Open AccessE-optimal Experimental Designs for Poisson Regression Models in Two and Three Variables
Author(s) -
Emmanuel Idowu Olamide,
Olusoga Akin Fasoranbaku,
Femi Barnabas Adebola
Publication year - 2021
Publication title -
tanzania journal of science/tanzania journal of science
Language(s) - English
Resource type - Journals
eISSN - 2507-7961
pISSN - 0856-1761
DOI - 10.4314/tjs.v47i3.11
Subject(s) - poisson regression , mathematics , design matrix , poisson distribution , statistics , regression analysis , linear regression , generalized linear model , proper linear model , context (archaeology) , variables , variable (mathematics) , logistic regression , regression diagnostic , optimal design , count data , polynomial regression , population , demography , sociology , biology , paleontology , mathematical analysis
In the context of generalized linear models, most of the recent studies were on logistic regression models and many of them focussed on optimal experimental designs with concentration on D-optimality. In this research, two- and three-variable Poisson regression models were considered for E-optimization on restricted design space [0, 1]. The two-variable Poisson regression model was not optimal at 3-design points, but was found to be E-optimal at 4-design points (1, 1), (0, 0), (0, 1) and (1, 0) with equal design weights of 0.25. The three-variable Poisson regression model was E-optimal at 4-design points (0, 0, 1), (0, 1, 0), (1, 1, 1) and (1, 0, 0) with each design point having design weights of 0.25. The prediction error variance (PEV) for the two-variable Poisson regression model is 0.35 and that of the three-variable Poisson regression model is 0.68. From this research, the two-variable Poisson regression model is preferred to the three-variable Poisson regression model because of smaller PEV.
Keywords: E-optimality; Fisher Information Matrix; Poisson Regression Model; Prediction Error Variance