An imputation method for mixed-type data using nonlinear principal component analysis

Imputation of missing data has always represented a problem for researchers from every field. A biased imputation may strongly affect research findings, leading to wrong conclusions. Furthermore, an imputation method may be satisfactory with certain types of data, but unsatisfactory with others. Recently, an imputation method based on the recursive use of nonlinear principal component analysis has been proposed for the specific case of constructing a composite indicator from ordinal data. This method alternates the nonlinear principal component analysis with the nearest neighbour method in order to detect the most appropriate donor for the imputation of missing categories of incomplete objects. In this work, we present an extension of this imputation method to the general case of constructing a composite indicator from mixed-type data, that is, data including both quantitative and qualitative variables. The problem of the evaluation of the most suitable distance between objects to be used in the nearest neighbour method, together with the choice of the set of the most appropriate donors, is considered. The proposed procedure is implemented using the R software. A simulation study is also implemented to test the relative performance of the proposed method when compared with other methods used in similar situations