Linear regression with bivariate response variable containing missing data. Strategies to increase prediction precision

Abstract

In this study we focus on prediction precision for linear regression with a bivariate response variable, where the response variable of primary interest contains missing data in the training data set. We derive and provide the maximum likelihood solution and a Bayesian method based on a conjugate prior distribution. In particular we evaluate strategies in how to “borrow prediction strength” from the full set of data to prediction associated with the missing data. Regularization of the maximum likelihood estimator is theoretically shown to be beneficial, and we derive methods for how to implement such regularization under frequentist and Bayesian inference, including available software as a R-package.

KEYWORDS:

• Bivariate linear regression
• Missing data
• Prediction error

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J07