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POSTERIOR MODE ESTIMATION FOR THE generalized linear-model

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1992年第3期44卷 417-434页

作者： EAVES, DM CHANG, T SIMON FRASER UNIV DEPT MATH & STATBURNABY V5A 1S6BCCANADA UNIV VIRGINIA DEPT MATHCHARLOTTESVILLEVA 22903

Posterior mode estimators are proposed, which arise from simply expressed prior opinion about expected outcomes, roughly as follows: a conjugate family of prior distributions is determined by a given variance function. Using a conjugate prior, a posterior mode estimator and its estimated (co-)variances are obtained through conventional maximum likelihood computations, by means of small alterations to the observed outcomes and/or to the modelled variance function. Within the conjugate family, for purposes of inference about the regression vector, a reference prior is proposed for a given choice of linear design of the canonical link. The resulting approximate reference inferences approximate the Bayesian inferences which arise from a "minimally informative" reference prior. A set of subjective prior upper and lower percentage points for the expected outcomes can be used to determine a conjugate family member. Alternatively, a set of subjective prior means and standard deviations determines a member. The subfamily of priors determinable by percentage points either includes or approximates the proposed reference prior.

关键词： CONJUGATE PRIOR CONTINGENCY TABLES EXPONENTIAL FAMILY FREQUENCY COUNTS generalized linear model JEFFREYS PRIOR LOGISTIC REGRESSION MULTINOMIAL OUTCOME MINIMALLY INFORMATIVE PRIOR NONlinear REGRESSION QUASI-LIKELIHOOD REFERENCE PRIOR REGRESSION VARIANCE FUNCTION

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UMP INVARIANT TESTS FOR A generalized linear-model

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JOURNAL OF MULTIVARIATE ANALYSIS 1992年第1期40卷 1-12页

作者： UKITA, Y NODA, K MIYAOKA, E SCI UNIV TOKYO TOKYO 162JAPAN

For a generalized normal linear model in which the covariance matrix Σ is positive definite symmetric, UMP invariant test procedures for some kinds of linear hypotheses are derived by transforming the model by an orthogonal matrix L , consisting of orthonormal eigenvectors of Σ as the columns vectors. Here it is assumed that Σ contains unknown elements but has a certain structure making all the elements of L known. A sufficient condition for this assumption is also obtained to examine whether the covariance matrix Σ has such a form.

关键词： DIAGONALIZATION generalized linear model ORTHOGONAL TRANSFORMATION REPEATED MEASURES model UMP INVARIANT TESTS

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Population decoding of motor cortical activity using a generalized linear model with hidden states

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JOURNAL OF NEUROSCIENCE METHODS 2010年第2期189卷 267-280页

作者： Lawhern, Vernon Wu, Wei Hatsopoulos, Nicholas Paninski, Liam Florida State Univ Dept Stat Tallahassee FL 32306 USA Univ Chicago Dept Organismal Biol & Anat Comm Computat Neurosci Chicago IL 60637 USA Univ Chicago Dept Organismal Biol & Anat Comm Neurobiol Chicago IL 60637 USA Columbia Univ Dept Stat New York NY 10027 USA

generalized linear models (GLMs) have been developed for modeling and decoding population neuronal spiking activity in the motor cortex. These models provide reasonable characterizations between neural activity and motor behavior. However, they lack a description of movement-related terms which are not observed directly in these experiments, such as muscular activation, the subject's level of attention, and other internal or external states. Here we propose to include a multi-dimensional hidden state to address these states in a GLM framework where the spike count at each time is described as a function of the hand state (position, velocity, and acceleration), truncated spike history, and the hidden state. The model can be identified by an Expectation-Maximization algorithm. We tested this new method in two datasets where spikes were simultaneously recorded using a multi-electrode array in the primary motor cortex of two monkeys. It was found that this method significantly improves the model-fitting over the classical GLM, for hidden dimensions varying from 1 to 4. This method also provides more accurate decoding of hand state (reducing the mean square error by up to 29% in some cases), while retaining real-time computational efficiency. These improvements on representation and decoding over the classical GLM model suggest that this new approach could contribute as a useful tool to motor cortical decoding and prosthetic applications. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Neural decoding Motor cortex generalized linear model Hidden states State-space model

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A unified approach to estimating association measures via a joint generalized linear model for paired binary data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2000年第1期29卷 143-156页

