Search results for "Generalized linear model"

Spatial Interaction between Neighbouring Counties: Cancer Mortality Data in Valencia (Spain)

1995

The statistical analysis of geographical mortality data has usually been approached via regression models that include appropriate covariates. These models assume stochastic independence of mortality counts for neighbouring sites, a questionable assumption that spatial automodels (Besag, 1974, Journal of the Royal Statistical Society, Series B 36, 192-236) make unnecessary. This paper presents the use of the autopoisson distribution in order to detect spatial interaction between neighbouring sites. If this interaction results in being nonsignificant, the auto-Poisson distribution reduces to a usual Poisson regression model, a particular case of generalized linear models (McCullagh and Nelde…

Influence of environmental factors on the spatial distribution and diversity of forest soil in Latvia

2012

This study was carried out to determine the spatial relationships between environmental factors (Quaternary deposits, topographical situation, land cover, forest site types, tree species, soil texture) and soil groups, and their prefix qualifiers (according to the international Food and Agricultural Organization soil classification system World Reference Base for Soil Resources [FAO WRB]). The results show that it is possible to establish relationships between the distribution of environmental factors and soil groups by applying the generalized linear models in data statistical analysis, using the R 2.11.1 software for processing data from 113 sampling plots throughout the forest terri…

On Rao Score and Pearson X2 Statistics in Generalized Linear Models

2005

The identity of the Rao score and PearsonX 2 statistics is well known in the areas where the latter was first introduced: goodness-of-fit in contingency tables and binary responses. We show in this paper that the same identity holds when the two statistics are used for testing goodness-of-fit of Generalized Linear Models. We also highlight the connections that exist between the two statistics when they are used for the comparison of nested models. Finally, we discuss some merits of these unifying results.

Data Analysis Using Hierarchical Generalized Linear Models with R

2019

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…

A note on adjusted responses, fitted values and residuals in Generalized Linear Models

2014

Adjusted responses, adjusted fitted values and adjusted residuals are known to play in Generalized Linear Models the role played in Linear Models by observations, fitted values and ordinary residuals. We think this parallelism, which was widely recognized and used in the early literature on Generalized Linear Models, has been somewhat overlooked in more recent presentations. We revise this parallelism, systematizing and proving some results that are either scattered or not satisfactorily spelled out in the literature. In particular, we formally derive the asymptotic dispersion matrix of the (scaled) adjusted residuals, by proving that in Generalized Linear Models the fitted values are asym…

dglars: An R Package to Estimate Sparse Generalized Linear Models

2014

dglars is a publicly available R package that implements the method proposed in Augugliaro, Mineo, and Wit (2013), developed to study the sparse structure of a generalized linear model. This method, called dgLARS, is based on a differential geometrical extension of the least angle regression method proposed in Efron, Hastie, Johnstone, and Tibshirani (2004). The core of the dglars package consists of two algorithms implemented in Fortran 90 to efficiently compute the solution curve: a predictor-corrector algorithm, proposed in Augugliaro et al. (2013), and a cyclic coordinate descent algorithm, proposed in Augugliaro, Mineo, and Wit (2012). The latter algorithm, as shown here, is significan…

Explaining German outward FDI in the EU: a reassessment using Bayesian model averaging and GLM estimators

2021

The last decades have seen an increasing interest in FDI and the process of production fragmentation. This has been particularly important for Germany as the core of the European Union (EU) production hub. This paper attempts to provide a deeper under standing of the drivers of German outward FDI in the EU for the period 1996–2012 by tackling the two main challenges faced in the modelization of FDI, namely the variable selection problem and the choice of the estimation method. For that purpose, we first extend previous BMA analysis developed by Camarero et al. (Econ Model 83:326–345, 2019) by including country-pair-fixed effects to select the appropriate set of variables. Second, we compare…

Change-points detection for variance piecewise constant models

2011

A new approach based on the fit of a generalized linear regression model is introduced for detecting change-points in the variance of heteroscedastic Gaussian variables, with piecewise constant variance function. This approach overcome some limitations of both exact and approximate well-known methods that are based on successive application of search and tend to overestimate the real number of changes in the variance of the series. The proposed method just requires the computation of a gamma GLM with log-link, resulting in a very efficient algorithm even with large sample size and many change points to be estimated.

Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter

2018

A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the $$\ell _1$$ or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this…