Journal of Statistics: Advances in Theory and Applications
EXPERIMENTS WITH BETA RESPONSEAuthor's: LUIS FERNANDO GRAJALES, RAYDONAL OSPINA and LUIS ALBERTO LÓPEZ
Pages: [105] - [130]
Received Date: December 20, 2012
Submitted by:
Many factorial experiments include continuous responses restricted to
the interval 
such as percentages, rates and indices
mainly found in industry and medicine. In order to explain the
response for some factors, usually the analysis of variance (ANOVA) is
the most common technique because the response is considered normally
distributed. However, normality and constant variance for errors is
difficult to achieve for response in 
This paper used beta regression models from
frequentist and Bayesian perspectives to estimate mean response for
factorial experiments with response in
The methodology is also compared with
normal regression models. Numerical results exhibit that coverage of
intervals with logit transformation was as good as the best function
link for beta regression. Also, Bayesian and frequentist lengths of
intervals are similar for logit link. The Bayesian model with probit
link presented the worst performance with respect to lengths of
intervals.
Bayesian analysis, beta regression model, confidence intervals, experimental design, fractional factorial, rates, transformations.
