The aim of this chapter is to provide an overview of recent developments in principal component analysis (PCA) methods when the data are incomplete. Missing data bring uncertainty into the analysis and their treatment requires statistical approaches that are tailored to cope with specific missing data processes (i.e., ignorable and nonignorable mechanisms).
We propose a method for estimating the size of a population in a multiple record system in the presence of missing data. The method is based on a latent class model where the parameters and the latent structure are estimated using a Gibbs sampler. The proposed approach is illustrated through the analysis of a data set already known in the literature, which consists of five registrations of neural tube defects.
The quantity and quality of administrative information available to National Statistical Institutes have been constantly increasing over the past several years. However, different sources of administrative data are not expected to each have the same population coverage, so that estimating the true population size from the collective set of data poses several methodological challenges that set the problem apart from a classical capture-recapture setting.
Quantile regression provides a detailed and robust picture of the distribution of a response variable, conditional on a set of observed covariates. Recently, it has be been extended to the analysis of longitudinal continuous outcomes using either time-constant or time-varying random parameters. However, in real-life data, we frequently observe both temporal shocks in the overall trend and individual-specific heterogeneity in model parameters. A benchmark dataset on HIV progression gives a clear example.
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