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…

Predictive mean matching (PMM) is a standard technique for the imputation of incomplete continuous data. PMM imputes an actual observed value, whose predicted value is among a set of k = 1 values (the so-called donor pool), which are closest to the one predicted for the missing case. PMM is usually better able to preserve the original distribution…

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model…

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

Regression methods can locate student test scores in a conditional distribution, given past scores. This article contrasts and clarifies two approaches to describing these locations in terms of readily interpretable percentile ranks or "conditional status percentile ranks." The first is Betebenner's quantile regression approach that results in…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

Develops and evaluates the linkage of the Armed Services Vocational Aptitude Battery to the mathematics scale of the National Assessment of Educational Progress. The accuracy of the proficiency distribution estimated from the projection was close to the accuracy of the distribution estimated from the large scale assessment. (SLD)