| The regression prediction method for inference from multivariate data with missing values is most useful when the covariates are predictive of the missing values and the probability of being missing. In these circumstances, predictions are particularly sensitive to model misspecification. One can make the model more robust and flexible using nonparametric regression. However, the high dimension of covariates leads to the "curse of dimensionality" problem. To address these problems, I propose a robust model-based method based on penalized splines (P-splines) of the response propensity scores. An estimator based on this method is called a propensity penalized spline prediction (PPSP) estimator. The key idea is to focus on correctly specifying the relationship between variables with missing values and propensity scores, since misspecification of this relationship leads to bias.; Valid estimates of variance of the PPSP estimator need to incorporate the added uncertainty due to nonresponse and propensity estimation. To account for the additional sources of variability, I develop methods based on the asymptotic variance, the bootstrap, and the multiple imputation.; The PPSP method is also extended to a general pattern of missing data by adapting and modifying Raghunathan et al.'s (2001) sequential regression multivariate imputation approach.; Simulation comparisons with other methods suggest that the proposed methods work well in a wide range of populations, with little loss of efficiency relative to parametric models when the latter are correct. |
