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Stochastic Complexity Based Estimation of Missing Elements in Questionnaire Data
 in Questionnaire Data”. the Annual American Educational Research Association Meeting, SIG Educational Statisticians
, 1998
"... this paper we study a new informationtheoretically justified approach to missing data estimation for multivariate categorical data. The approach discussed is a modelbased imputation procedure relative to a model class (i.e., a functional form for the probability distribution of the complete data m ..."
Abstract

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this paper we study a new informationtheoretically justified approach to missing data estimation for multivariate categorical data. The approach discussed is a modelbased imputation procedure relative to a model class (i.e., a functional form for the probability distribution of the complete data matrix), which in our case is the set of multinomial models with some independence assumptions. Based on the given model class assumption an informationtheoretic criterion can be derived to select between the different complete data matrices. Intuitively this general criterion, called stochastic complexity, represents the shortest code length needed for coding the complete data matrix relative to the model class chosen. Using this informationtheoretic criteria, the missing data problem is reduced to a search problem, i.e., finding the data completion with minimal stochastic complexity. In the experimental part of the paper we present empirical results of the approach using two real data sets, and compare these results to those achived by commonly used techniques such as case deletion and imputating sample averages. Introduction