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Journal of Probability and Statistics
Volume 2011 (2011), Article ID 290380, 20 pages
http://dx.doi.org/10.1155/2011/290380
Research Article

Missing-Values Adjustment for Mixed-Type Data

Dipartimento di Economia e Statistica, Università della Calabria, Via Pietro Bucci, Cubo 1C, 87036 Rende (Cosenza), Italy

Received 9 December 2010; Revised 25 May 2011; Accepted 1 July 2011

Academic Editor: Murray Clayton

Copyright © 2011 Agostino Tarsitano and Marianna Falcone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a new method of single imputation, reconstruction, and estimation of nonreported, incorrect, implausible, or excluded values in more than one field of the record. In particular, we will be concerned with data sets involving a mixture of numeric, ordinal, binary, and categorical variables. Our technique is a variation of the popular nearest neighbor hot deck imputation (NNHDI) where “nearest” is defined in terms of a global distance obtained as a convex combination of the distance matrices computed for the various types of variables. We address the problem of proper weighting of the partial distance matrices in order to reflect their significance, reliability, and statistical adequacy. Performance of several weighting schemes is compared under a variety of settings in coordination with imputation of the least power mean of the Box-Cox transformation applied to the values of the donors. Through analysis of simulated and actual data sets, we will show that this approach is appropriate. Our main contribution has been to demonstrate that mixed data may optimally be combined to allow the accurate reconstruction of missing values in the target variable even when some data are absent from the other fields of the record.