## A sequential distance-based approach for imputing missing data: forward imputation.(English)Zbl 1414.62220

Summary: Missing data recurrently affect datasets in almost every field of quantitative research. The subject is vast and complex and has originated a literature rich in very different approaches to the problem. Within an exploratory framework, distance-based methods such as nearest-neighbour imputation (NNI), or procedures involving multivariate data analysis (MVDA) techniques seem to treat the problem properly. In NNI, the metric and the number of donors can be chosen at will. MVDA-based procedures expressly account for variable associations. The new approach proposed here, called Forward Imputation, ideally meets these features. It is designed as a sequential procedure that imputes missing data in a step-by-step process involving subsets of units according to their “completeness rate”. Two methods within this context are developed for the imputation of quantitative data. One applies NNI with the Mahalanobis distance, the other combines NNI and principal component analysis. Statistical properties of the two methods are discussed, and their performance is assessed, also in comparison with alternative imputation methods. To this purpose, a simulation study in the presence of different data patterns along with an application to real data are carried out, and practical hints for users are also provided.

### MSC:

 62H25 Factor analysis and principal components; correspondence analysis 62-07 Data analysis (statistics) (MSC2010) 62-04 Software, source code, etc. for problems pertaining to statistics 62H99 Multivariate analysis

### Software:

missForest; R; ElemStatLearn; missMDA; GenForImp; sn
Full Text:

### References:

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