Search results for "P-spline"

Adaptive P-splines via L1-type penalty in generalized additive models

2022

A flexible approach to the crossing hazards problem

2010

We propose a simple and flexible framework for the crossing hazards problem. The method is not confined to two-sample problems, but may also work with continuous exposure variables whose effect changes its sign at some time-point of the observed follow-up time. Penalized partial likelihood estimation relies upon the assumption of a smooth hazard ratio via low-rank basis splines with a conventional difference penalty to ensure smoothness, and additional ad hoc penalties to obtain restricted estimates useful in the context of crossing hazards. The framework naturally also leads to a statistical test that has good power for revealing a global effect under several alternatives, including crossi…

Fitting generalized linear models with unspecified link function: A P-spline approach

2008

Generalized linear models (GLMs) outline a wide class of regression models where the effect of the explanatory variables on the mean of the response variable is modelled throughout the link function. The choice of the link function is typically overlooked in applications and the canonical link is commonly used. The estimation of GLMs with unspecified link function is discussed, where the linearity assumption between the link and the linear predictor is relaxed and the unspecified relationship is modelled flexibly by means of P-splines. An estimating algorithm is presented, alternating estimation of two working GLMs up to convergence. The method is applied to the analysis of quit behavior of…

Multiple smoothing parameters selection in additive regression quantiles

2021

We propose an iterative algorithm to select the smoothing parameters in additive quantile regression, wherein the functional forms of the covariate effects are unspecified and expressed via B-spline bases with difference penalties on the spline coefficients. The proposed algorithm relies on viewing the penalized coefficients as random effects from the symmetric Laplace distribution, and it turns out to be very efficient and particularly attractive with multiple smooth terms. Through simulations we compare our proposal with some alternative approaches, including the traditional ones based on minimization of the Schwarz Information Criterion. A real-data analysis is presented to illustrate t…

Long gaps in multivariate spatio-temporal data: an approach based on functional data analysis

2015

The main aim of this paper is to perform Functional Principal Component Analysis (FPCA) taking into account spatio-temporal correlation structures, in order to fill in missing values in spatio-temporal multivariate data set. A spatial and a spatio-temporal variant of the classical temporal FPCA is considered; in other words, FPCA is carried out after modeling data with respect to more than one dimension: space (long, lat) or space+time. Moreover, multidimensional FPCA is extended to multivariate context (more than one variable). Information on spatial or spatiotemporal structures are efficiently extracted by applying Generalized Additive Models (GAMs). Both simulation studies and some perfo…

Functional principal component analysis for multivariate multidimensional environmental data

2015

Data with spatio-temporal structure can arise in many contexts, therefore a considerable interest in modelling these data has been generated, but the complexity of spatio-temporal models, together with the size of the dataset, results in a challenging task. The modelization is even more complex in presence of multivariate data. Since some modelling problems are more natural to think through in functional terms, even if only a finite number of observations is available, treating the data as functional can be useful (Berrendero et al. in Comput Stat Data Anal 55:2619–2634, 2011). Although in Ramsay and Silverman (Functional data analysis, 2nd edn. Springer, New York, 2005) the case of multiva…

P-spline quantile regression: a new algorithm for smoothing parameter selection

Comparing Spatial and Spatio-temporal FPCA to Impute Large Continuous Gaps in Space

2018

Multivariate spatio-temporal data analysis methods usually assume fairly complete data, while a number of gaps often occur along time or in space. In air quality data long gaps may be due to instrument malfunctions; moreover, not all the pollutants of interest are measured in all the monitoring stations of a network. In literature, many statistical methods have been proposed for imputing short sequences of missing values, but most of them are not valid when the fraction of missing values is high. Furthermore, the limitation of the methods commonly used consists in exploiting temporal only, or spatial only, correlation of the data. The objective of this paper is to provide an approach based …

Analyzing Temperature Effects on Mortality Within theREnvironment: The Constrained Segmented Distributed Lag Parameterization

2010

Here we present and discuss the R package modTempEff including a set of functions aimed at modelling temperature effects on mortality with time series data. The functions fit a particular log linear model which allows to capture the two main features of mortality- temperature relationships: nonlinearity and distributed lag effect. Penalized splines and segmented regression constitute the core of the modelling framework. We briefly review the model and illustrate the functions throughout a simulated dataset.

Adaptive smoothing spline using non-convex penalties

2022

We propose a new adaptive penalty for smoothing via penalized splines. The new form of adaptive penalization is based on penalizing the differences of the coefficients of adjacent bases, using non-convex penalties. This makes possible to estimate curves with varying amounts of smoothness. Comparisons with respect to some competitors are presented.