Prediction Using Many Samples with Models Possibly Containing Partially Shared Parameters

Abstract

We consider prediction based on a main model. When the main model shares partial parameters with several other helper models, we make use of the additional information. Specifically, we propose a Model Averaging Prediction (MAP) procedure that takes into account data related to the main model as well as data related to the helper models. We allow the data related to different models to follow different structures, as long as they share some common covariate effect. We show that when the main model is misspecified, MAP yields the optimal weights in terms of prediction. Further, if the main model is correctly specified, then MAP will automatically exclude all incorrect helper models asymptotically. Simulation studies are conducted to demonstrate the superior performance of MAP. We further implement MAP to analyze a dataset related to the probability of credit card default.

keyword:

• Model averaging
• Multiple samples
• Prediction
• Shared parameters

Supplementary Materials

In the supplementary materials, we first give proofs of theoretical results in Section S.1. Second, we provide discussion the variance of the averaging prediction in Section S.2. Third, in Section S.3, we provide details of simulation settings, additional simulation designs and results, comparison with pooled regression, illustration of weight consistency, as well as pre-analysis of real data.

Acknowledgments

The authors thank the Editor, AE, and reviewers for the comments and suggestions that improve the article.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Zhang’s work is partially supported by China NNSF grant (71925007, 72091212 and 12288201) and the CAS Project for Young Scientists in Basic Research (YSBR-008). MA’s Work is partially supported by grants from National Sciences Foundation and National Institute of Health.