Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

Researchers are increasingly using observational or nonrandomized data to estimate causal treatment effects. Essential to the production of high-quality evidence is the ability to reduce or minimize the confounding that frequently occurs in observational studies. When using the potential outcome framework to define causal treatment effects, one…

The logistic person response function (PRF) models the probability of a correct response as a function of the item locations. Reise (2000) proposed to use the slope parameter of the logistic PRF as a person-fit measure. He reformulated the logistic PRF model as a multilevel logistic regression model and estimated the PRF parameters from this…

Ordered latent class analysis (OLCA) can be used to approximate unidimensional latent distributions. The main objective of this study is to evaluate the method of OLCA in detecting non-normality of an unobserved continuous variable (i.e., a common factor) used to explain the covariation between dichotomous item-level responses. Using simulation,…

The person-response function (PRF) relates the probability of an individual's correct answer to the difficulty of items measuring the same latent trait. Local deviations of the observed PRF from the expected PRF indicate person misfit. We discuss two new approaches to investigate person fit. The first approach uses kernel smoothing to estimate…