Scale validation is vital to psychological research because it ensures that scores from measurement scales represent the intended construct. Factor analysis fit indices are commonly used to provide quantitative evidence that a proposed factor structure is plausible. However, there is mismatch between guidelines for evaluating fit of factor models…

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational…

In educational and psychological research, we are often interested in discrete latent states of individuals responding to an assessment (e.g., proficiency or non-proficiency on educational standards, the presence or absence of a psychological disorder). Diagnostic classification models (DCMs; also called cognitive diagnostic models [CDMs]) are a…

Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or…