Influence on Confidence Regions for Regression Coefficients in Generalized Linear Models

1990 ◽  
Vol 85 (410) ◽  
pp. 393-397 ◽  
Author(s):  
William Thomas
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Confidence Regions ◽  
Regression Coefficients

Posterior contraction in sparse generalized linear models

Biometrika ◽  
2020 ◽  
Author(s):  
Seonghyun Jeong ◽  
Subhashis Ghosal
Keyword(s):  
Generalized Linear Models ◽  
Bayesian Methods ◽  
Generalized Linear Model ◽  
Linear Models ◽  
Continuous Distribution ◽  
Fractional Power ◽  
Regression Coefficients ◽  
Link Function ◽  
Convergence Properties ◽  
Set Up

Summary We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others.

scholarly journals Penalized Likelihood Estimation of Gamma Distributed Response Variable via Corrected Solution of Regression Coefficients

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Rasaki Olawale Olanrewaju
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Penalized Likelihood ◽  
Likelihood Estimation ◽  
Regression Coefficients ◽  
Response Variable ◽  
Penalized Likelihood Estimation ◽  
Selection Operator ◽  
Minimax Concave Penalty

A Gamma distributed response is subjected to regression penalized likelihood estimations of Least Absolute Shrinkage and Selection Operator (LASSO) and Minimax Concave Penalty via Generalized Linear Models (GLMs). The Gamma related disturbance controls the influence of skewness and spread in the corrected path solutions of the regression coefficients.

Independently Interpretable Lasso for Generalized Linear Models

2020 ◽  
Vol 32 (6) ◽  
pp. 1168-1221
Author(s):  
Masaaki Takada ◽  
Taiji Suzuki ◽  
Hironori Fujisawa
Keyword(s):  
Generalized Linear Models ◽  
Regularization Method ◽  
Linear Models ◽  
Estimation Error ◽  
Real Data ◽  
Regression Coefficients ◽  
Learning Problems ◽  
High Dimensional ◽  
Optimal Convergence Rate ◽  
Sparse Regularization

Sparse regularization such as [Formula: see text] regularization is a quite powerful and widely used strategy for high-dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by several studies. However, one of the biggest issues in sparse regularization is that its performance is quite sensitive to correlations between features. Ordinary [Formula: see text] regularization selects variables correlated with each other under weak regularizations, which results in deterioration of not only its estimation error but also interpretability. In this letter, we propose a new regularization method, independently interpretable lasso (IILasso), for generalized linear models. Our proposed regularizer suppresses selecting correlated variables, so that each active variable affects the response independently in the model. Hence, we can interpret regression coefficients intuitively, and the performance is also improved by avoiding overfitting. We analyze the theoretical property of the IILasso and show that the proposed method is advantageous for its sign recovery and achieves almost minimax optimal convergence rate. Synthetic and real data analyses also indicate the effectiveness of the IILasso.

Effect of Different Dentifrices, Bleaching with 35% Hydrogen Peroxide, and Red Wine on Surface Color and Roughness of Bovine Enamel

2020 ◽  
Vol 02 ◽  
Author(s):  
RM Garcia ◽  
WF Vieira-Junior ◽  
JD Theobaldo ◽  
NIP Pini ◽  
GM Ambrosano ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Generalized Linear Models ◽  
Repeated Measures ◽  
Red Wine ◽  
Linear Models ◽  
Artificial Saliva ◽  
Surface Color ◽  
Dental Bleaching ◽  
Surface Alteration ◽  
Bovine Enamel

Objective: To evaluate color and roughness of bovine enamel exposed to dentifrices, dental bleaching with 35% hydrogen peroxide (HP), and erosion/staining by red wine. Methods: Bovine enamel blocks were exposed to: artificial saliva (control), Oral-B Pro-Health (stannous fluoride with sodium fluoride, SF), Sensodyne Repair & Protect (bioactive glass, BG), Colgate Pro-Relief (arginine and calcium carbonate, AR), or Chitodent (chitosan, CHI). After toothpaste exposure, half (n=12) of the samples were bleached (35% HP), and the other half were not (n=12). The color (CIE L*a* b*, ΔE), surface roughness (Ra), and scanning electron microscopy were evaluated. Color and roughness were assessed at baseline, post-dentifrice and/or -dental bleaching, and after red wine. The data were subjected to analysis of variance (ANOVA) (ΔE) for repeated measures (Ra), followed by Tukey ́s test. The L*, a*, and b* values were analyzed by generalized linear models (a=0.05). Results: The HP promoted an increase in Ra values; however, the SF, BG, and AR did not enable this alteration. After red wine, all groups apart from SF (unbleached) showed increases in Ra values; SF and AR promoted decreases in L* values; AR demonstrated higher ΔE values, differing from the control; and CHI decreased the L* variation in the unbleached group. Conclusion: Dentifrices did not interfere with bleaching efficacy of 35% HP. However, dentifrices acted as a preventive agent against surface alteration from dental bleaching (BG, SF, and AR) or red wine (SF). Dentifrices can decrease (CHI) or increase (AR and SF) staining by red wine.

Economic burden of readmission due to postoperative cerebrospinal fluid leak in Chinese patients

2020 ◽  
Vol 9 (16) ◽  
pp. 1105-1115
Author(s):  
Shuqing Wu ◽  
Xin Cui ◽  
Shaoyu Zhang ◽  
Wenqi Tian ◽  
Jiazhen Liu ◽  
...  
Keyword(s):  
Cerebrospinal Fluid ◽  
Generalized Linear Models ◽  
Economic Burden ◽  
Linear Models ◽  
Chinese Patients ◽  
Cerebrospinal Fluid Leakage ◽  
Index Hospitalization ◽  
Real World Data ◽  
Factors Associated ◽  
Hospitalization Cost

Aim: This real-world data study investigated the economic burden and associated factors of readmissions for cerebrospinal fluid leakage (CSFL) post-cranial, transsphenoidal, or spinal index surgeries. Methods: Costs of CSFL readmissions and index hospitalizations during 2014–2018 were collected. Readmission cost was measured as absolute cost and as percentage of index hospitalization cost. Factors associated with readmission cost were explored using generalized linear models. Results: Readmission cost averaged US$2407–6106, 35–94% of index hospitalization cost. Pharmacy costs were the leading contributor. Generalized linear models showed transsphenoidal index surgery and surgical treatment for CSFL were associated with higher readmission costs. Conclusion: CSFL readmissions are a significant economic burden in China. Factors associated with higher readmission cost should be monitored.

Determination of Enzyme or Binding Constants Using Generalized Linear Models, with Particular Reference to Michaelis–Menten Models

1989 ◽  
Vol 78 (5) ◽  
pp. 413-416
Author(s):  
Gerald Van Belle ◽  
Sue Leurgans ◽  
Pat Friel ◽  
Sunwei Guo ◽  
Mark Yerby
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Binding Constants
Sign in / Sign up

Export Citation Format

Share Document