Using Pooled Heteroskedastic Ordered Probit Models to Improve Small-Sample Estimates of Latent Test Score Distributions

Author/s: 

Benjamin R. Shear

,

sean f. reardon

Year of Publication: 
2019

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 number of ordered “proficiency” levels. HETOP models can be used to estimate means and standard deviations of the underlying (latent) test score distributions, but may yield biased or very imprecise estimates when group sample sizes are small. A simulation study demonstrates that pooled HETOP models can reduce the bias and sampling error of standard deviation estimates when group sample sizes are small. An analysis of real test score data suggests the pooled models are likely to improve estimates in applied contexts.

Primary Research Area:

APA Citation

Shear, B.R., & Reardon, S.F. (2019). Using Pooled Heteroskedastic Ordered Probit Models to Improve Small-Sample Estimates of Latent Test Score Distributions.