Suchergebnisse

The prediction of out-of-sample values is an interesting problem in any regression model. In the context of penalized smoothing using a mixed-model reparameterization, a general framework has been proposed for predicting in additive models but without interaction terms. The aim of this paper is to generalize this work, extending the methodology proposed in the multidimensional case, to models that include interaction terms, i.e., when prediction is carried out in a multidimensional setting. Our method fits the data, predicts new observations at the same time, and uses constraints to ensure a consistent fit or impose further restrictions on predictions. We have also developed this method for the so-called smooth-ANOVA model, which allows us to include interaction terms that can be decomposed into the sum of several smooth functions. We also develop this methodology for the so-called smooth-ANOVA models, which allow us to include interaction terms that can be decomposed as a sum of several smooth functions. To illustrate the method, two real data sets were used, one for predicting the mortality of the U.S. population in a logarithmic scale, and the other for predicting the aboveground biomass of Populus trees as a smooth function of height and diameter. We examine the performance of interaction and the smooth-ANOVA model through simulation studies. ; This research was funded in part by Ministerio de Ciencia e Innovación grant numbers PID2019-104901RB-I00. The third author gratefully acknowledges support by the Department of Education, Language Policy and Culture from the Basque Government (BERC 2018-2021 program), the Spanish Ministry of Economy and Competitiveness MINECO and FEDER: PID2020- 115882RB-I00/AEI/10.13039/501100011033 funded by Agencia Estatal de Investigación and acronym "S3M1P4R", and BCAM Severo Ochoa excellence accreditation SEV-2017-0718).

We present several methods for prediction of new observations in penalized regression using different methodologies, based on the methods proposed in: i) Currie et al. (2004), ii) Gilmour et al. (2004) and iii) Sacks et al. (1989). We extend the method introduced by Currie et al. (2004) to consider the prediction of new observations in the mixed model framework. In the context of penalties based on differences between adjacent coefficients (Eilers & Marx (1996)), the equivalence of the different methods is shown. We demonstrate several properties of the new coefficients in terms of the order of the penalty. We also introduce the concept memory of a P-spline, this new idea gives us information on how much past information we are using to predict. The methodology and the concept of memory of a P-spline are illustrated with three real data sets, two of them on the yearly mortality rates of Spanish men and other on rental prices. ; The first and the second authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness MTM2014-52184-P. The third author acknowledges financial support from the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.

Epidemiological data are frequently recorded at coarse spatio-temporal resolutions. The aggregation process is done for several reasons: to protect confidential patients' information, to compare with other datasets at a coarser resolution than the original, or to summarize data in a compact manner. However, we lose detailed patterns that follow the original data, which can be of interest for researchers and public health officials. In this paper we propose the use of the penalized composite link model (Eilers, 2007), together with its mixed model representation, to estimate the underlying trend behind grouped data at a finer spatio-temporal resolution. Also, this model allows the incorporation of fine-scale population into the estimation procedure. We assume the underlying trend is smooth across space and time. The mixed model representation enables the use of sophisticated algorithms such as the SAP algorithm of RodríguezÁlvarez et al. (2015) for fast estimation of the amount of smoothness. We illustrate our proposal with the analysis of data obtained during the largest outbreak of Q fever in the Netherlands. ; The first and the second authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness grants MTM2011-28285-C02-02 and MTM2014-52184-P. The third author acknowledges financial support from the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.

We propose a semiparametric nonlinear mixed-effects model (SNMM) using penalized splines to classify longitudinal data and improve the prediction of a binary outcome. The work is motivated by a study in which different hormone levels were measured during the early stages of pregnancy, and the challenge is using this information to predict normal versus abnormal pregnancy outcomes. The aim of this paper is to compare models and estimation strategies on the basis of alternative formulations of SNMMs depending on the characteristics of the data set under consideration. For our motivating example, we address the classification problem using a particular case of the SNMM in which the parameter space has a finite dimensional component (fixed effects and variance components) and an infinite dimensional component (unknown function) that need to be estimated. The nonparametric component of the model is estimated using penalized splines. For the parametric component, we compare the advantages of using random effects versus direct modeling of the correlation structure of the errors. Numerical studies show that our approach improves over other existing methods for the analysis of this type of data. Furthermore, the results obtained using our method support the idea that explicit modeling of the serial correlation of the error term improves the prediction accuracy with respect to a model with random effects, but independent errors. ; The first author was supported by Proyecto DI Regular 37.0/2016 VRIEA PUCV; FONDECYT grants 1120739, 1130233, and 1141256; Ministerio de Economía y Competitividad and FEDER, Spain, grants MTM2013-40941-P and MTM2016-74931-P; FONDAP grant 15130011; and grant 16-MATH-03 SIDRE from CONICYT MATH-AmSud Program. The third author was supported by FONDECYT grant 1141256; and grant 16-MATH-03 SIDRE from CONICYT MATH-AmSud Program. The fourth author was supported by the Basque Government through the BERC 360 2014-2017 and the Department of Education, Language Policy and Culture of the Basque Government IT-620-13 programs and Basque Government Industry Department under the ELKARTEK Program, by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and MTM2014-52184-P, and by the RISE Horizon 2020 European Project GEAGAM (644602). The fifth author was funded by grants MTM2014-56535-R and ECO2015-66593-P of the Ministerio de Economía y Competitividad, Spain. Contributions of the second, fourth, and fifth authors were partially supported by grants FONDECYT1120739 and 1141256 while visiting PUCV and CIMFAV-UV.

We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (J Am Stat Assoc 72(358):320-338, 1977)'s work, but it is able to deal with models that have a precision matrix for the random effect vector that is linear in the inverse of the variance parameters (i.e., the precision parameters). We call the method SOP (separation of overlapping precision matrices). SOP is based on applying the method of successive approximations to easy-to-compute estimate updates of the variance parameters. These estimate updates have an appealing form: they are the ratio of a (weighted) sum of squares to a quantity related to effective degrees of freedom. We provide the sufficient and necessary conditions for these estimates to be strictly positive. An important application field of SOP is penalised regression estimation of models where multiple quadratic penalties act on the same regression coefficients. We discuss in detail two of those models: penalised splines for locally adaptive smoothness and for hierarchical curve data. Several data examples in these settings are presented. ; This research was supported by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and through projects MTM2017-82379-R funded by (AEI/FEDER, UE) and acronym "AFTERAM", MTM2014-52184-P and MTM2014-55966-P. The MRI/DTI data were collected at Johns Hopkins University and the Kennedy-Krieger Institute. We are grateful to Pedro Caro and Iain Currie for useful discussions, to Martin Boer and Cajo ter Braak for the detailed reading of the paper and their many suggestions, and to Bas Engel for sharing with us his knowledge. We are also grateful to the two peer referees for their constructive comments of the paper.