Value-added to what? The paradox of multidimensionality

Previous research has demonstrated conclusively that value-added inferences are sensitive to the choice of outcome measure within the domains of math and reading. This implies that math and reading are multidimensional domains. However, conventional factor analyses offer little support of this interpretation. In this study some conceptual distinctions are explored with respect to what it is that tests of math and reading uniquely measure. This is done by using longitudinal item response data from grades 5 to 9 to contrast undimensional item response theory model estimates of ability with the estimates from a bifactor item response theory model. These different variable estimates are used as competing outcomes measures for a school-level value-added model. It is shown that (1) the bifactor model produces domain-specific estimates that appear interpretable, and (2) that when a simple average is computed for value-added estimates in math and reading, this is equivalent to estimating value-added on a general factor common to math and reading tests.