Missing values in multi-level simultaneous component analysis

Component analysis of data with missing values is often performed with algorithms of iterative imputation. However, this approach is prone to overfitting problems. As an alternative, Josse et al. (2009) proposed a regularized algorithm in the framework of Principal Component Analysis (PCA). Here we use a similar approach to deal with missing values in multi-level simultaneous component analysis (MLSCA), a method dedicated to explore multivariate multilevel data (e.g., individuals nested within groups). We discuss the properties of the regularized algorithm, the expected behavior under the missing (completely) at random (M(C)AR) mechanisms and possible dysmonotony problems. We explain the importance of separating the deviations due to sampling fluctuations and due to missing data. On the basis of a comparative extensive simulation study, we show that the regularized method generally performs well and clearly outperforms an EM-type of algorithm.