Clustering Data with Non-Ignorable Missingness using Semi-Parametric Mixture Models
Résumé
We are concerned in clustering continuous data sets subject to non-ignorable missingness. We perform clustering with a specific semi-parametric mixture, under the assumption of conditional independence given the component. The mixture model is used for clustering and not for estimating the density of the full variables (observed and unobserved), thus we do not need other assumptions on the component distribution or to specify the missingness mechanism. Estimation is performed by maximizing an extension of smoothed likelihood allowing missingness. This optimization is achieved by a Majorization-Minorization algorithm. We illustrate the relevance of our approach by numerical experiments on simulated and benchmark data. Under mild assumptions, we show the identifiability of the model defining the distribution of the observed data and the monotonicity of the algorithm. We also propose an extension of this new method to the case of mixed-type data that we illustrate on a real data set. The proposed method is implemented in the R package MNARclust available on CRAN.
Domaines
Statistiques [math.ST]Origine | Fichiers produits par l'(les) auteur(s) |
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