Estimating and Comparing Growth Using Longitudinal Interim Achievement Data with Seasonal Trends

Abstract

Sources of longitudinal achievement data are increasing thanks partially to the expansion of available interim assessments. These tests are often used to monitor the progress of students, classrooms, and schools within and across school years. Yet, few statistical models equipped to approximate the distinctly seasonal patterns in the data exist, nor is there much guidance on how to choose among models. In this study, we present a general statistical model motivated by the seasonal character of interim achievement data and conduct analyses aimed at reducing barriers to the generation of empirical benchmarks for repeated measures achievement data. The model is designed to combine features from traditional polynomial models that estimate year-to-year growth but ignore within-year gains and losses with those from piecewise models, which directly estimate within-year gains/losses but do not include terms for year-to-year growth. Implications for research and policy are discussed.

Keywords:

• Interim achievement data
• effect sizes
• student achievement
• student growth
• growth modeling
• progress monitoring

Notes

1 Because we did not actually fit the piecewise model for our analyses, Figure 1 uses stylized versions of the piecewise model, but the TP and CP are based on actual model-based predictions of scores.

2 The actual CP we eventually describe is a blend of a quadratic cross-grade prediction for Fall status, a linear function for the within-grade linear slope term, and a constant within-grade quadratic term. Growth in Fall scores across the three grade levels is thus one of three sets of between-grade curve components in the CP. Summing them at each set of instructional weeks gives you the predicted score per the CP. Thus, the CP might better be thought of as not actually having a single, smooth Fall-to-Fall curve as depicted; rather, the components of the Fall-to-Fall growth model can be produced by combining constituent parts of the CP. We include the Fall-to-Fall curve mainly for didactic purposes.

3 We decided to use Fall-to-Fall growth rather than Spring-to-Spring because it simplifies the design matrices somewhat, but the supplemental materials show how to re-parameterize the model for Spring-to-Spring growth.