scholarly journals Conditions for Consistency of a Log-Likelihood-Based Information Criterion in Normal Multivariate Linear Regression Models under the Violation of the Normality Assumption

2015 ◽  
Vol 45 (1) ◽  
pp. 21-56 ◽  
Author(s):  
Hirokazu Yanagihara
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Information Criterion ◽  
Multivariate Linear Regression ◽  
Linear Regression Models ◽  
Normality Assumption ◽  
Log Likelihood

scholarly journals Bayesian model evidence as a practical alternative to deviance information criterion

2018 ◽  
Vol 5 (3) ◽  
pp. 171519 ◽  
Author(s):  
C. M. Pooley ◽  
G. Marion
Keyword(s):  
Linear Regression ◽  
Bayesian Model ◽  
Regression Models ◽  
Deviance Information Criterion ◽  
Information Criterion ◽  
The Other ◽  
Model Choice ◽  
Linear Regression Models ◽  
True Model ◽  
Model Evidence

While model evidence is considered by Bayesian statisticians as a gold standard for model selection (the ratio in model evidence between two models giving the Bayes factor), its calculation is often viewed as too computationally demanding for many applications. By contrast, the widely used deviance information criterion (DIC), a different measure that balances model accuracy against complexity, is commonly considered a much faster alternative. However, recent advances in computational tools for efficient multi-temperature Markov chain Monte Carlo algorithms, such as steppingstone sampling (SS) and thermodynamic integration schemes, enable efficient calculation of the Bayesian model evidence. This paper compares both the capability (i.e. ability to select the true model) and speed (i.e. CPU time to achieve a given accuracy) of DIC with model evidence calculated using SS. Three important model classes are considered: linear regression models, mixed models and compartmental models widely used in epidemiology. While DIC was found to correctly identify the true model when applied to linear regression models, it led to incorrect model choice in the other two cases. On the other hand, model evidence led to correct model choice in all cases considered. Importantly, and perhaps surprisingly, DIC and model evidence were found to run at similar computational speeds, a result reinforced by analytically derived expressions.

Influence Diagnostics for Elliptical Multivariate Linear Regression Models

2003 ◽  
Vol 32 (3) ◽  
pp. 625-641 ◽  
Author(s):  
José A. Díaz-García ◽  
Manuel Galea Rojas ◽  
Víctor Leiva-Sánchez
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Multivariate Linear Regression ◽  
Linear Regression Models ◽  
Influence Diagnostics

Different Depths May Not Determine the Fluid Resuscitation Volume in Early-stage Management of Severe Burns: a Model-Comparison Retrospective Analysis of Fluid Volume Determining Factors

2021 ◽  
Author(s):  
Fanggang Ning ◽  
Huihao Jiang ◽  
Jiaming Qiu ◽  
Lifang Wang
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Early Stage ◽  
Information Criterion ◽  
Ratio Test ◽  
Stage Management ◽  
Linear Regression Models ◽  
Severe Burns ◽  
Different Depths ◽  
Paired T Test

Abstract Background Large-volume fluid resuscitation remains irreplaceable in the early-stage management of severe burns. We aimed to explore the relationship between fluid volume and other indicators. Method Data of severe burn patients with successful resuscitation in the early stage was collected. Correlation and linear regression analyses were performed. Multiple linear regression models, related goodness-of-fit assessment (adjusted R-square and Akaike Information Criterion), scatter plots and paired t-test for two models, and a likelihood ratio test were performed. Results 96 patients were included. The median of total burn area (TBA) was 70%TBSA, with full thickness burn area (FTBA)/TBA of 0.4, a resuscitation volume of 1.93 mL/kg/%TBSA. Among volume-correlated indicators, two linear regression models were established (Model 1: TBA × weight and tracheotomy; and Model 2: FTBA × weight, partial thickness burn area (PTBA) × weight, and tracheotomy). For these models, close values of Akaike Information Criterion, adjusted R-squares, outliers of the prediction range, and the result of paired t-test, all suggest similarity between two models estimations, while the likelihood ratio test for coefficients of FTBA × weight and PTBA × weight showed a statistical difference. Conclusion inhalational injury and decompression surgery only correlated with volume, while Tracheotomy, TBA × weight, FTBA × weight, and PTBA × weight correlated with and were accepted in linear models of volume. Although FTBA and PTBA differed statistically, there may be no need to distinguish them when estimating the resuscitation volume requirements in this patient set. Further study about different depths fluid should be conducted.

Sign in / Sign up

Export Citation Format

Share Document