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Going beyond oracle property: Selection consistency and uniqueness of local solution of the generalized linear model

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STATISTICAL METHODOLOGY 2016年第0期32卷 147-160页

作者： Ng, Chi Tim Oh, Seungyoung Lee, Youngjo Chonnam Natl Univ Dept Stat Kwangju 500757 South Korea Seoul Natl Univ Dept Stat Seoul 151747 South Korea

Recently, the selection consistency of penalized least square estimators has received a great deal of attention. For the penalized likelihood estimation with certain non-convex penalties, search space can be constructed within which there exists a unique local minimizer that exhibits selection consistency in high-dimensional generalized linear models under certain conditions. In particular, we prove that the SCAD penalty of Fan and Li (2001) and a new modified version of the unbounded penalty of Lee and Oh (2014) can be employed to achieve such a property. These results hold even for the non-sparse cases where the number of relevant covariates increases with the sample size. Simulation studies are provided to compare the performance of SCAD penalty and the newly proposed penalty. (C) 2016 Elsevier B.V. All rights reserved.

关键词： generalized linear model Penalized likelihood estimation Oracle property SCAD penalty Selection consistency

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Analyzing longitudinal data and use of the generalized linear model in health and social sciences

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QUALITY & QUANTITY 2016年第2期50卷 693-707页

作者： Arnau, Jaume Bono, Roser Bendayan, Rebecca Blanca, Maria J. Univ Barcelona Fac Psychol Dept Behav Sci Methodol Passeig Vall dHebron 171 Barcelona 08035 Spain Univ Barcelona Inst Brain Cognit & Behav IR3C Barcelona Spain Univ Malaga Fac Psychol Dept Psychobiol & Behav Sci E-29071 Malaga Spain

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.

关键词： generalized linear model Longitudinal data Marginal model Random effects model Transition model

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A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data

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ACCIDENT ANALYSIS AND PREVENTION 2016年第Jun.期91卷 10-18页

作者： Shirazi, Mohammadali Lord, Dominique Dhavala, Soma Sekhar Geedipally, Srinivas Reddy Texas A&M Univ Zachry Dept Civil Engn College Stn TX 77843 USA Perceptron Learning Solut Pvt Ltd Bengaluru India Texas A&M Univ Texas A&M Transportat Inst College Stn TX 77843 USA

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.

关键词： Negative binomial Dirichlet process generalized linear model Crash data

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Post-model-Selection Prediction Intervals for generalized linear models

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SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY 2024年第SUPPL 1期86卷 301-326页

作者： Dustin, Dean Clarke, Bertrand Charles Schwab 9800 Schwab Way Lone Tree CO 80124 USA Univ Nebraska Lincoln Dept Stat 340 Hardin Hall North Lincoln NE 68583 USA

We give two prediction intervals for generalized linear models that take model selection uncertainty into account. The first is a straightforward extension of asymptotic normality results and the second includes an extra optimization that improves nominal coverage for small-to-moderate samples. Both PI's are wider than would be obtained without incorporating model selection uncertainty. We compare these two PI's with three other PI's. Two are based on bootstrapping procedures and the third is based on a PI from Bayes model averaging. We argue that for general usage the optimized asymptotic normality PI's work best unless sample sizes are large in which case the PI's based only on asymptotic arguments that include model selection will be easier and equivalent. In an Appendix we extend our results to generalized linear Mixed models.

关键词： Prediction interval generalized linear model post-model selection

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Post-averaging inference for optimal model averaging estimator in generalized linear models

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ECONOMETRIC REVIEWS 2024年第2-4期43卷 98-122页

作者： Yu, Dalei Lian, Heng Sun, Yuying Zhang, Xinyu Hong, Yongmiao Xi An Jiao Tong Univ Sch Math & Stat Dept Stat Xian Peoples R China City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing Peoples R China Chinese Acad Sci Ctr Forecasting Sci Beijing Peoples R China Univ Chinese Acad Sci Sch Econ & Management Beijing Peoples R China Univ Chinese Acad Sci MOE Social Sci Lab Digital Econ Forecasts & Policy Beijing Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China

This article considers the problem of post-averaging inference for optimal model averaging estimators in a generalized linear model (GLM). We establish the asymptotic distributions of optimal model averaging estimators for GLMs. The asymptotic distributions of the model averaging estimators are nonstandard, depending on the configuration of the penalty term in the weight choice criterion. We also propose a feasible simulation-based confidence interval estimator and investigate its asymptotic properties rigorously. Monte Carlo simulations verify the usefulness of our theoretical results, and the proposed methods are employed to analyze a stock car racing dataset.

关键词： Asymptotic distribution generalized linear model model selection optimal model averaging

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The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

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JOURNAL OF TRANSPORTATION SAFETY & SECURITY 2016年第1期8卷 18-35页

作者： Zha, Liteng Lord, Dominique Zou, Yajie Texas A&M Univ Zachry Dept Civil Engn College Stn TX USA Univ Washington Dept Civil & Environm Engn Seattle WA USA

This article documents the application of the Poisson inverse Gaussian (PIG) regression model for modeling motor vehicle crash data. The PIG distribution, which mixes the Poisson distribution and inverse Gaussian distribution, has the potential for modeling highly dispersed count data due to the flexibility of inverse Gaussian distribution. The objectives of this article were to evaluate the application of PIG regression model for analyzing motor vehicle crash data and compare the results with negative binomial (NB) model, especially when varying dispersion parameter is introduced. To accomplish these objectives, NB and PIG models were developed with fixed and varying dispersion parameters and compared using two data sets. The results of this study show that PIG models perform better than the NB models in terms of goodness-of-fit statistics. Moreover, the PIG model can perform as well as the NB model in capturing the variance of crash data. Lastly, PIG models demonstrate almost the same prediction performance compared to NB models. Considering the simple form of PIG model and its easiness of applications, PIG model could be used as a potential alternative to the NB model for analyzing crash data.

