<i>P</i>-spline ANOVA-type interaction models for spatio-temporal smoothing

Lee, Dae‐Jin; Durbán, Maŕıa

doi:10.1177/1471082x1001100104

Cited by 83 publications

(114 citation statements)

References 29 publications

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“…For the sake of clarity, we focused here in a GAMM specified in terms of univariate effects jointly with a 2D interaction surface. Nevertheless, the mschall algorithm can be also easily extended to deal with factor-by-surface interactions as well as with ANOVA-type interactions (Lee and Durbán 2011).…”

Section: Discussionmentioning

confidence: 99%

“…Specifically, the only requirement will be to specify the form of the matrix Λ involved in the expression of the estimate of each variance component (see (6)). This feature makes, for instance, straightforward the extension of the m-schall algorithm to deal with the ANOVA-type decomposition presented in Lee and Durbán (2011). We therefore focus here on presenting more complex extensions.…”

Section: Some Extensionsmentioning

confidence: 99%

“…The random effects have covariance matrix G, which depends on two variance components τ 2 1 and τ 2 2 . To obtain the mixed model representation (4), we follow the proposal by Lee (2010), Lee and Durbán (2011). Their approach is based on the Singular Value Decomposition…”

Section: Mixed Model Representationmentioning

confidence: 99%

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Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

et al. 2014

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Abstract:A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods (PQL), closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that can considerably reduce the computational load. The proposed algorithm can be seen as a generalization of the algorithm by Schall (1991) -for variance components estimation -to deal with non-standard structures of the covariance matrix of the random effects. The practical performance of the proposed computational algorithm is evaluated by means of simulations, and comparisons with alternative methods are made on the basis of the mean square error criterion and the computing time. Finally, we illustrate our proposal with the analysis of two real datasets: a two dimensional example of historical records of monthly precipitation data in USA and a three dimensional one of mortality data from respiratory disease according to the age at death, the year of death and the month of death.Keywords: Smoothing; P-splines; Tensor product; Anisotropic penalty; Mixed Models. July 29, 2013Abstract A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods (PQL), closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that can considerably reduce the computational load. The proposed algorithm can be seen as a generalization of the algorithm by Schall (1991) -for variance components estimation -to deal with non-standard structures of the covariance matrix of the random effects. The practical performance of the proposed computational algorithm is evaluated by means of simulations, and comparisons with alternative methods are made on the basis of the mean square error criterion and the computing time. Finally, we illustrate our proposal with the analysis of two real datasets: a two dimensional example of historical records of monthly precipitation data in USA and a three dimensional one of mortality data from respiratory disease according to the age at death, the year of death and the month of death.1

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Section: Discussionmentioning

confidence: 99%

Section: Some Extensionsmentioning

confidence: 99%

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Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

et al. 2014

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“…The extension of such methods in a Bayesian framework has been proposed by [21], using a random walk prior on the spline coefficients to impose smoothness and a Gamma prior on the precision of the random walk. P-splines have been used as a general tool to model smooth surfaces in several contexts involving spatial data [22][23][24][25][26] but to the best of our knowledge they have not been used for modelling point process data so far. By means of Bayesian P-splines, the spatial effect in model (2) is modelled as:…”

Section: Managing the Spatial Effect Via Bayesian P-splinesmentioning

confidence: 99%

Bayesian P-splines and advanced computing in R for a changepoint analysis on spatio-temporal point processes

Altieri

Greco

Illian

et al. 2016

Journal of Statistical Computation and Simulation

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. (2016) Bayesian P-splines and advanced computing in R for a changepoint analysis on spatio-temporal point processes. Journal of Statistical Computation and Simulation, 86(13), pp. 2531-2545. (doi:10.1080/00949655.2016 This is the author's final accepted version.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.http://eprints.gla.ac.uk/116178/ This work presents advanced computational aspects of a new method for changepoint detection on spatio-temporal point process data. We summarise the methodology, based on building a Bayesian hierarchical model for the data and declaring prior conjectures on the number and positions of the changepoints, and show how to take decisions regarding the acceptance of potential changepoints. The focus of this work is about choosing an approach that detects the correct changepoint and delivers smooth reliable estimates in a feasible computational time; we propose Bayesian P-splines as a suitable tool for managing spatial variation, both under a computational and a model fitting performance perspective. The main computational challenges are outlined and a solution involving parallel computing in R is proposed and tested on a simulation study. An application is also presented on a dataset of seismic events in Italy over the last 20 years.

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“…With this kind of data it is possible to estimate not only spatial trends, but also spatio-temporal trends in a nonparametric way (Lee and Durbán 2011), so as to capture region-specific nonlinear time trends net of the effect of spatial autocorrelation. In other words, this approach allows to answer questions like: How do unobserved timerelated factors (i.e.…”

Section: Introductionmentioning

confidence: 99%

Advances in Spatial Econometrics: Parametric vs. Semiparametric Spatial Autoregressive Models

Basile

Mı́nguez

2017

Springer Proceedings in Complexity

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Abstract. In this Chapter we provide a critical review of parametric and semiparametric spatial econometric approaches. We focus on the capability of each class of models to fit the main features of spatial data (such as strong and weak cross-sectional dependence, spatial heterogeneity, nonlinearities, and time persistence), leaving aside the technicalities related to the estimation methods. We also provide a brief discussion of the existent software developed to estimate most of the econometric models exposed in this Chapter.

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P-spline ANOVA-type interaction models for spatio-temporal smoothing

Cited by 83 publications

References 29 publications

Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

Bayesian P-splines and advanced computing in R for a changepoint analysis on spatio-temporal point processes

Advances in Spatial Econometrics: Parametric vs. Semiparametric Spatial Autoregressive Models

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