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

Author

Listed:
  • Natália Caroline Costa Oliveira

    (Universidade Federal de Minas Gerais)

  • Vinícius Diniz Mayrink

    (Universidade Federal de Minas Gerais)

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.

Suggested Citation

  • Natália Caroline Costa Oliveira & Vinícius Diniz Mayrink, 2024. "Generalized mixed spatiotemporal modeling with a continuous response and random effect via factor analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 723-752, July.
    • Handle: RePEc:spr:stmapp:v:33:y:2024:i:3:d:10.1007_s10260-024-00755-z
    DOI: 10.1007/s10260-024-00755-z
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    References listed on IDEAS

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    1. Vinicius Mayrink & Dani Gamerman, 2009. "On computational aspects of Bayesian spatial models: influence of the neighboring structure in the efficiency of MCMC algorithms," Computational Statistics, Springer, vol. 24(4), pages 641-669, December.
    2. Vinícius Diniz Mayrink & Renato Valladares Panaro & Marcelo Azevedo Costa, 2021. "Structural equation modeling with time dependence: an application comparing Brazilian energy distributors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 353-383, June.
    3. Lopes, Hedibert Freitas & Gamerman, Dani & Salazar, Esther, 2011. "Generalized spatial dynamic factor models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1319-1330, March.
    4. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    5. Figueroa-Zúñiga, Jorge I. & Arellano-Valle, Reinaldo B. & Ferrari, Silvia L.P., 2013. "Mixed beta regression: A Bayesian perspective," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 137-147.
    6. G. O. Roberts & S. K. Sahu, 1997. "Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 291-317.
    7. Erick da Conceição Amorim & Vinícius Diniz Mayrink, 2020. "Clustering non-linear interactions in factor analysis," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 329-352, December.
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