A seasonal dynamic measurement model for summer learning loss

Research conducted in US schools shows summer learning loss in test scores. If this summer loss is not incorporated into models of student ability growth, assumptions will be violated because fall scores will be overestimated and spring scores will be underestimated, which can be particularly problematic when evaluating teacher or school effectiveness. Statistical methods for summer loss have remained relatively undeveloped and often rely on lagged-time or piecewise models, which commonly saturate the mean structure and become reparameterizations of empirical means. Compound polynomial models have recently been introduced and simultaneously model within-year and between-year growth processes in test scores. However, these models operate with polynomial functions of time, which can have limited interpretative utility. In this article, we propose incorporating seasonality within the dynamic measurement modelling (DMM) framework. DMM reparametrizes non-linear growth models to directly estimate interpretable quantities (e.g. learning capacity as an upper asymptote on growth). Borrowing from ecological models proposed for body mass of cold-climate species, we show how DMM can incorporate seasonality to provide more interpretable parameters as well as to explicitly include summer learning loss as a parameter in the model.