A sequential distance-based approach for imputing missing data : the forward imputation

A recurring problem in multivariate data analysis (MVDA), potentially sparing no field of application, is the treatment of incomplete information. The subject is vast and complex, and has originated a literature rich of very different approaches. In an exploratory framework distance-based methods and procedures involving MVDA techniques can treat the problem properly. The nearest-neighbour imputation (NNI) method is distancebased in that detects sets of “donors” for incomplete units on the basis of their mutual nearness measured by a specific metric. MVDA techniques, such as PCA, through an iterative minimization of a loss-function, can recover values for incomplete units taking into account associations between variables. Both approaches have attractive features. In NNI, the metric and the number of donors can be chosen at will. The MVDA-based approach expressly accounts for variable associations. The approach here proposed, called forward imputation, ideally meets these features. It is developed as a distance-based approach that imputes missing values sequentially by alternating a MVDA technique and the NNI method. The MVDA technique could be any. Given the wide range of possibilities, attention here is confined to PCA. Comparisons with alternative imputation methods are then performed in presence of different data patterns