Penalized regression with individual deviance effects

Perperoglou, Aris; Eilers, Paul H.C.

doi:10.1007/s00180-009-0180-x

Cited by 19 publications

(14 citation statements)

References 29 publications

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“…Although this is a large system of equations, it is well structured and should not cause any problems in programming and estimation. Moreover, Perperoglou and Eilers (2010) and Eilers et al (2006) suggest some computational tricks to make estimation even easier.…”

Section: Survival With Poisson Regressionmentioning

confidence: 99%

Fitting survival data with penalized Poisson regression

Perperoglou

2011

Stat Methods Appl

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Section: Survival With Poisson Regressionmentioning

confidence: 99%

Fitting survival data with penalized Poisson regression

Perperoglou

2011

Stat Methods Appl

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“…These different viewpoints allow for the use of an algorithm that was first suggested by [17] to estimate the variance of the random effect in a random effects model. Variations of the algorithm have also been published in [6,7].…”

Section: Penalty Optimizationmentioning

confidence: 99%

“…We view penalized splines as random effects whose variance depends on the penalty weight. This is not a completely new approach but has only been applied to one dimension before (see [5][6][7][8]). We will revise the algorithm and extend it to apply to two dimensional smoothing.…”

Section: Introductionmentioning

confidence: 99%

Two dimensional smoothing via an optimised Whittaker smoother

Zuliana

Perperoglou

2017

Big Data Anal

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Background: In many applications where moderate to large datasets are used, plotting relationships between pairs of variables can be problematic. A large number of observations will produce a scatter-plot which is difficult to investigate due to a high concentration of points on a simple graph. In this article we review the Whittaker smoother for enhancing scatter-plots and smoothing data in two dimensions. To optimise the behaviour of the smoother an algorithm is introduced, which is easy to programme and computationally efficient. Results: The methods are illustrated using a simple dataset and simulations in two dimensions. Additionally, a noisy mammography is analysed. When smoothing scatterplots the Whittaker smoother is a valuable tool that produces enhanced images that are not distorted by the large number of points. The methods is also useful for sharpening patterns or removing noise in distorted images. Conclusion:The Whittaker smoother can be a valuable tool in producing better visualisations of big data or filter distorted images. The suggested optimisation method is easy to programme and can be applied with low computational cost.

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“…As a solution for the overdispersion problem, we propose to introduce individual random effects for the logarithms of the expected values, one for each group count. This can be viewed as an adaptation of the PRIDE ('penalized regression with individual deviance ef-195 fects') approach given by Perperoglou and Eilers (2010) and Lee and Durbán (2009). Here, we develop this idea under the CLMM framework; thus we will refer to this approach throughout the paper as CLMM-P.…”

Section: Overdispersionmentioning

confidence: 99%

“…This extension allow us to analyse the distribution of mortality rates (disease incidence, fertility or others vital rates) in a finer spatial resolution than the original, under the modest assumption of smoothness. Moreover, it implies an improvement over previous related works ( Lee and Durbán, 2009;Perperoglou and Eilers, 2010) in terms of the visualization of the underlying mortality 125 risk (the previous cited works only give mortality risk estimates for each unit, while our approach provides a mortality risk surface across coarse units) and the incorporation of fine-scale information in the mortality risk estimation. We also choose to represent the PCLM as a mixed model.…”

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confidence: 92%

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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Penalized regression with individual deviance effects

Cited by 19 publications

References 29 publications

Fitting survival data with penalized Poisson regression

Fitting survival data with penalized Poisson regression

Two dimensional smoothing via an optimised Whittaker smoother

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

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