Generalized mixed spatio-temporal modeling: random effect via factor analysis with nonlinear interaction

This study uses factor analysis to explore areal data collected in space and time. The main goal is to incorporate a framework with nonlinear interactions to handle a spatio-temporal random effect in the structure of a mixed generalized linear regression. The spatial dependence between regions is established through the CAR model specified for each column of the loadings matrix. Temporal dependence is considered to associate the columns of the factor scores matrix. The presence of nonlinear interactions intends to expand cluster configurations since new types of groups can emerge as a combination of the effects of the main factors and the interaction. The logistic and Poisson cases are the main focus, but the study can be extended to other generalized linear models originated from the exponential family. A simulation study investigates the performance of the proposed approach. This work was motivated by the analysis of electrocardiogram data related to patients affected by acute myocardial infarction. The data were collected through a telediagnostic system, covering the Brazilian state of Minas Gerais, and maintained by the Telehealth Center (Hospital das Clínicas, UFMG). This is a joint work with Milton P. S. Ferreira (Hence Analytics) and Antônio L. P. Ribeiro (Faculdade de Medicina, UFMG).