Statistics, Department of


First Advisor

Walt W. Stroup

Second Advisor

Erin E. Blankenship

Date of this Version



J.M. Garai. A Characterization of a Value Added Model and a New Multi-Stage Model For Estimating Teacher Effects Within Small School Systems. PhD thesis, University of Nebraska-Lincoln, Lincoln, NE, 2017.


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Statistics, Under the Supervision of Professors Walter W. Stroup and Erin E. Blankenship. Lincoln, Nebraska: August, 2017

Copyright (c) 2017 Julie M. Garai


At both the national and state level there is increasing pressure to develop metrics to determine if school systems are meeting educational objectives. All states mandate some form of assessment by standardized tests. One method currently used to model student test scores is Value Added Modeling (VAM), which models student scores as a product of classroom and school environments. One VAM approach is the Tennessee Value Added Assessment System (TVAAS) which models student gains from year to year. Teacher effects are included in this layered model, which estimates the teacher’s added value to a student score through best linear unbiased prediction.

Research using VAM typically occurs in school systems with a large number of students (e.g. New York City, Los Angeles, Chicago, etc.) or in statewide assessments that are combined across school districts (e.g. Tennessee). VAM performance in school systems with small numbers of students is unknown.

One common issue with estimation based on small samples is lack of precision. An area of statistics that has developed methodology for small sample sizes is small area estimation. One approach in this area is indirect estimation which links similar subjects together allowing the small groups to “borrow strength” from each other.

This dissertation introduces a multi-stage model that incorporates small area estimation techniques with the traditional TVAAS. The performance of both the multi-stage and TVAAS models are studied through data simulated for small school systems. The precision of predicted teacher value added scores is assessed for both modeling methods.

Adviser: Walter W. Stroup, Erin E. Blankenship