Structural equation modeling (SEM) applications routinely employ a trilogy of significance tests that includes the likelihood ratio test, Wald test, and score test or modification index. Researchers use these tests to assess global model fit, evaluate whether individual estimates differ from zero, and identify potential sources of local misfit,…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…

When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…

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…

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

Utilizing planned missing data (PMD) designs (ex. 3-form surveys) enables researchers to ask participants fewer questions during the data collection process. An important question, however, is just how few participants are needed to effectively employ planned missing data designs in research studies. This article explores this question by using…

Many psychological processes are characterized by recurrent shifts between distinct regimes or states. Examples that are considered in this paper are the switches between different states associated with premenstrual syndrome, hourly fluctuations in affect during a major depressive episode, and shifts between a "hot hand" and a…

Nearly all quantitative analyses in higher education draw from incomplete datasets-a common problem with no universal solution. In the first part of this paper, we explain why missing data matter and outline the advantages and disadvantages of six common methods for handling missing data. Next, we analyze real-world data from 5,905 students across…

Two methods, direct maximum likelihood (ML) and the expectation maximization (EM) algorithm, can be used to obtain ML parameter estimates for structural equation models with missing data (MD). Although the 2 methods frequently produce identical parameter estimates, it may be easier to satisfy missing at random assumptions using EM. However, no…

Often, all of the variables in a model are latent, random, or subject to measurement error, or there is not an obvious dependent variable. When any of these conditions exist, an appropriate method for estimating the linear relationships among the variables is Least Principal Components Analysis. Least Principal Components are robust, consistent,…