Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models

2011 ◽  
Vol 55 (11) ◽  
pp. 2908-2924 ◽  
Author(s):  
Małgorzata Żak-Szatkowska ◽  
Małgorzata Bogdan
Keyword(s):  
Generalized Linear Models ◽  
Bayesian Information Criterion ◽  
Linear Models ◽  
Information Criterion

scholarly journals Why analyze germination experiments using Generalized Linear Models?

2018 ◽  
Vol 40 (3) ◽  
pp. 281-287 ◽  
Author(s):  
Fábio Janoni Carvalho ◽  
Denise Garcia de Santana ◽  
Lúcio Borges de Araújo
Keyword(s):  
Generalized Linear Models ◽  
Binomial Distribution ◽  
Goodness Of Fit ◽  
Linear Models ◽  
Information Criterion ◽  
Binomial Model ◽  
Inappropriate Use ◽  
Copaiba Oil ◽  
Germination Experiments ◽  
Combined Data

Abstract: We compared the goodness of fit and efficiency of models for germination. Generalized Linear Models (GLMs) were performed with a randomized component corresponding to the percentage of germination for a normal distribution or to the number of germinated seeds for a binomial distribution. Lower levels of Akaikes’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) combined, data adherence to simulated envelopes of normal plots and corrected confidence intervals for the means guaranteed the binomial model a better fit, justifying the importance of GLMs with binomial distribution. Some authors criticize the inappropriate use of analysis of variance (ANOVA) for discrete data such as copaiba oil, but we noted that all model assumptions were met, even though the species had dormant seeds with irregular germination.

Large-scale model selection in misspecified generalized linear models

Biometrika ◽  
2021 ◽  
Author(s):  
Emre Demirkaya ◽  
Yang Feng ◽  
Pallavi Basu ◽  
Jinchi Lv
Keyword(s):  
Model Selection ◽  
Generalized Linear Models ◽  
Large Scale ◽  
Linear Models ◽  
Information Criterion ◽  
Scale Model ◽  
High Dimensional ◽  
Model Selection Consistency ◽  
New Information ◽  
Large Scale Model

Summary Model selection is crucial both to high-dimensional learning and to inference for contemporary big data applications in pinpointing the best set of covariates among a sequence of candidate interpretable models. Most existing work assumes implicitly that the models are correctly specified or have fixed dimensionality, yet both are prevalent in practice. In this paper, we exploit the framework of model selection principles under the misspecified generalized linear models presented in Lv and Liu (2014) and investigate the asymptotic expansion of the posterior model probability in the setting of high-dimensional misspecified models.With a natural choice of prior probabilities that encourages interpretability and incorporates the Kullback–Leibler divergence, we suggest the high-dimensional generalized Bayesian information criterion with prior probability for large-scale model selection with misspecification. Our new information criterion characterizes the impacts of both model misspecification and high dimensionality on model selection. We further establish the consistency of covariance contrast matrix estimation and the model selection consistency of the new information criterion in ultra-high dimensions under some mild regularity conditions. The numerical studies demonstrate that our new method enjoys improved model selection consistency compared to its main competitors.

scholarly journals Comparison of Frequentist and Bayesian Generalized Linear Models for Analyzing the Effects of Fungicide Treatments on the Growth and Mortality of Piper Nigrum

Agronomy ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 2524
Author(s):  
Bao V. Q. Le ◽  
Anh Nguyen ◽  
Otto Richter ◽  
Truc T. Nguyen
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
Piper Nigrum ◽  
Foot Rot ◽  
Multiple Treatment ◽  
Combined Application ◽  
Rot Disease ◽  
Pepper Plants

Foot rot disease poses a devastating threat to pepper agriculture. In Vietnam, conventionally, fungicides are the control methods used against the disease. However, the practical effectiveness of fungicide treatment has yet to be quantitatively assessed. To fill this gap a three-factorial experiment was conducted, the factors of which were fungicide application, soil type, and infection pathway, with plant mortality and plant growth as the target variables. Two of the most common fungicides were chosen, including Agrifos 400 (potassium phosphonate) and Aliette 800WG (fosetyl-Al). The two fungicides were used in multiple treatment plans, with soil drenching selected as the means of controlling foot rot disease on red basalt soil and red basalt soil added with organic matter in a greenhouse experiment. Three-month-old pepper (Piper nigrum) plants were treated with Agrifos (application interval of 10 and 20 days), Aliette (application interval of 30 and 60 days), and a combination of both fungicides at half doses. Pepper plants were infected with the fungus Pythium spp. from soil or by direct inoculation. To assess the effect of fungicides on foot rot mortality and the growth of pepper plants, multiple generalized linear models were set up using frequentist and Bayesian approaches. Generally, both procedures suggest the same conclusions for model selection in terms of the Akaike information criterion (AIC) and the deviance information criterion (DIC). Fungicide type was found to be the main factor that affected the survival of plants. Most of the treatments (except Aliette, with an interval of 60 days) effectively reduced the mortality. The usage of fungicides affected the growth of plants in interaction with soil types. Aliette suppressed the growth of plants, especially on red soil, while Agrifos had no effect on the growth of pepper plants. The combined application of Agrifos and Aliette with half doses proves to be a promising solution for balancing cost and effectiveness in protecting plants against foot rot pathogens without affecting their growth. In our case, under the inhomogeneity of variance and unbalanced samples, the Bayesian inference appeared to be the most useful because of its flexibility in terms of model structure.

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

scholarly journals Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates

2021 ◽  
pp. 096228022110082
Author(s):  
Yang Li ◽  
Wei Ma ◽  
Yichen Qin ◽  
Feifang Hu
Keyword(s):  
Generalized Linear Models ◽  
Treatment Effect ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Asymptotic Results ◽  
Adaptive Randomization ◽  
Adjustment Method ◽  
Inflated Type

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

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