Summary Recent work by Reiss and Ogden provides a theoretical basis for sometimes preferring restricted maximum likelihood (REML) to generalized cross-validation (GCV) smoothing parameter selection in semiparametric regression. However, existing REML or marginal (ML) based methods linear models (GLMs) use iterative ML estimation of the parameters working approximations GLM. Such indirect schemes need not converge fail do so non-negligible proportion practical analyses. By contrast, very...

Summary I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized methods. The are constructed a simple transformation and truncation basis that arises from solution thin plate spline smoothing problem optimal in sense is designed to result minimum possible perturbation given dimension used construct smoother. By making use Lanczos iteration change computationally efficient. allow approximate models with large data sets, avoid...

Representation of generalized additive models (GAM's) using penalized regression splines allows GAM's to be employed in a straightforward manner methods. Not only is inference facilitated by this approach, but it also possible integrate model selection the form smoothing parameter into fitting computationally efficient well founded criteria such as cross-validation. The current and methods for are usually effective, do not provide level numerical stability which users linear packages,...

Summary Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants ridge regression. Selecting the correct weights for penalties is critical part using these in single-penalty case analyst has several well-founded techniques to choose from. However, many problems suggest formulation employing multiple penalties, here general methodology lacking. A wide family with can be fitted data by iterative solution...

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or mixed models). Such schemes fail to converge a non-negligible proportion of models, with failure being particularly frequent in the presence concurvity. If is performed by optimizing `whole model' criteria these problems disappear, but until now attempts do this have employed finite difference based optimization which are inefficient, and can...

A general method for constructing low-rank tensor product smooths use as components of generalized additive models or mixed is presented. penalized regression approach adopted in which several variables are constructed from each variable separately, these "marginal" being represented using a basis with an associated quadratic wiggliness penalty. The offer advantages: (i) they have one penalty per covariate and hence invariant to linear rescaling covariates, making them useful when there no...

This paper discusses a general framework for smoothing parameter estimation models with regular likelihoods constructed in terms of unknown smooth functions covariates. Gaussian random effects and parametric may also be present. By construction the method is numerically stable convergent, enables uncertainty to quantified. The latter us fix well known problem AIC such models. are represented by reduced rank spline like smoothers, associated quadratic penalties measuring function smoothness....

Journal Article On p-values for smooth components of an extended generalized additive model Get access Simon N. Wood Department Mathematical Sciences, University Bath, Bath BA2 7AY, U.K.s.wood@bath.ac.uk Search other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 100, Issue 1, March 2013, Pages 221–228, https://doi.org/10.1093/biomet/ass048 Published: 19 October 2012 history Received: 01 November 2011 Accepted: July

Summary We consider an application in electricity grid load prediction, where generalized additive models are appropriate, but the data set's size can make their use practically intractable with existing methods. therefore develop practical model fitting methods for large sets case which smooth terms represented by using penalized regression splines. The iterative update schemes to obtain factors of matrix while requiring only subblocks be computed at any one time. show that efficient...

Abstract. We study the coverage properties of Bayesian confidence intervals for smooth component functions generalized additive models (GAMs) represented using any penalized regression spline approach. The are usual generalization first proposed by Wahba and Silverman in 1983 1985, respectively, to GAM context. present simulation evidence showing these have close nominal ‘across‐the‐function’ frequentist probabilities, except when truth is a straight line/plane function. extend argument...

A framework is presented for generalized additive modelling under shape constraints on the component functions of linear predictor GAM. We represent constrained model components by mildly non-linear extensions P-splines. Models can contain multiple and unconstrained terms as well multi-dimensional smooths. The considered are sign first or/and second derivatives smooth terms. key advantage approach that it facilitates efficient estimation smoothing parameters an integral part estimation, via...

We propose a novel framework for fitting additive quantile regression models, which provides well calibrated inference about the conditional quantiles and fast automatic estimation of smoothing parameters, model structures as diverse those usable with distributional GAMs, while maintaining equivalent numerical efficiency stability. The proposed methods are at once statistically rigorous computationally efficient, because they based on general belief updating Bissiri et al. (2016) to loss...

This article provides a tutorial for analyzing pupillometric data. Pupil dilation has become increasingly popular in psychological and psycholinguistic research as measure to trace language processing. However, there is no general consensus about procedures analyze the data, with most studies extracted features from pupil data instead of trajectories directly. Recent have started apply nonlinear regression other methods directly, utilizing all available information continuously measured...

We develop scalable methods for fitting penalized regression spline based generalized additive models with of the order 104 coefficients to up 108 data. Computational feasibility rests on: (i) a new iteration scheme estimation model and smoothing parameters, avoiding poorly scaling matrix operations; (ii) parallelization iteration's pivoted block Cholesky basic (iii) marginal discretization covariates reduce memory footprint, efficient computing required crossproducts directly from discrete...

In the last two decades, growth of computational resources has made it possible to handle generalized additive models (GAMs) that formerly were too costly for serious applications. However, in model complexity not been matched by improved visualizations development and results presentation. Motivated an industrial application electricity load forecasting, we identify areas where lack modern visualization tools GAMs is particularly severe, address shortcomings existing methods proposing a set...

Generalized additive models are generalized linear in which the predictor includes a sum of smooth functions covariates, where shape is to be estimated. They have also been beyond original model setting distributions outside exponential family and situations multiple parameters response distribution may depend on sums covariates. The widely used computational inferential framework terms represented as latent Gaussian processes, splines, or random effects reviewed, paying particular attention...