Bayesian analysis of covariance under inverse Gaussian model

Abstract

This paper considers the problem of analysis of covariance (ANCOVA) under the assumption of inverse Gaussian distribution for response variable from the Bayesian point of view. We develop a fully Bayesian model for ANCOVA based on the conjugate prior distributions for parameters contained in the model. The Bayes estimator of parameters, ANCOVA model and adjusted effects for both treatments and covariates along with predictive distribution of future observations are developed. We also provide the essentials for comparing adjusted treatments effects and adjusted factor effects. A simulation study and a real world application are also performed to illustrate and evaluate the proposed Bayesian model.

Keywords:

• Bayesian analysis
• analysis of covariance
• inverse Gaussian
• covariate
• factor

AMS Classifications:

• 62F15
• 62J10

JEL Classifications:

• C51
• C30

Disclosure statement

No potential conflict of interest was reported by the authors.