This article describes an extension to the use of heteroskedastic ordered probit (HETOP) models to estimate latent distributional parameters from grouped, ordered-categorical data by pooling across multiple waves of data. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in…

Measurement invariance is crucial for making valid comparisons across different groups (Kline, 2016; Vandenberg, 2002). To address the challenges associated with invariance testing such as large sample size requirements, the complexity of the model, etc., applied researchers have incorporated parcels. Parcels have been shown to alleviate skewness,…

This paper describes a method for pooling grouped, ordered-categorical data across multiple waves to improve small-sample heteroskedastic ordered probit (HETOP) estimates of latent distributional parameters. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in each of a small…

Linking score scales across different tests is considered speculative and fraught, even at the aggregate level. We introduce and illustrate validation methods for aggregate linkages, using the challenge of linking U.S. school district average test scores across states as a motivating example. We show that aggregate linkages can be validated both…

When there are no personal consequences associated with test performance for examinees, rapid guessing (RG) is a concern and can differ between subgroups. To date, the impact of differential RG on item-level measurement invariance has received minimal attention. To that end, a simulation study was conducted to examine the robustness of the…

Linking score scales across different tests is considered speculative and fraught, even at the aggregate level (Feuer et al., 1999; Thissen, 2007). We introduce and illustrate validation methods for aggregate linkages, using the challenge of linking U.S. school district average test scores across states as a motivating example. We show that…

Component Universe Score Profile analysis (CUSP) is introduced in this paper as a psychometric alternative to multivariate profile analysis. The theoretical foundations of CUSP analysis are reviewed, which include multivariate generalizability theory and constrained principal components analysis. Because CUSP is a combination of generalizability…

The National Education Longitudinal Study of 1988 (NELS:88) is a large-scale, national longitudinal study designed and sponsored by the National Center for Education Statistics (NCES), with support from other government agencies. Beginning in the spring of 1988 with a cohort of eighth graders (25,000) attending public and private schools across…