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Author: Jan Ulbricht
Publisher:
ISBN: 9783868536317
Category :
Languages : de
Pages : 198
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Author: Jan Ulbricht
Publisher:
ISBN: 9783868536317
Category :
Languages : de
Pages : 198
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Author: Asokan Mulayath Variyath
Publisher:
ISBN: 9780494236796
Category :
Languages : en
Pages : 168
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Author: Chon Sam
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Andreas Groll
Publisher: Cuvillier Verlag
ISBN: 3736939639
Category : Business & Economics
Languages : en
Pages : 175
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Book Description
A regression analysis describes the dependency of random variables in the form of a functional relationship. One distinguishes between the dependent response variable and one or more independent influence variables. There is a variety of model classes and inference methods available, ranging from the conventional linear regression model up to recent non- and semiparametric regression models. The so-called generalized regression models form a methodically consistent framework incorporating many regression approaches with response variables that are not necessarily normally distributed, including the conventional linear regression model based on the normal distribution assumption as a special case. When repeated measurements are modeled in addition to fixed effects also random effects or coefficients can be included. Such models are known as Random Effects Models or Mixed Models. As a consequence, regression procedures are applicable extremely versatile and consider very different problems. In this dissertation regularization techniques for generalized mixed models are developed that are able to perform variable selection. These techniques are especially appropriate when many potential influence variables are present and existing approaches tend to fail. First of all a componentwise boosting technique for generalized linear mixed models is presented which is based on the likelihood function and works by iteratively fitting the residuals using weak learners. The complexity of the resulting estimator is determined by information criteria. For the estimation of variance components two approaches are considered, an estimator resulting from maximizing the profile likelihood, and an estimator which can be calculated using an approximative EM-algorithm. Then the boosting concept is extended to mixed models with ordinal response variables. Two different types of ordered models are considered, the threshold model, also known as cumulative model, and the sequential model. Both are based on the assumption that the observed response variable results from a categorized version of a latent metric variable. In the further course of the thesis the boosting approach is extended to additive predictors. The unknown functions to be estimated are expanded in B-spline basis functions, whose smoothness is controlled by penalty terms. Finally, a suitable L1-regularization technique for generalized linear models is presented, which is based on a combination of Fisher scoring and gradient optimization. Extensive simulation studies and numerous applications illustrate the competitiveness of the methods constructed in this thesis compared to conventional approaches. For the calculation of standard errors bootstrap methods are used.
Author: Gang Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 276
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Author: Borko D. Jovanovic
Publisher:
ISBN:
Category : Linear models (Statistics)
Languages : en
Pages : 354
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Author: Jinzhu Jiang
Publisher:
ISBN:
Category : Linear models (Statistics)
Languages : en
Pages : 105
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High-dimensional data are widely encountered in a great variety of areas such as bioinformatics, medicine, marketing, and finance over the past few decades. The curse of high-dimensionality presents a challenge in both methodological and computational aspects. Many traditional statistical modeling techniques perform well for low-dimensional data, but their performance begin to deteriorate when being extended to high-dimensional data. Among all modeling techniques, variable selection plays a fundamental role in high-dimensional data modeling. To deal with the high-dimensionality problem, a large amount of variable selection approaches based on regularization have been developed, including but not limited to LASSO (Tibshirani, 1996), SCAD (Fan and Li, 2001), Dantzig selector (Candes and Tao, 2007). However, as the dimensionality getting higher and higher, those regularization approaches may not perform well due to the simultaneous challenges in computational expediency, statistical accuracy, and algorithm stability (Fan et al., 2009). To address those challenges, a series of feature screening procedures have been proposed. Sure independence screening (SIS) is a well-known procedure for variable selection in linear models with high and ultrahigh dimensional data based on the Pearson correlation (Fan and Lv, 2008). Yet, the original SIS procedure mainly focused on linear models with the continuous response variable. Fan and Song (2010) also extended this method to generalized linear models by ranking the maximum marginal likelihood estimator (MMLE) or maximum marginal likelihood itself. In this dissertation, we consider extending the SIS procedure to high-dimensional generalized linear models with binary response variable. We propose a two-stage feature screening procedure for generalized linear models with a binary response based on point-biserial correlation. The point-biserial correlation is an estimate of the correlation between one continuous variable and one binary variable. The two-stage point-biserial sure independence screening (PB-SIS) can be implemented in a straightforward way as the original SIS procedure, but it targets more specifically on high-dimensional generalized linear models with the binary response variable. In the first stage, we perform the SIS procedure by using point-biserial correlation to reduce the high dimensionality of a model to a moderate size. In the second stage, we apply a regularization method, such as LASSO, SCAD, or MCP, to further select important variables and find the final spare model. We establish the sure screening property under certain conditions for the PB-SIS method for high-dimensional generalized linear models with the binary response variable. The sure independence property for PB-SIS shows that our proposed method can select all the important variables in the screened submodel with probability very close to one. We also conduct simulation studies for generalized linear models with binary response variable by generating data from different link functions. To evaluate the performance of our proposed method, we compare the proportion of submodel with size d that contains all the true predictors among 1000 simulations, P , and computing time for our proposed method with MMLE and Kolmogorov filter methods after the first stage screening. We also compare the performance of two-stage PB-SIS methods with different penalized methods by using different tuning parameter selection criteria. The simulation results demonstrate that PB-SIS outperforms the Kolmogorov filter methods in both the selection accuracy and computational cost in different settings and has almost the same selection accuracy as MMLE but with much lower computational cost. A real data application is given to illustrate the performance of the proposed two-stage PB-SIS method.
Author: Ludwig Fahrmeir
Publisher: Springer Science & Business Media
ISBN: 1489900101
Category : Mathematics
Languages : en
Pages : 440
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Book Description
Concerned with the use of generalised linear models for univariate and multivariate regression analysis, this is a detailed introductory survey of the subject, based on the analysis of real data drawn from a variety of subjects such as the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account.
Author: Michael Smithson
Publisher: SAGE Publications
ISBN: 1544334524
Category : Social Science
Languages : en
Pages : 136
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Book Description
This book introduces researchers and students to the concepts and generalized linear models for analyzing quantitative random variables that have one or more bounds. Examples of bounded variables include the percentage of a population eligible to vote (bounded from 0 to 100), or reaction time in milliseconds (bounded below by 0). The human sciences deal in many variables that are bounded. Ignoring bounds can result in misestimation and improper statistical inference. Michael Smithson and Yiyun Shou's book brings together material on the analysis of limited and bounded variables that is scattered across the literature in several disciplines, and presents it in a style that is both more accessible and up-to-date. The authors provide worked examples in each chapter using real datasets from a variety of disciplines. The software used for the examples include R, SAS, and Stata. The data, software code, and detailed explanations of the example models are available on an accompanying website.
Author: Ming-Hui Chen
Publisher:
ISBN:
Category : Logistic regression analysis
Languages : en
Pages : 54
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Book Description
