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…

Steinley (2007) provided a lower bound for the sum-of-squares error criterion function used in K-means clustering. In this article, on the basis of the lower bound, the authors propose a method to distinguish between 1 cluster (i.e., a single distribution) versus more than 1 cluster. Additionally, conditional on indicating there are multiple…

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…

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…

The call for researchers to report and interpret effect sizes and their corresponding confidence intervals has never been stronger. However, there is confusion in the literature on the definition of effect size, and consequently the term is used inconsistently. We propose a definition for effect size, discuss 3 facets of effect size (dimension,…

This article presents marginal structural models with inverse propensity weighting (IPW) for assessing mediation. Generally, individuals are not randomly assigned to levels of the mediator. Therefore, confounders of the mediator and outcome may exist that limit causal inferences, a goal of mediation analysis. Either regression adjustment or IPW…

In this article, I show how item response models can be used to capture multiple response processes in psychological applications. Intuitive and analytical responses, agree-disagree answers, response refusals, socially desirable responding, differential item functioning, and choices among multiple options are considered. In each of these cases, I…

Although randomized studies have high internal validity, generalizability of the estimated causal effect from randomized clinical trials to real-world clinical or educational practice may be limited. We consider the implication of randomized assignment to treatment, as compared with choice of preferred treatment as it occurs in real-world…

Racial/ethnic diversity has become an increasingly important variable in the social sciences. Research from multiple disciplines consistently demonstrates the tremendous impact of ethnic diversity on individuals and organizations. Investigators use a variety of measures, and their choices can affect the conclusions that can be drawn and limit the…

Muthen and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By…

The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main…

We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by…

The conventional fixed-effects (FE) and random-effects (RE) confidence intervals that are used to assess the average alpha reliability across multiple studies have serious limitations. The FE method, which is based on a constant coefficient model, assumes equal reliability coefficients across studies and breaks down under minor violations of this…

In addition to evaluating a structural equation model (SEM) as a whole, often the model parameters are of interest and confidence intervals for those parameters are formed. Given a model with a good overall fit, it is entirely possible for the targeted effects of interest to have very wide confidence intervals, thus giving little information about…