In this article, we consider the quasi-likelihood equation Sigma(n)(i=1) X-i(y(i) - mu(X-i'beta)) = 0 for generalized linear models (GLMs). Under some mild conditions, including the convergent system {e(i) = y(i) ...
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In this article, we consider the quasi-likelihood equation Sigma(n)(i=1) X-i(y(i) - mu(X-i'beta)) = 0 for generalized linear models (GLMs). Under some mild conditions, including the convergent system {e(i) = y(i) - mu(X-i'beta(0)), i >= 1} which is defined by Lai et al. (1979), we obtain the asymptotic existence of the solution (beta) over cap (n) to the above equation and show that (beta) over cap (n) - beta(0) = O((lambda) over bar (1/2)(n) (log (lambda) over bar (n))(delta/2)/(lambda) under bar (n)) a.s., where beta(0) is the true value of parameter beta and (lambda) under bar (n)((lambda) over bar (n)) denotes the smallest (largest) eigenvalue of Sigma(n)(i=1) XiXt' satisfying ((lambda) over bar (1/2)(n) (log (lambda) over bar (n))(delta/2))/(lambda) under bar (n) -> 0 as n -> infinity for given delta > 1. We also present the asymptotic normality of (beta) over cap (n) for univariate GLMs, based on which "studentized" large sample confidence intervals for beta(0) are constructed. Simulation results and related remarks are given.
Fire-related heat and endozoochory by elephants have independently been found to be important for savanna plant seed germination, yet there is little information on how heat affects germination of elephant-dispersed s...
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Fire-related heat and endozoochory by elephants have independently been found to be important for savanna plant seed germination, yet there is little information on how heat affects germination of elephant-dispersed seeds. We measured the germination behavior (time to germination and proportion of seeds germinating) of 11 species of seeds extracted from African savanna elephant dung and subjected them to various intensities of heat as a proxy for fire exposure. The effects of heat were inconsistent and varied significantly by species, with some species having increased time to germination in response to heat and others having reduced time to germination. More studies are needed to expand the number of seed species examined and tease apart the interaction between elephant-mediated endozoochory and fire.
The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is perfor...
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The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse generalized linear models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance of the modified versions of the BIC is illustrated with an extensive simulation study and a real data analysis. Also, simplified versions of the modified BIC, based on least squares regression, are investigated. (C) 2011 Elsevier B.V. All rights reserved.
Both social structural factors and direct sensory experiences can contribute to the development of environmental perceptions and concerns. We use two separate surveys of Utah adults to explore the association between ...
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Both social structural factors and direct sensory experiences can contribute to the development of environmental perceptions and concerns. We use two separate surveys of Utah adults to explore the association between sociodemographic characteristics and participation in recreational activities on water quality perceptions and concerns. We find that engaging in outdoor recreation is systematically associated with more positive water quality perceptions and higher levels of concern about impaired water quality. However, water quality perceptions appear to be shaped more by social characteristics (age, education, gender, race, religion, and income) and by generic measures of overall recreation behavior than by indicators of participation in particular forms of outdoor recreational activity. There is modest evidence that hikers, birdwatchers, and anglers are generally more likely to express concerns about impaired water quality, while boaters have more positive perceptions and lower levels of concern. Management implications: The baseline results of this study can be used by water managers in Utah to track shifts in public attitudes toward water quality as the state grapples with rapid climatic and demographic changes in the coming years. Certain types of water recreation (e.g. hiking and birdwatching) are consistently predictive of greater concern about poor water quality. More frequent participation in these types of recreation may lead to increased receptivity to public policies aimed at addressing water quality problems. Some demographic groups in our sample are more likely to engage in outdoor recreation, which may have important implications for public engagement.
A metal foam represents a promising material since it keeps the high mechanical properties of the metal while reducing the weight up to 90%. Among several manufacturing processes, the investment casting is a foundry p...
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A metal foam represents a promising material since it keeps the high mechanical properties of the metal while reducing the weight up to 90%. Among several manufacturing processes, the investment casting is a foundry process flexible enough to be suitable both for stochastic and for regular foams. This paper presents an experimental determination of the manufacturing process of metal regular foams by investment casting. The goal is to derive experimentally an actual "formability map". The use of logistic regression and response surface design is proposed as an effective tool for determining a statistical model of the metal foam casting process. (C) 2017 The Authors. Published by Elsevier B.V.
We present a two-step approach to classification problems in the large P, small N setting, where the number of predictors may be larger than the sample size. We assume that the association between the predictors and t...
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We present a two-step approach to classification problems in the large P, small N setting, where the number of predictors may be larger than the sample size. We assume that the association between the predictors and the class variable has an approximate linear-logistic form, but we allow the class boundaries to be nonlinear. We further assume that the number of true predictors is relatively small. In the first step, we use a binomial generalizedlinear model to identify which predictors are associated with each class and then restrict the data set to these predictors and run a nonlinear classifier, such as a random forest or a support vector machine. We show that, without the variable screening step, the classification performance of both the random forest and support vector machine is degraded when many among the P predictors are not related to the class.
This article introduces a parametric robust way of determining the mean-variance relationship in the setting of generalized linear models. More specifically, the normal likelihood is properly amended to become asympto...
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This article introduces a parametric robust way of determining the mean-variance relationship in the setting of generalized linear models. More specifically, the normal likelihood is properly amended to become asymptotically valid even if normality fails. Consequently, legitimate inference for the parametric relationship between mean and variance could be derived under model misspecification. More details are given to the scenario when the variance is proportional to an unknown power of the mean function. The efficacy of the novel technique is demonstrated via simulations and the analysis of two real data sets. (c) 2010 Elsevier B.V. All rights reserved.
In this article, we propose two novel diagnostic measures for the deletion of influential observations for regression parameters in the setting of generalized linear models. The proposed diagnostic methods are capable...
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In this article, we propose two novel diagnostic measures for the deletion of influential observations for regression parameters in the setting of generalized linear models. The proposed diagnostic methods are capable for detecting the influential observations under model misspecification, as long as the true underlying distributions have finite second moments. More specifically, it is demonstrated that the Poisson likelihood function can be properly adjusted to become asymptotically valid for practically all underlying discrete distributions. The adjusted Poisson regression model that achieves the robustness property is presented. Simulation studies and an illustration are performed to demonstrate the efficacy of the two novel diagnostic procedures. (C) 2010 Elsevier B.V. All rights reserved.
In the modeling of ordinal responses in psychological measurement and survey-based research, response styles that represent specific answering patterns of respondents are typically ignored. One consequence is that est...
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In the modeling of ordinal responses in psychological measurement and survey-based research, response styles that represent specific answering patterns of respondents are typically ignored. One consequence is that estimates of item parameters can be poor and considerably biased. The focus here is on the modeling of a tendency to extreme or middle categories. An extension of the partial credit model is proposed that explicitly accounts for this specific response style. In contrast to existing approaches, which are based on finite mixtures, explicit person-specific response style parameters are introduced. The resulting model can be estimated within the framework of generalized mixed linearmodels. It is shown that estimates can be seriously biased if the response style is ignored. In applications, it is demonstrated that a tendency to extreme or middle categories is not uncommon. A software tool is developed that makes the model easy to apply.
The realm of medical statistics or epidemiology encourages the repeated application of few variants of generalizedlinear model. This work has identified a situation in understanding the risk factor modelling for diab...
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