Flexible smoothing with P-splines: a unified approach

Currie, Iain D.; Durbán, Maŕıa

doi:10.1191/1471082x02st039ob

Cited by 123 publications

(127 citation statements)

References 25 publications

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“…To estimate model (2) subject to the penalization defined in (3), we adopt here the equivalence between P-splines and generalized linear mixed models (GLMMs) (Lin and Zhang 1999, Currie and Durban 2002, Wand 2003. Under this approach, the design matrix B and the vector of regression coefficients θ in (2) are reformulated in such a way that…”

Section: Mixed Model Representationmentioning

confidence: 99%

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: Mixed Model Representationmentioning

confidence: 99%

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

et al. 2014

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“…For the other quantities, it is sufficient to use cubic B-splines (that is, bdeg 1 = bdeg 2 = 3) and quadratic penalties (q 1 = q 2 = 2). For a further discussion, see Eilers and Marx (1996), Currie and Durbán (2002) and Eilers et al (2015). Considering the regression basis in Eq.…”

Section: The Spatial Clmmmentioning

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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“…The parameters were estimated by non-linear seemingly unrelated regression, and weights we included in the model fitting to account for heteroscedasticity. We used a multidimensional P-spline for height and diameter (see Equation (5)) for each of the of the components of the models, and the weights used were the reciprocal of the smoothed squared residuals, as in Currie and Durbán (2002). In Table 3, we compare the models using the same measures of goodness of fit that appear in Parresol (2001): the Fit Index (pseudo R 2 ) and the Root Mean Square Error (RMSE).…”

Section: Modelmentioning

confidence: 99%

Smooth additive mixed models for predicting aboveground biomass

Sánchez-González¹,

Durbán

Lee

et al. 2016

JABES

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Aboveground biomass estimation in short-rotation forestry plantations is an essential step in the development of crop management strategies as well as allowing the economic viability of the crop to be determined prior to harvesting. Hence, it is important to develop new methodologies that improve the accuracy of predictions, using only a minimum set of easily obtainable information i.e. diameter and height. Many existing models base their predictions only on diameter (mainly due to the complexity of including further covariates), or rely on complicated equations to obtain biomass predictions. However, in tree species, it is important to include height when estimating aboveground biomass because this will vary from one genotype to another. This work proposes the use of a more flexible and easy to implement model for predicting aboveground biomass (stem, branches and total) as a smooth function of height and diameter using smooth additive mixed models which preserve the additive property necessary to model the relationship within wood fractions, and allows the inclusion of random e↵ects and interaction terms. The model is applied to the analysis of three trials carried out in Spain, where nine clones at three di↵erent sites are compared. Also, an analysis of slash pine data is carried out in order to compared with the approach proposed by Parresol (2001)

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Flexible smoothing with P-splines: a unified approach

Cited by 123 publications

References 25 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

Smooth additive mixed models for predicting aboveground biomass

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