作者：
Sun, TianqiLi, WeiyuLin, LuShandong Univ
Zhongtai Secur Inst Financial Studies 27 Shanda Nanlu Jinan 250100 Shandong Peoples R China Shandong Univ
Natl Ctr Appl Math Shandong 126 Shanda lu Jinan 250100 Shandong Peoples R China
Matrix-variate generalized linear model (mvGLM) has been investigated successfully under the framework of tensor generalized linear model, because matrix-form data can be regarded as a specific tensor (2-dimension). B...
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Matrix-variate generalized linear model (mvGLM) has been investigated successfully under the framework of tensor generalized linear model, because matrix-form data can be regarded as a specific tensor (2-dimension). But there are few works focusing on matrix-form data with measurement error (ME), since tensor in conjunction with ME is relatively complex in structure. In this paper we introduce a mvGLM to primarily explore the influence of ME in the model with matrix-form data. We calculate the asymptotic bias based on error-prone mvGLM, and then develop bias-correction methods to tackle the affect of ME. Statistical properties for all methods are established, and the practical performance of all methods is further evaluated in analysis on synthetic and real data sets.
In the health and social sciences, longitudinal data have often been analyzed without taking into account the dependence between observations of the same subject. Furthermore, consideration is rarely given to the fact...
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In the health and social sciences, longitudinal data have often been analyzed without taking into account the dependence between observations of the same subject. Furthermore, consideration is rarely given to the fact that longitudinal data may come from a non-normal distribution. In addition to describing the aims and types of longitudinal designs this paper presents three approaches based on generalized estimating equations that do take into account the lack of independence in data, as well as the type of distribution. These approaches are the marginal model (population-average model), the random effects model (subject-specific model), and the transition model (Markov model or auto-correlation model). Finally, these models are applied to empirical data by means of specific procedures included in SAS, namely GENMOD, MIXED, and GLIMMIX.
Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel ...
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Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel and innovative multi-parameter models to analyze such data. These multi-parameter models have been proposed for overcoming the limitations of the traditional negative binomial (NB) model, which cannot handle this kind of data efficiently. The research documented in this paper continues the work related to multi-parameter models. The objective of this paper is to document the development and application of a flexible NB generalized linear model with randomly distributed mixed effects characterized by the Dirichlet process (NB-DP) to model crash data. The objective of the study was accomplished using two datasets. The new model was compared to the NB and the recently introduced model based on the mixture of the NB and Lindley (NB-L) distributions. Overall, the research study shows that the NB-DP model offers a better performance than the NB model once data are over-dispersed and have a heavy tail. The NB-DP performed better than the NB-L when the dataset has a heavy tail, but a smaller percentage of zeros. However, both models performed similarly when the dataset contained a large amount of zeros. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data, such as the identification of outliers and sources of dispersion. (C) 2016 Elsevier Ltd. All rights reserved.
This work introduces specific tools based on phi-divergences to select and check generalized linear models with binary data. A backward selection criterion that helps to reduce the number of explanatory variables is c...
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This work introduces specific tools based on phi-divergences to select and check generalized linear models with binary data. A backward selection criterion that helps to reduce the number of explanatory variables is considered. Diagnostic methods based on divergence measures such as a new measure to detect leverage points and two indicators to detect influential points are introduced. As an illustration, the diagnostics are applied to human psychology data. (C) 2009 Elsevier B.V. All rights reserved.
generalized linear models (GLMs) are widely used for data analysis;however, their maximum likelihood estimators can be sensitive to outliers. We propose new statistical models that allow robust inferences from the GLM...
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generalized linear models (GLMs) are widely used for data analysis;however, their maximum likelihood estimators can be sensitive to outliers. We propose new statistical models that allow robust inferences from the GLM class of models, including Poisson and binomial GLMs, and their extension to generalizedlinear mixed models. The likelihood score equations from the new models give estimators with bounded influence, so that the resulting estimators are robust against outliers while maintaining high efficiency in the absence of outliers.
We propose a method to correct the significance level for a series of tests corresponding to several transformations of an explanatory variable in generalized linear model. Correlation between score tests are derived ...
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We propose a method to correct the significance level for a series of tests corresponding to several transformations of an explanatory variable in generalized linear model. Correlation between score tests are derived to apply the proposed method. (C) 2004 Elsevier B.V. All rights reserved.
In a generalized linear model of binary data, we consider models based on a general link function including a logistic regression model and a probit model as special cases. For testing the null hypothesis H-0 that the...
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In a generalized linear model of binary data, we consider models based on a general link function including a logistic regression model and a probit model as special cases. For testing the null hypothesis H-0 that the considered model is correct, we consider a family of phi-divergence goodness-of-fit test statistics C-phi that includes a power divergence family of statistics R-a. We propose a transformed C-phi statistics that improves the speed of convergence to a chi-square limiting distribution and show numerically that the transformed R-a statistic performs well. We also give a real data example of the transformed R-a statistic being more reliable than the original R-a statistic for testing H-0. (C) 2013 Elsevier Inc. All rights reserved.
The generalized linear model (GLM) encompasses many discrete and continuous models and it is particularly useful for analyzing discrete data. However, in many real life applications, the full distributional assumption...
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The generalized linear model (GLM) encompasses many discrete and continuous models and it is particularly useful for analyzing discrete data. However, in many real life applications, the full distributional assumption of the GLM cannot be justified. Further, the GLM cannot accommodate over-dispersion in the data. Since the inception of the GLM by Nelder and Wedderburn (1972) a number of its extensions have been proposed in the literature for robust analysis of discrete data. The purpose of this paper is to critically review these extensions. Applications to over-dispersed Poisson and binomial models are shown. Some simulations are conducted to compare, in terms of bias and efficiency, the estimates of mean and the dispersion parameters by different methods. Applications to some biological and environmental data are given. Copyright (c) 2007 John Wiley & Sons, Ltd.
Suppose that Y = f(X(tau)beta)+epsilon Here f is a smooth but unknown function, beta is a k x 1 parameter vector to be estimated and epsilon(i) is a random error with mean 0 and variance sigma(2). The asymptotically l...
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Suppose that Y = f(X(tau)beta)+epsilon Here f is a smooth but unknown function, beta is a k x 1 parameter vector to be estimated and epsilon(i) is a random error with mean 0 and variance sigma(2). The asymptotically linear estimator of beta is constructed based on the model Y-i = f(X(i)(tau)beta)+epsilon(i), i = 1 ... n, when the density functions of epsilon and X are unknown.
We consider generalized linear models where a predictor is measured with error. The efficient score test for the effect of that predictor depends on the regression of the true predictor on its observed surrogate. Usin...
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We consider generalized linear models where a predictor is measured with error. The efficient score test for the effect of that predictor depends on the regression of the true predictor on its observed surrogate. Using validation data, we estimate the regression by nonparametric techniques. The resulting semiparametric score test is shown to be nearly asymptotically efficient.
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