Search results for "Uncertainty"

A network analysis of student mobility patterns from high school to master’s

2021

Human migration involves the movement of people from one place to another. An example of undirected migration is Italian student mobility where students move from the South to the Center-North. This kind of mobility has become of general interest, and this work explores student mobility from Sicily towards universities outside the island. The data used in this paper regards six cohorts of students, from 2008/09 to 2013/14. In particular, our goal is to study the 3-step migration path: the area of origin (Sicilian provinces), the regional university for the bachelor’s degree, and the regional university for the master’s. Our analysis is conducted by building a multipartite network with four …

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.

Global and multiple test procedures using ordered p-values—a review

2004

This paper reviews global and multiple tests for the combination ofn hypotheses using the orderedp-values of then individual tests. In 1987, Rohmel and Streitberg presented a general method to construct global level α tests based on orderedp-values when there exists no prior knowledge regarding the joint distribution of the corresponding test statistics. In the case of independent test statistics, construction of global tests is available by means of recursive formulae presented by Bicher (1989), Kornatz (1994) and Finner and Roters (1994). Multiple test procedures can be developed by applying the closed test principle using these global tests as building blocks. Liu (1996) proposed represe…

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

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…

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…

Differential geometric least angle regression: a differential geometric approach to sparse generalized linear models

2013

Summary Sparsity is an essential feature of many contemporary data problems. Remote sensing, various forms of automated screening and other high throughput measurement devices collect a large amount of information, typically about few independent statistical subjects or units. In certain cases it is reasonable to assume that the underlying process generating the data is itself sparse, in the sense that only a few of the measured variables are involved in the process. We propose an explicit method of monotonically decreasing sparsity for outcomes that can be modelled by an exponential family. In our approach we generalize the equiangular condition in a generalized linear model. Although the …