Locally A-optimal Design for Poisson Regression Model with Two Parameters | ||||
| The Egyptian Statistical Journal | ||||
| Volume 69, Issue 1, June 2025, Page 206-222 PDF (1.34 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2025.362653.1074 | ||||
 View on SCiNiTO | ||||
| Author | ||||
Tofan Kumar Biswal  
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| Ph.D. Scholar, Department of Statistics, Central University of Odisha, Koraput, India | ||||
| Abstract | ||||
| Generalized linear model (GLM) which is regarded as an extension of standard linear regression in that it allows continuous or discrete data from one-parameter exponential family distributions to be paired with explanatory variables using appropriate link functions. Generalized linear models include several types such as Poisson, Gamma, Logistic models among others. Generalized linear models are generally utilized in studies when the responses are categorical type, however in the case of count data, the investigator proceeds to the Poisson model.An algebraic method for constructing A-optimal design for two parameters Poisson regression model including intercept parameter is presented. As we know, the Fisher information matrix depends on the unknown parameters of the model. In such a case, an experimenter must take the strategy of discovering local optimal designs, that is, first predict the best value for the parameters and then compute the optimal designs. The support points and weights are calculated numerically through Mathematica software. Also, the necessary and sufficient conditions of this optimality criterion are confirmed through the equivalence theorem. | ||||
| Keywords | ||||
| Poisson regression model; Local optimal design; Fisher information matrix; A-optimal design; Equivalence theorem | ||||
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