Penalized structural equation models (PSEM) is a new powerful estimation technique that can be used to tackle a variety of difficult structural estimation problems that can not be handled with previously developed methods. In this paper we describe the PSEM framework and illustrate the quality of the method with simulation studies.…

Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…

Measures initially designed to be single-trait often yield data that are compatible with both an essentially unidimensional factor-analysis (FA) solution and a correlated-factors solution. For these cases, this article proposes an approach aimed at providing information for deciding which of the two solutions is the most appropriate and useful.…

The purpose of this article is twofold. The first is to provide evaluative information on the recovery of model parameters and their standard errors for the two-parameter item response theory (IRT) model using different estimation methods by Mplus. The second is to provide easily accessible information for practitioners, instructors, and students…

This methodological paper examines current conceptions of reliability in chemistry education research (CER) and provides recommendations for moving beyond the current reliance on reporting coefficient alpha (a) as reliability evidence without regard to its appropriateness for the research context. To help foster a better understanding of…

Since Cronbach's (1951) elaboration of a from its introduction by Guttman (1945), this coefficient has become ubiquitous in characterizing assessment instruments in education, psychology, and other social sciences. Also ubiquitous are caveats on the calculation and interpretation of this coefficient. This article summarizes a recent contribution…

With the increasing refinement of language processing models and the new discoveries about which variables can modulate these processes, stimuli selection for experiments with a factorial design is becoming a tough task. Selecting sets of words that differ in one variable, while matching these same words into dozens of other confounding variables…

American Educational Research Association (AERA) standards stipulate that researchers show evidence of the internal structure of instruments. Confirmatory factor analysis (CFA) is one structural equation modeling procedure designed to assess construct validity of assessments that has broad applicability for counselors interested in instrument…

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…

Exploratory factor analysis (EFA) is a common technique utilized in the development of assessment instruments. The key question when performing this procedure is how to best estimate the number of factors to retain. This is especially important as under- or over-extraction may lead to erroneous conclusions. Although recent advancements have been…

A promising "underlying bivariate normal" approach was proposed by Jöreskog and Moustaki for use in the factor analysis of ordinal data. This was a limited information approach that involved the maximization of a composite likelihood function. Its advantage over full-information maximum likelihood was that very much less computation was…

When the factor analysis model holds, component loadings are linear combinations of factor loadings, and vice versa. This interrelation permits us to define new optimization criteria and estimation methods for exploratory factor analysis. Although this article is primarily conceptual in nature, an illustrative example and a small simulation show…

Factor analysis is a statistical method for describing the associations among sets of observed variables in terms of a small number of underlying continuous latent variables. Various authors have proposed multilevel extensions of the factor model for the analysis of data sets with a hierarchical structure. These Multilevel Factor Models (MFMs)…

Researchers must make numerous choices when conducting factor analyses, each of which can have significant ramifications on the model results. They must decide on an appropriate sample size to achieve accurate parameter estimates and adequate power, a factor model and estimation method, a method for determining the number of factors and evaluating…

In this article, we present a Bayes factor solution for inference in multiple regression. Bayes factors are principled measures of the relative evidence from data for various models or positions, including models that embed null hypotheses. In this regard, they may be used to state positive evidence for a lack of an effect, which is not possible…