Search results for "Linear model"

Subject-specific odds ratios in binomial GLMMs with continuous response

2007

In a regression context, the dichotomization of a continuous outcome variable is often motivated by the need to express results in terms of the odds ratio, as a measure of association between the response and one or more risk factors. Starting from the recent work of Moser and Coombs (Odds ratios for a continuous outcome variable without dichotomizing, Statistics in Medicine, 2004, 23, 1843-1860), in this article we explore in a mixed model framework the possibility of obtaining odds ratio estimates from a regression linear model without the need of dichotomizing the response variable. It is shown that the odds ratio estimators derived from a linear mixed model outperform those from a binom…

Methods and Tools for Bayesian Variable Selection and Model Averaging in Normal Linear Regression

2018

In this paper, we briefly review the main methodological aspects concerned with the application of the Bayesian approach to model choice and model averaging in the context of variable selection in regression models. This includes prior elicitation, summaries of the posterior distribution and computational strategies. We then examine and compare various publicly available R-packages, summarizing and explaining the differences between packages and giving recommendations for applied users. We find that all packages reviewed (can) lead to very similar results, but there are potentially important differences in flexibility and efficiency of the packages.

Extending conventional priors for testing general hypotheses in linear models

2007

We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are 'proper objective priors' to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full-rank linear models. We extend these priors to deal with general hypotheses in general linear models, not necessarily of full rank. The resulting priors, which we call 'conventional priors', are expressed as a generalizat…

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…