An Application of Multiple Linear Regression in
Determining Longitudinal Teacher Effectiveness

Robert L. Mendro , Heather R. Jordan, Elvia Gomez
Mark C. Anderson, Karen L. Bembry
Dallas Independent School District
Dallas, Texas

Abstract

This paper considers the use of multiple linear regression (MLR) techniques, particularly hierarchical linear modeling (HLM), in an application of determining longitudinal teacher effectiveness. The research literature on the use of regression techniques with student outcomes in identifying teacher effectiveness is inconsiderable. Identification of effective teachers through student outcomes is only being attempted in a relatively few number of sites. This study reports on a research project which used an application of multiple linear regression in determining teacher effectiveness over a three-year period and the design and implementation of a HLM model to analyze longitudinal teacher effectiveness data.

Introduction

The use of multiple linear regression models to determine school effectiveness has been recommended for several decades, although practical, unbiased applications of the same have not been implemented on more than trial bases before the 1990s (Webster, 1995; Webster and Mendro, 1997). Further, they have gone unused in the estimation of teacher effectiveness. Raudenbush and Bryk (1989) discuss the use of HLM in determining school and teacher effectiveness and discuss how several models might apply to the analysis of both. They discuss the problems which might be encountered in the application of both conventional and HLM models to the problem of identifying effective schools and make a number of recommendations for conducting these studies. Sanders (Sanders and Horn, 1993) has applied mixed models, based on those of Henderson (1984), a more general case of HLM analysis, to the identification of effective schools and teachers in Tennessee. However, due to the restrictions of working with a statewide database with limited variable sets, Sanders was unable to incorporate a number of the variables and concerns proposed by Raudenbush and Bryk in the implementation of these models. The intent of this paper was to conduct an actual analysis of teacher effectiveness in a large urban school district, using multiple linear regression, to examine the actual effects of using specific concomitant data elements in the model. Then, to determine the utility of these indices, the next step in the research was to analyze the longitudinal effects identified for teachers using an appropriate hierarchical linear model and determine whether the effectiveness estimates were related to real longitudinal effects as shown in student academic growth. This part of the study expanded greatly initial research reported by Sanders and Rivers (1996) both methodologically and in terms of generalizability.

The use of student data to assess teacher effectiveness in actual applications is a recent phenomenon (Sanders and Horn, 1993; Webster, Mendro, Orsak and Weerasinghe, 1997; Schalock, Schalock, and Girod, 1997; Kingston and Reidy, 1997). There has been considerable debate about the methodology and appropriateness of the using student data at all (Darling-Hammond, 1997; Glass, 1990; Raudenbush and Bryk, 1989; Millman, 1981; Webster, 1995; Webster and Mendro, 1997; Thum and Bryk, 1997). The successful application of unbiased methods of determining teacher effectiveness has been limited to a few locations. However, results from recent research at two of these locations related to long-term teacher effectiveness has been remarkably consistent (Sanders and Rivers, 1996; Jordan, Mendro, and Weerasinghe, 1997). Sanders and Rivers produced a seminal study on longitudinal teacher effectiveness. Jordan, et. al., extended the study across a wide range of grades. Using two different methods of determining teacher effectiveness, two different criterion measures, three different large urban populations, and two different analysis methods, the studies found highly similar distributions of teacher effectiveness. At the one grade the analyses had in common, distributions were nearly identical (Jordan, Mendro, and Weerasinghe, 1997).