Generalized mixed spatio-temporal modeling: Random effect via factor analysis with nonlinear interaction for cluster detection

Abstract

In this study, we develop factor analysis to explore areal data collected in space and time. The main goal is to incorporate the 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 is intended to improve cluster detection, since new types of groups can emerge as a combination of the main factors effects and the interaction effect. Our study is focused on the logistic and Poisson cases, but it can be extended to other generalized linear models that originated from distributions of the exponential family. A comprehensive simulation study is conducted to investigate the performance of the proposed approach. This work was motivated by the analysis of electrocardiogram (ECG) data related to patients affected by acute myocardial infarction (AMI). The data were collected between 2013 and 2016 through an ECG telediagnostic system covering the state of Minas Gerais in Brazil. The system is maintained by the Telehealth Center within the Hospital das Clínicas of the Federal University of Minas Gerais. The methodology proposed defining nonlinear interaction in the spatio-temporal setting and the analysis of the novel ECG data set are the central contributions of the paper.