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Open-ended, short-answer questions, referred to as constructed responses (CR), allow students to express knowledge and skills through their own words. While CRs can reduce the likelihood of guessin...

This article suggests two alternative statistical approaches for estimating student growth percentiles (SGP). The first is to estimate percentile ranks of current test scores conditional on past test scores directly, by modeling the conditional cumulative distribution functions, rather than indirectly through quantile regressions. This would remove the need for post hoc procedures required to ensure monotonicity of the estimated quantile functions, and for inversion of those functions to obtain SGP. We provide a brief empirical example demonstrating this approach and its potential benefits for handling discreteness of the observed test scores. The second suggestion is to estimate SGP directly from longitudinal item-level data, using multidimensional item response theory models, rather than from test scale scores. This leads to an isomorphism between using item-level data from one test to make inferences about latent student achievement, and using item-level data from multiple tests administered over time ...