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.

中文翻译：

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夏季学习损失的季节动态度量模型

在美国学校进行的研究显示，夏季学习成绩有所下降。如果这个暑假的损失没有纳入学生能力发展的模型中，则会违反假设，因为秋季分数将被高估而春季分数将被低估，这在评估老师或学校的效能时尤其成问题。夏季损失的统计方法仍相对欠发达，通常依赖于滞后时间模型或分段模型，这些模型通常会使均值结构饱和并成为经验均值的重新参数化。最近引入了复合多项式模型，并同时在测试分数中对年内和年间增长过程进行了建模。但是，这些模型使用时间的多项式函数运行，这可能具有有限的解释效用。在本文中，我们建议将季节性因素纳入动态测量模型（DMM）框架中。DMM重新设置了非线性增长模型，以直接估算可解释的数量（例如，学习能力是增长的上渐进线）。从针对寒冷气候物种体重提出的生态模型中借用，我们展示了DMM如何结合季节性来提供更多可解释的参数，并明确将夏季学习损失作为模型中的参数。