|
Abstract:
|
The purpose of this paper is to develop and demonstrate the use of Bayesian dynamic borrowing as a means of systematically utilizing historical information with applications to large-scale assessments. The degree of borrowing depends on the heterogeneity among historical data and current data. A joint prior distribution over the historical and current data sets is specified with the degree of heterogeneity across the data sets controlled by the variance of the joint distribution. We demonstrate Bayesian dynamic borrowing in both single-level and multilevel models. We also discuss the power prior and compare its performance to Bayesian dynamic borrowing in single-level and multilevel models. Two case studies using data from the PISA 2018 reveal the utility of Bayesian dynamic borrowing in terms of predictive accuracy. Two simulation studies reveal the utility of Bayesian dynamic borrowing over simple pooling and power priors in cases where the historical data is heterogeneous compared to current data based on bias, MSE, total effective sample size and prediction. In cases of homogeneous historical data, Bayesian dynamic borrowing performs similarly to data pooling and power priors.
|
