Matrizes de vizinhança não espaciais em modelos espaço-temporais da classe STARMA: um estudo de caso aplicado a dados epidemiológicos

Abstract

In this work, the feasibility of using neighborhood matrices (W) based on non-spatial criteria in space-time models of the autoregressive and moving average class (STARMA) was studied. The data used consist of a space-time series composed of nine temporal series measuring the incidence of tuberculosis, observed monthly between 2002 and 2022, in the cities of Belo Horizonte, Betim, Contagem, Ibirité, Nova Lima, Ribeirão das Neves, Sabará, Santa Luzia, and Vespasiano in the state of Minas Gerais, Brazil. To evaluate the impact of the W matrix on model fitting, the contiguity matrix and five other matrices constructed by non-spatial criteria were used, aiming to describe not only interactions between areas but also within areas. These matrices were generated by a Municipal Socioeconomic Index (IMS) derived from linear combinations of two socioeconomic variables: the most recent municipal Human Development Index (HDI) and the average of the 2021 to 2023 assessments from Previne Brasil, a program that evaluates the quality of service provided by municipal Primary Health Care (PHC). Six STARMA models were fitted with the defined neighborhood matrices. Model fitting was carried out in three stages: identification, estimation, and diagnosis. The Bayesian Information Criterion (BIC) was used for model selection. It was concluded that the best model was obtained with a non-spatial W, strongly correlated with the quality of municipal primary health care. In predictions, the mean absolute percentage error (MAPE) was used as a criterion, observing that the model fitted with the contiguity matrix had approximately 5% less error compared to the model that best fitted the data. This work also demonstrated the need for further studies regarding the use of non-spatial matrices to address questions such as: are non-spatial W matrices relevant only for STARMA-class space-time models? Are the models to which this type of matrix is suitable suitable for all types of data? What is the optimal way to create the index that optimizes the construction of the non-spatial W matrix?