SIS 2023 - Statistical Learning, Sustainability and Impact Evaluation. Book of Short papers

We consider the case of a multivariate random vector that obeys a linear mixed model when the vector itself lies in a lower dimensional subspace. This situation suggests that this subspace can be modeled by the probabilistic (random-effects) principal components. By reason of this, the random vector follows at the same time two different models. We employ a linear predictor adjusted by the residual part of the probabilistic principal components that results not explained by the linear model. The new predictor can be considered as the vector of scores that comes from that principal components, enhanced by the linear mixed model. The application to the official Italian well-being data shows some features of the method.