Abstract

Analysis of variance (ANOVA) literature is antique and based on restrictive assumptions. Hence, existing models are inappropriate for correctly analyzing complex and diverse data. This paper focuses on developing flexible models for analyzing ANOVA-type data using a Bayesian nonparametric inference approach to circumvent such limitations. Specifically, our strategy considers the definition of latent binary variables, which identify each treatment level with different random distributions. These distributions are modeled via infinite mixture models, where the mixing distributions follow a dependent Dirichlet process with shared weights. In our specification, the binary latent variables map the hypotheses. Then, the prior distribution on the hypothesis space is defined with a distribution over the binary vector. In summary, we relax the classical ANOVA assumptions and propose models for testing ANOVA-related hypotheses considering data in different supports. Our methodology is implemented in an R-package called ANOVABNPTestR, which provides easy-to-use functions for continuous, counting, and binary outcomes.