Search results for " Linear"
showing 10 items of 643 documents
An introduction to Bayesian reference analysis: inference on the ratio of multinomial parameters
1998
This paper offers an introduction to Bayesian reference analysis, often described as the more successful method to produce non-subjective, model-based, posterior distributions. The ideas are illustrated in detail with an interesting problem, the ratio of multinomial parameters, for which no model-based Bayesian analysis has been proposed. Signposts are provided to the huge related literature.
Robust estimation and regression with parametric quantile functions
2022
A new, broad family of quantile-based estimators is described, and theoretical and empirical evidence is provided for their robustness to outliers in the response. The proposed method can be used to estimate all types of parameters, including location, scale, rate and shape parameters, extremes, regression coefficients and hazard ratios, and can be extended to censored and truncated data. The described estimator can be utilized to construct robust versions of common parametric and semiparametric methods, such as linear (Normal) regression, generalized linear models, and proportional hazards models. A variety of significant results and applications is presented to show the flexibility of the…
Fast and universal estimation of latent variable models using extended variational approximations
2022
AbstractGeneralized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has gained considerable popularity in recent years, e.g., in the analysis of multivariate abundance data in ecology. One of the main features of GLLVMs is their capacity to handle a variety of responses types, such as (overdispersed) counts, binomial and (semi-)continuous responses, and proportions data. On the other hand, the inclusion of unobserved latent variables poses a major computational challenge, as the resulting marginal likelihood function involves an intractable integral for non-normally distributed responses. This has spurred research into a number of approx…
Identifying crime generators and spatially overlapping high-risk areas through a nonlinear model: A comparison between three cities of the Valencian …
2021
The behavior and spatial distribution of crime events can be explained through the characterization of an area in terms of its demography, socioeconomy, and built environment. In particular, recent studies on the incidence of crime in a city have focused on the identification of features of the built environment (specific places or facilities) that may increase crime risk within a certain radius. However, it is hard to identify environmental characteristics that consistently explain crime occurrence across cities and crime types. This article focuses on the assessment of the effect that certain types of places have on the incidence of property crime, robbery, and vandalism in three cities o…
Estimating the decomposition of predictive information in multivariate systems
2015
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of co…
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.
Analyzing environmental‐trait interactions in ecological communities with fourth‐corner latent variable models
2021
In ecological community studies it is often of interest to study the effect of species related trait variables on abundances or presence-absences. Specifically, the interest may lay in the interactions between environmental and trait variables. An increasingly popular approach for studying such interactions is to use the so-called fourth-corner model, which explicitly posits a regression model where the mean response of each species is a function of interactions between covariate and trait predictors (among other terms). On the other hand, many of the fourth-corner models currently applied in the literature are too simplistic to properly account for variation in environmental and trait resp…
A Software Tool for the Exponential Power Distribution: The normalp Package
2005
In this paper we present the normalp package, a package for the statistical environment R that has a set of tools for dealing with the exponential power distribution. In this package there are functions to compute the density function, the distribution function and the quantiles from an exponential power distribution and to generate pseudo-random numbers from the same distribution. Moreover, methods concerning the estimation of the distribution parameters are described and implemented. It is also possible to estimate linear regression models when we assume the random errors distributed according to an exponential power distribution. A set of functions is designed to perform simulation studi…
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.