作者： Qu, YS Tan, M Rybicki, L Fred Hutchinson Canc Res Ctr Canc Prevent Res Program Seattle WA 98109 USA St Jude Childrens Res Hosp Dept Biostat & Epidemiol Memphis TN 38139 USA Cleveland Clin Fdn Dept Biostat & Epidemiol Cleveland OH 44195 USA

Paired binary data arise frequently in biomedical studies with unique features of their own. For instance, in clinical studies involving pails such as ears, eyes etc., often both the intrapair association parameter and the event probability are of interest. In addition, we may be interested in the dependence of the association parameter on certain covariates as well. Although various methods have been proposed to model paired binary data, this paper proposes a unified approach for estimating various intrapair measures under a generalized linear model with simultaneous maximum likelihood estimates of the marginal probabilities and the intrapair association. The methods are illustrated with a twin morbidity study.

关键词： generalized linear model intrapair association measures logistic regression

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PLASQ: a generalized linear model-based procedure to determine allelic dosage in cancer cells from SNP array data

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BIOSTATISTICS 2007年第2期8卷 323-336页

作者： Laframboise, Thomas Harrington, David Weir, Barbara A. Dana Farber Canc Inst Dept Med Oncol Boston MA 02115 USA Harvard Univ Sch Publ Hlth Dept Biostat Boston MA 02115 USA

Human cancer is largely driven by the acquisition of mutations. One class of such mutations is copy number polymorphisms, comprised of deviations from the normal diploid two copies of each autosomal chromosome per cell. We describe a probe-level allele-specific quantitation (PLASQ) procedure to determine copy number contributions from each of the parental chromosomes in cancer cells from single-nucleotide polymorphism (SNP) microarray data. Our approach is based upon a generalized linear model that takes advantage of a novel classification of probes on the array. As a result of this classification, we are able to fit the model to the data using an expectation-maximization algorithm designed for the purpose. We demonstrate a strong model fit to data from a variety of cell types. In normal diploid samples, PLASQ is able to genotype with very high accuracy. Moreover, we are able to provide a generalized genotype in cancer samples (e.g. CCCCT at an amplified SNP). Our approach is illustrated on a variety of lung cancer cell lines and tumors, and a number of events are validated by independent computational and experimental means. An R software package containing the methods is freely available.

关键词： allelic imbalance cancer genomics DNA copy number expectation-maximization algorithm generalized linear model single nucleotide polymorphism array

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Evaluating the double Poisson generalized linear model

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ACCIDENT ANALYSIS AND PREVENTION 2013年第Oct.期59卷 497-505页

作者： Zou, Yaotian Geedipally, Srinivas Reddy Lord, Dominique Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA Texas A&M Univ Syst Texas Transportat Inst Arlington TX 76013 USA Texas A&M Univ Zachry Dept Civil Engn College Stn TX 77843 USA

The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been investigated and applied since its first introduction two decades ago. The hurdle for applying the DP is related to its normalizing constant (or multiplicative constant) which is not available in closed form. This study proposed a new method to approximate the normalizing constant of the DP with high accuracy and reliability. The DP GLM and COM-Poisson GLM were developed using two observed over-dispersed datasets and one observed under-dispersed dataset. The modeling results indicate that the DP GLM with its normalizing constant approximated by the new method can handle crash data characterized by over- and under-dispersion. Its performance is comparable to the COM-Poisson GLM in terms of goodness-of-fit (GOF), although COM-Poisson GLM provides a slightly better fit. For the over-dispersed data, the DP GLM performs similar to the NB GLM. Considering the fact that the DP GLM can be easily estimated with inexpensive computation and that it is simpler to interpret coefficients, it offers a flexible and efficient alternative for researchers to model count data. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Double Poisson Normalizing constant Conway-Maxwell-Poisson Gamma model generalized linear model

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Laws of iterated logarithm for quasi-maximum likelihood estimator in generalized linear model

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2008年第3期138卷 611-617页

作者： Xiao, Zhihong Liu, Luqin Huazhong Agr Univ Sch Sci Wuhan 430070 Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China

For the case that the expectation of the response variable Y is correctly specified in the generalized linear model (GLM), under some regular assumptions, we obtain and prove the law of the iterated logarithm and Chung type law of the iterated logarithm for the quasi-maximum likelihood estimator (QMLE)beta(n) in this model. (C) 2007 Published by Elsevier B.V.

