This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

The linear logistic model with relaxed assumption is extended to designs with any number of time points or with different sets of items presented on different occasions, provided that one unidimensional subscale is available per latent trait. A sample application is presented. (SLD)

A crossed random effects model is presented that applies to data with a nested structure to provide maximum likelihood estimates through the EM algorithm. The procedure is illustrated in studies of neighborhood and school effects on educational attainment in Scotland and classroom effects on mathematics learning in the United States. (SLD)

Using longitudinal data on career paths of 3,941 special educators, maximum likelihood estimators are derived for the parameters of a discrete-time hazard model, and it is shown that the model can be fit using standard logistic regression software. Illustrative computer codes from the Statistical Analysis System (SAS) are offered. (SLD)