Generalized Linear Array Models with Applications to Multidimensional Smoothing

Currie, Iain D.; Durbán, Maŕıa; Eilers, Paul H.C.

doi:10.1111/j.1467-9868.2006.00543.x

Cited by 165 publications

(206 citation statements)

References 26 publications

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“…by Currie et al (2006) can be used for the construction of the model matrices involved in the linear system (17), thus improving the speed of the estimation algorithm.…”

Section: Computational Aspectsmentioning

confidence: 99%

“…Following the paper by Currie et al (2006) we modeled the number of deaths with a 3D P-spline model (with age, year and month as covariates) with Poisson error and log-link.…”

Section: Respiratory Datamentioning

confidence: 99%

“…Since the number of deaths in 1972 was an extreme oulier, we removed this year from the analyses by giving it a weight of zero (see Currie et al 2006). To speed up the computational time, an initial estimate of β t , α t t was obtained by assuming log{(y + 0.5) /d} as an initial estimate of Xβ + Zα, where y and d are the vectors containing the number of deaths and the number of days per month respectively.…”

Section: Respiratory Datamentioning

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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“…by Currie et al (2006) can be used for the construction of the model matrices involved in the linear system (17), thus improving the speed of the estimation algorithm.…”

Section: Computational Aspectsmentioning

confidence: 99%

“…Following the paper by Currie et al (2006) we modeled the number of deaths with a 3D P-spline model (with age, year and month as covariates) with Poisson error and log-link.…”

Section: Respiratory Datamentioning

confidence: 99%

Section: Respiratory Datamentioning

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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“…Several 100 applications of the PCLM can be found in Eilers (2012). For illustration purposes, let us consider the number of deaths from respiratory disease of American population in January 1959, from ages 1 to 120 (see Currie et al, 2006, for more details about these data). Figure 1 shows the counts per age-at-death (vertical lines) and the smooth trend that follow these 105 counts (g = 1).…”

Section: The Pclm Approachmentioning

confidence: 99%

Penalized composite link models for aggregated spatial count data: A mixed model approach

et al. 2016

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Mortality data provide valuable information for the study of the spatial distribution of mortality risk, in disciplines such as spatial epidemiology and public health. However, they are frequently available in an aggregated form over irregular geographical units, hindering the visualization of the underlying mortality risk. Also, it can be of interest to obtain mortality risk estimates on a finer spatial resolution, such that they can be linked to potential risk factors that are usually measured in a different spatial resolution. In this paper, we propose the use of the penalized composite link model and its mixed model representation. This model considers the nature of mortality rates by incorporating the population size at the finest resolution, and allows the creation of mortality maps at a finer scale, thus reducing the visual bias resulting from the spatial aggregation within original units. We also extend the model by considering individual random effects at the aggregated scale, in order to take into account the overdispersion. We illustrate our novel proposal using two datasets: female deaths by lung cancer in Indiana, USA, and male lip cancer incidence in Scotland counties. We also compare the performance of our proposal with the area-to-point Poisson kriging approach.

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“…We present the array algorithm in a nutshell here; for a more detailed account one should consult Currie et al (2006) or Eilers et al (2006). Assume that the T × A matrix Z = BAB is a model for the expected values of the matrix Y of the same size.…”

Section: Efficient Computation Using Array Regressionmentioning

confidence: 99%

Bilinear modulation models for seasonal tables of counts

et al. 2009

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We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Twodimensional trends and modulation are estimated using a tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of a quasi-information criterion. Computationally efficient estimation is achieved using array regression techniques, avoiding excessively large matrices. The model is applied to female death rate in the US due to cerebrovascular diseases and respiratory diseases.

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Generalized Linear Array Models with Applications to Multidimensional Smoothing

Cited by 165 publications

References 26 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

Penalized composite link models for aggregated spatial count data: A mixed model approach

Bilinear modulation models for seasonal tables of counts

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