  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 parameters of interest are functions across this
domain. The algorithm simultaneously selects the relevant spline basis
functions and regressors that are used to model the fixed-effects relationship
between the response variable and the covariates. In this way, it automatically
shrinks to zero irrelevant parts of the functional coefficients or the entire
effect of irrelevant regressors. The algorithm is based on iterative
optimisation and uses an adaptive least absolute shrinkage and selector
operator (LASSO) penalty function, wherein the weights are obtained by the
unpenalised f-HDGM maximum-likelihood estimators. The computational burden of
maximisation is drastically reduced by a local quadratic approximation of the
likelihood. Through a Monte Carlo simulation study, we analysed the performance
of the algorithm under different scenarios, including strong correlations among
the regressors. We showed that the penalised estimator outperformed the
unpenalised estimator in all the cases we considered. We applied the algorithm
to a real case study in which the recording of the hourly nitrogen dioxide
concentrations in the Lombardy region in Italy was modelled as a functional
process with several weather and land cover covariates.
