Model Selection for Nearly Replicated Data Based on All Possible Subsets

• Activity Number: 568
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Zugui Zhang*+
• Companies: Christiana Care Health System
• Keywords: Model Selection ; conceptual predictive statistic ; replicated data ; all possible subsets ; lack-of-fit test ; predictor variables

Abstract

The approach of conceptual predictive statistic (Cp) suggests an objective standard for the selection of an appropriate model from a potentially large class of candidate models, by examining any candidate model whether the values of Cp are around the number of parameters in the model. In this study, I proposed conceptual predictive statistics with replication using estimation of the true variance from replicated data. And then, I developed conceptual predictive statistics without replication using results from the lack-of-fit test procedures for regression. When similar settings of the predictor variables occur, near replication procedures are applied to obtain an estimate of variance, which is utilized in conceptual predictive statistics, Cp. A function of near replication procedures was used to group values of the response, based on similar settings of the predictor variables or close proximity in the space of predictor variables, to obtain an estimate of variance. The performances of the proposed conceptual predictive statistics with nearly replication in simulation studies, in which all possible subsets are considered, are more reliable and much better than the performances