关键词： generalized linear model quasi-maximum likelihood estimator law of iterated logarithm

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The effect of meteorological variables on salmonellosis incidence in Kermanshah, West of Iran: a generalized linear model with negative binomial approach

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JOURNAL OF ENVIRONMENTAL HEALTH SCIENCE AND ENGINEERING 2021年第1期19卷 1171-1177页

作者： Nili, Sairan Khanjani, Narges Bakhtiari, Bahram Jahani, Yunes Dalaei, Hamideh Kurdistan Univ Med Sci Fac Hlth Dept Publ Hlth Sanandaj Iran Kerman Univ Med Sci Neurol Res Ctr Kerman Iran Kerman Univ Med Sci Sch Publ Hlth Dept Epidemiol & Biostat Kerman *** Iran Shahid Bahonar Univ Kerman Fac Agr Water Engn Dept Kerman Iran Kerman Univ Med Sci Modeling Hlth Res Ctr Inst Futures Studies Hlth Kerman Iran Res Deputy Iranian Meteorol Org IRIMO Tehran Iran

Purpose Salmonella is one of the main causes of gastroenteritis, and its incidence may be affected by meteorological variables. This is the first study about the effect of climatic factors on salmonella incidence in Kermanshah, Iran. Methods Data about salmonellosis cases in Kermanshah were inquired from Center for Communicable Disease Control, at the Ministry of Health and Medical Education of Iran, for the 2008 to 2018 time-frame. Meteorological variables including maximum, minimum and mean of temperature and humidity, sunshine hours and rainfall were inquired for the same time frame. Negative binomial generalized linear models (GLM) were used to assess the effect of meteorological variables on the weekly incidence of salmonellosis. Results During the years under study, 569 confirmed cases were registered in Kermanshah province. Study results showed a 3 % increase in salmonellosis incidence, after 1 % increase in minimum humidity in the week before (incidence rate ratio (IRR): 1.03;95 % confidence interval (CI):1.02-1.05) and also a 4 % increase in incidence for 1 degrees C increase in mean temperature in the same week (IRR: 1.04;95 % CI:1.02-1.06). Conclusions Increase in minimum humidity and mean temperature may have a role in increasing the incidence of salmonellosis in Iran.

关键词： Forecasting generalized linear model Negative binomial regression Salmonellosis Environment Iran Kermanshah

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THE ASYMPTOTIC RELATIVE EFFICIENCY OF SCORE TESTS IN A generalized linear-model WITH SURROGATE COVARIATES

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BIOMETRIKA 1988年第3期75卷 507-514页

作者： TOSTESON, TD TSIATIS, AA HARVARD UNIV SCH MED DANA FARBER CANC INST BOSTON MA 02115 USA

In many epidemiological studies, the exposure variable of interest cannot be measured directly. The classical approaches to errors in variables in regression do not extend easily to the nonlinear models commonly used in epidemiological research. Furthermore, the traditional additive measurement error model cannot adequately represent many surrogate relationships. By considering the effect of using surrogate independent variables on the efficient score statistic, some of the difficulties inherent in the estimation problem may be avoided. For the null hypothesis of no association, a simple and flexible procedure can be used to calculate the optimal score test. The asymptotic relative efficiency of this test to the test based upon the true exposures is derived. The optimal test is also compared to the naive procedure of substituting the surrogate into the score test for the true exposure.

关键词： generalized linear model Null hypothesis Radiation dosage Mathematical vectors linear transformations Chemical hazards Disease models Epidemiology

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Multiple imputation for gamma outcome variable using generalized linear model

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2017年第10期87卷 1980-1988页

作者： Gupta, Vinay K. Grover, Gurprit Univ Delhi Dept Stat Delhi India

We used a proper multiple imputation (MI) through Gibbs sampling approach to impute missing values of a gamma distributed outcome variable which were missing at random, using generalized linear model (GLM) with identity link function. The missing values of the outcome variable were multiply imputed using GLM and then the complete data sets obtained after MI were analysed through GLM again for the estimation purpose. We examined the performance of the proposed technique through a simulation study with the data sets having four moderate and large proportions of missing values, 10%, 20%, 30% and 50%. We also applied this technique on a real life data and compared the results with those obtained by applying GLM only on observed cases. The results showed that the proposed technique gave better results for moderate proportions of missing values.

关键词： Multiple imputation generalized linear model gamma distribution missing data identity link function

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