Generalized mixed spatiotemporal modeling with a continuous response and random effect via factor analysis

Natália Caroline Costa Oliveira () and Vinícius Diniz Mayrink ()
Additional contact information
Natália Caroline Costa Oliveira: Universidade Federal de Minas Gerais
Vinícius Diniz Mayrink: Universidade Federal de Minas Gerais

Statistical Methods & Applications, 2024, vol. 33, issue 3, No 1, 723-752

Abstract: Abstract This work focuses on Generalized Linear Mixed Models that incorporate spatiotemporal random effects structured via Factor Model (FM) with nonlinear interaction between latent factors. A central aspect is to model continuous responses from Normal, Gamma, and Beta distributions. Discrete cases (Bernoulli and Poisson) have been previously explored in the literature. Spatial dependence is established through Conditional Autoregressive (CAR) modeling for the columns of the loadings matrix. Temporal dependence is defined through an Autoregressive AR(1) process for the rows of the factor scores matrix. By incorporating the nonlinear interaction, we can capture more detailed associations between regions and factors. Regions are grouped based on the impact of the main factors or their interaction. It is important to address identification issues arising in the FM, and this study discusses strategies to handle this obstacle. To evaluate the performance of the models, a comprehensive simulation study, including a Monte Carlo scheme, is conducted. Lastly, a real application is presented using the Beta model to analyze a nationwide high school exam called ENEM, administered between 2015 and 2021 to students in Brazil. ENEM scores are accepted by many Brazilian universities for admission purposes. The real analysis aims to estimate and interpret the behavior of the factors and identify groups of municipalities that share similar associations with them.

Keywords: Regression; Interaction; MCMC; Multivariate analysis; Areal data (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10260-024-00755-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stmapp:v:33:y:2024:i:3:d:10.1007_s10260-024-00755-z

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10260/PS2

DOI: 10.1007/s10260-024-00755-z

Access Statistics for this article

Statistical Methods & Applications is currently edited by Tommaso Proietti

More articles in Statistical Methods & Applications from Springer, Società Italiana di Statistica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().