We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with embedded spatiotemporal dynamics to model georeferenced data observed in a functional domain. Thus, the regression coefficients are functions. The algorithm simultaneously selects the relevant spline basis functions and regressors that are used to model the fixed effects. In this way, it automatically shrinks to zero irrelevant parts of the functional coefficients or the entire function for an irrelevant regressor. The algorithm is based on an adaptive LASSO penalty function, with weights obtained by the unpenalised f-HDGM maximum likelihood estimators. The computational burden of maximisation is drastically reduced by a local quadratic approximation of the log-likelihood. A Monte Carlo simulation study provides insight in prediction ability and parameter estimate precision, considering increasing spatiotemporal dependence and cross-correlations among predictors. Further, the algorithm behaviour is investigated when modelling air quality functional data with several weather and land cover covariates. Within this application, we also explore some scalability properties of our algorithm. Both simulations and empirical results show that the prediction ability of the penalised estimates are equivalent to those provided by the maximum likelihood estimates. However, adopting the so-called one-standard-error rule, we obtain estimates closer to the real ones, as well as simpler and more interpretable models.

Maranzano, P., Otto, P., Fassò, A. (2023). Adaptive LASSO estimation for functional hidden dynamic geostatistical models. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, 37(9), 3615-3637 [10.1007/s00477-023-02466-5].

Adaptive LASSO estimation for functional hidden dynamic geostatistical models

Maranzano, Paolo
;
2023

Abstract

We propose a novel model selection algorithm based on a penalized maximum likelihood estimator (PMLE) for functional hidden dynamic geostatistical models (f-HDGM). These models employ a classic mixed-effect regression structure with embedded spatiotemporal dynamics to model georeferenced data observed in a functional domain. Thus, the regression coefficients are functions. The algorithm simultaneously selects the relevant spline basis functions and regressors that are used to model the fixed effects. In this way, it automatically shrinks to zero irrelevant parts of the functional coefficients or the entire function for an irrelevant regressor. The algorithm is based on an adaptive LASSO penalty function, with weights obtained by the unpenalised f-HDGM maximum likelihood estimators. The computational burden of maximisation is drastically reduced by a local quadratic approximation of the log-likelihood. A Monte Carlo simulation study provides insight in prediction ability and parameter estimate precision, considering increasing spatiotemporal dependence and cross-correlations among predictors. Further, the algorithm behaviour is investigated when modelling air quality functional data with several weather and land cover covariates. Within this application, we also explore some scalability properties of our algorithm. Both simulations and empirical results show that the prediction ability of the penalised estimates are equivalent to those provided by the maximum likelihood estimates. However, adopting the so-called one-standard-error rule, we obtain estimates closer to the real ones, as well as simpler and more interpretable models.
Articolo in rivista - Articolo scientifico
Adaptive LASSO; Air quality Lombardy; Functional HDGM; Geostatistical models; Model selection; Penalized maximum likelihood;
English
17-mag-2023
2023
37
9
3615
3637
open
Maranzano, P., Otto, P., Fassò, A. (2023). Adaptive LASSO estimation for functional hidden dynamic geostatistical models. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, 37(9), 3615-3637 [10.1007/s00477-023-02466-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/415677
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