Predictive model in the presence of missing data: the centroid criterion for variable selection

Abstract

We have shown the almost sure convergence of the centroid criterion and simulations were performed to build its empirical distribution.We compared our method to a subjective deletion method, two simple imputation methods and to the multiple imputation method. ResultsThe hierarchical cluster analysis built 2 clusters of covariates and 6 remaining covariates. After the selection of the nearest covariate to the centroid of each cluster, we computed a stepwise linear regression model. The model was adequate (R 2 =90.02%) and the cross-validation showed low prediction errors (2.23 10 -3 ).The empirical distribution of the criterion provided empirical mean (31.91) and median (32.07) close to the theoretical value (32.03).The comparisons showed that deletion and simple imputation methods provided models of inferior quality than the multiple imputation method and the centroid method. ConclusionWhen the number of continuous covariates is greater than the sample size because of missing process, the usual procedures are biased. Our selection procedure based on the centroid criterion is a valid alternative to compose a set of predictors.