Mallows model averaging with effective model size in fragmentary data prediction

Most existing model averaging methods consider fully observed data while fragmentary data, in which not all the covariate data are available for many subjects, becomes more and more popular nowadays with the increasing data sources in many areas such as economics, social sciences and medical studies. The main challenge of model averaging in fragmentary data is that the samples to fit candidate models are different to the sample used for weight selection, which introduces bias to the Mallows criterion in the classical Mallows Model Averaging (MMA). A novel Mallows model averaging method that utilizes the “effective model size” taking different samples into consideration is proposed and its asymptotic optimality is established. Empirical evidences from a simulation study and a real data analysis are presented. The proposed Effective Mallows Model Averaging (EMMA) method not only provides a novel solution to the fragmentary data prediction, but also sheds light on model selection when candidate models have different sample sizes, which has rarely been discussed in the literature.