Model Adequacy Checking for Applying Harmonic Regression to Assessment Quality Control

In recent years, harmonic regression models have been applied to implement quality control for educational assessment data consisting of multiple administrations and displaying seasonality. As with other types of regression models, it is imperative that model adequacy checking and model fit be appropriately conducted. However, there has been no literature on how to perform a comprehensive model adequacy evaluation when applying harmonic regression models to sequential data with seasonality in the educational assessment field. This paper is intended to fill this gap with an illustration of real data from an English language assessment. Two types of cross-validation, leave-one-out and out-of-sample, were designed to measure prediction errors and check model validation. Three types of R-squared (, , and ) and various residual diagnostics were applied to check model adequacy and model fitting.