the data-generating mechanism behind the psychological process under investigation contains only a deterministic trend. However, if a…

Profile data abound in a broad range of research settings. Often it is of considerable theoretical importance to address specific structural questions with regard to the major pattern as included in such data. A key challenge in this regard pertains to identifying which type of interaction (double ordinal, mixed ordinal/disordinal, double…

McLachlan (2011) and Vermunt (2011) each provided thoughtful replies to our original article (Steinley & Brusco, 2011). This response serves to incorporate some of their comments while simultaneously clarifying our position. We argue that greater caution against overparamaterization must be taken when assuming that clusters are highly elliptical…