关键词： Poisson-inverse Gaussian Poisson-gamma generalized linear model traffic crashes

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Prediction of Single Neural Firings for Hodgkin-Huxley Neuron by Fitting generalized linear model 34

Prediction of Single Neural Firings for Hodgkin-Huxley Neuro...

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34th Chinese Control Conference (CCC)

作者： Wei, Xile Shi, Dingtian Lu, Meili Deng, Bin Yu, Haitao Wang, Jiang Tianjin Univ Tianjin Key Lab Proc Measurement & Control Sch Elect Engn & Automat Tianjin 300072 Peoples R China Tianjin Univ Technol & Educ Sch Informat Technol & Engn Tianjin 300222 Peoples R China

ISBN: (纸本)9789881563897

At the single neuron level, neural information processing involves the transformation of input stimulation into an output spike train. Here a generalized linear model (GLM) is used to reconstruct the mapping from stimulation to firing trains of single neuron for Hudgkin-Huxley (H-H) model. Firstly, H-H model is stimulated by the white noise to generate the input-output data samples used to construct GLM. Then, the parameters of GLM are estimated according to the maximum likelihood of the spike time serial of spike trains extracted from action potential of H-H. After that, the input-output mapping of spike trains evoked by white noise for H-H is successfully reconstructed. Through comparing the inter spike interval (ISI) and Pearson's correlation coefficient, it also proves that the established GLM provides a good reproduction and prediction of the firing information for H-H. These studies provide us a new insight into coding processes and information tansfer of single neural.

关键词： generalized linear model Hodgkin-Huxley Neuron Spike trains Prediction

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Negative Binomial-generalized Exponential Distribution: generalized linear model and its Applications

Negative Binomial-Generalized Exponential Distribution: Gene...

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作者： Vangala, Prathyusha Texas A&M University

学位级别：master

modelling crash data has been an integral part of the research done in highway safety. Different tools have been suggested by researchers to analyze crash data. One such tool, which was recently proposed, is the Negative Binomial generalized Exponential (NB-GE) distribution. As the name suggests, it is a combination of Negative Binomial and generalized Exponential distribution. This distribution has three parameters and can handle over-dispersed crash data which are characterized by a large number of zeros and/or long tail. This research seeks to develop a generalized linear model (GLM) for NB-GE distribution and discuss its applications in crash data analysis. The NB-GE GLM was applied to two over-dispersed crash datasets and its performance was compared to Negative Binomial-Lindley (NB-L) and Negative Binomial (NB) models using various statistical measures. It was found that NB-GE performs almost as well as NB-L model and performs much better than the NB model. This research tried to determine the percentage of zeroes and the dispersion in the dataset where the NB-GE model is recommended over the NB model for ranking sites. Datasets were simulated for different scenarios. It was found that for high dispersion the NB-GE model performs better than the NB model when the percentage of zero counts in the dataset is greater than 80%. When dataset has lower than 80% zeroes then NB model and NB-GE model perform similarly. Hence for lower percentages NB model would be preferred as it is simpler and easier to use

关键词： Negative Binomial-generalized Exponential generalized linear model

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A generalized single-index linear threshold model for identifying treatment-sensitive subsets based on multiple covariates and longitudinal measurements

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2023年第4期51卷 1171-1189页

作者： Ge, Xinyi Peng, Yingwei Tu, Dongsheng Queens Univ Dept Math & Stat Kingston ON Canada Queens Univ Dept Publ Hlth Sci Kingston ON Canada Queens Univ Canadian Canc Trials Grp Kingston ON Canada

Identification of a subset of patients who may be sensitive to a specific treatment is an important step towards personalized medicine. We consider the case where the effect of a treatment is assessed by longitudinal measurements, which may be continuous or categorical, such as quality of life scores assessed over the duration of a clinical trial. We assume that multiple baseline covariates, such as age and expression levels of genes, are available, and propose a generalized single-index linear threshold model to identify the treatment-sensitive subset and assess the treatment-by-subset interaction after combining these covariates. Because the model involves an indicator function with unknown parameters, conventional procedures are difficult to apply for inferences of the parameters in the model. We define smoothed generalized estimating equations and propose an inference procedure based on these equations with an efficient spectral algorithm to find their solutions. The proposed procedure is evaluated through simulation studies and an application to the analysis of data from a randomized clinical trial in advanced pancreatic cancer.

关键词： Clinical studies combination of covariates generalized linear model longitudinal data predictive markers repeated measurements

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generalized linear models for ordered categorical data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第3期52卷 670-683页

作者： Holm, Sture Chalmers & Gothenburg Univ Dept Math Sci SE-41296 Gothenburg Sweden

Categorical scale data are only ordinal and defined on a finite set. Continuous scale data are only ordinal and defined on a bounded interval. Due to that character, the statistical methods for scale data ought to be based on orders between outcomes only and not any metric involving distance measure. For simple two-sample scale data, variants of classical rank methods are suitable. For regression type of problems, there are known good generalized linear models for separate categories for a long time. In the present article is suggested a new generalized linear type of model based on non parametric statistics for the whole scale. Asymptotic normality for those statistics is also shown and illustrated. Both fixed and random effects are considered.

关键词： generalized linear model rank methods scale data

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