D - Optimal Design Of Multi - Factor Poisson Regression Model

With the rapid development of information in modern society, a large amount of information exists in the form of data, and the diversity of information results in the diversity of data form. The traditional linear model has great limitations in dealing with the discrete data, that requires the use of generalized linear model. Poisson regression model is an important branch of the generalized linear model, which is mainly used to study the count data. The optimal design problem of Poisson regression model has attracted more attention in recent years. Most of the existing researches focus on the quantitative factors in the model, less on the Poisson regression model with qualitative factors. And the design problem of single factor is more simple than multi-factor, its research is relatively mature. So this paper aims to multi factor complex problems into simple single factor and mainly studies on the following two aspects:For the D-optimal problem of the Poisson regression model with many quantitative fac-tors, firstly we eliminate the dependence of the parameters by the canonical transformation of the regression function; then the problem is transformed into the D-optimal design of the part-ly heteroscedastic multi-factor linear additive model; we define a new optimal criterion for the heteroscedastic sub-model, compute the directional derivative to obtain its equivalent condition and construct the algorithm accordingly; lastly prove that the D-optimal design is the product of optimal designs of sub-models, by means of centralized transformation on the regression function and the general equivalence theorem.For the D-optimal problem of multi factor Poisson regression model with both quantitative factors and qualitative factors, firstly we introduced dummy variables by convention; then trans-form the problem into the D-optimal design of the heteroscedastic multi-factor linear additive model with qualitative factors by the canonical transformation; lastly use the conclusion of the first part to solve the problems.Both the two aspects of research indicate that the problem of the design of multi factor Pois-son regression model can be simplified into the single factor design problem. In addition, the two types of problems are demonstrated by examples.