International Biometric Society Double Generalized Linear Model From a Bayesian Perspective

The variability modelling under experimental designs became popular due to the Genichi Ta-guchi works, that highlights the importance to deal with control and noise factors in industrial experiments, as a way to reduce loss and to optimize the quality of related processes and products. If factors are acting over the variation, the usual normal regression models (that are based on constant variance) will be based on inflated variation measures, guiding to misleading conclusions. For count and proportion data, these noise factors can generate an overdispersion effect, underestimating the variability and, consequently, indicating erroneous significatively effects [3]. Some statistical models were proposed, based on the classical generalized linear models for a joint modelling strategy [4], where the extended quasi-likelihood function was used in the estimation algorithm. However, this approach is highly dependent of asymptotic results and so, large samples are required to produce reliable inference. A Bayesian joint modelling for data with normal distribution that independs of large samples was proposed by [1]. It allows the use of prior knowledge about the control and noise effects and is adequated for many small sample agricultural experiments