An Empirical Comparison of Statistical Models for Value-Added Assessment of School Performance

Abstract

Hierarchical Linear Models (HLM) have been used extensively for value-added analysis, adjusting for important student and school-level covariates such as socioeconomic status. A recently proposed alternative, the Layered Mixed Effects Model (LMEM) also analyzes learning gains, but ignores sociodemographic factors. Other features of LMEM, such as its ability to apportion credit for learning gains among multiple schools and its utilization of incomplete observations, make it appealing. A third model that is appealing due to its simplicity is the Simple Fixed Effects Models (SFEM). Statistical and computing specifications are given for each of these models. The models were fitted to obtain value-added measures of school performance by grade and subject area, using a common data set with two years of test scores. We investigate the practical impact of differences among these models by comparing their value-added measures. The value-added measures obtained from the SFEM were highly correlated with those from the LMEM. Thus, due to its simplicity, the SFEM is recommended over LMEM. Results of comparisons of SFEM with HLM were equivocal. Inclusion of student level variables such as minority status and poverty leads to results that differ from those of the SFEM. The question of whether to adjust for such variables is, perhaps, the most important issue faced when developing a school accountability system. Either inclusion or exclusion of them is likely to lead to a biased system. Which bias is most tolerable may depend on whether the system is to be a high-stakes one.

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