A doubly restricted exponential dispersion model. Issue 11 (3rd June 2019)

• Record Type: Journal Article
• Authors: Grajales, Luis Fernando; Ospina, Raydonal; López, Luis A.; Melo, Oscar O.
• Is Part Of: Communications in statistics. Volume 48:Issue 11(2019)
• Page Start: 2827
• Page End: 2841
• Publication Date: 2019-06-03
• Subjects: Beta distribution -- two-parameter exponential family -- generalized linear models -- linear restrictions -- maximum likelihood estimation -- penalized likelihood -- varying dispersion; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1473427
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this paper, we propose and develop a doubly restricted exponential dispersion model, i.e. a varying dispersion generalized linear model with two sets of restrictions, a set of linear restrictions for the mean response, and at the same time, for another set of linear restrictions for the dispersion of the distribution. This model would be useful to consider several situations where it is necessary to control/analyze drug-doses, active effects in factorial experiments, mean-variance relationships, among other situations. A penalized likelihood function is proposed and developed in order to achieve the restricted parameters and to develop the inferential results. Several special cases from the literature are commented on. A simply restricted varying dispersion beta regression model is exemplified by means of real and simulated data. Satisfactory and promising results are found.