The R-optimal Design Of The Logistic Regression Model

In recent years,research on the optimal design of generalized linear models has been continuously developed.Considering that the logistic regression model in the generalized linear model is widely used in the academic fields such as clinical research,epidemiology and predictive medicine,this dissertation starts from the logistic regression model with fixed intercept and random intercept,and constructs the corresponding model R-optimal design Solution method.In the fixed intercept logistic regression model,consider the single factor and two factors.First,the directional derivative theory is used to write specific sensitivity functions,and the general equivalence theorem of R-optimal criteria is deduced,an iterative algorithm for R-optimal design is constructed,and then the initial parameters?₁ are taken for the single-factor model.Given the initial design of the two design points,an iterative algorithm is used to solve the R-optimal design under the design,and the reliability and accuracy of the verification results are plotted.Also select the initial parameters?₁,?₂ in the two-factor model and give the initial design of nine design points,use the same method to solve the R-optimal design under the design,and use image verification.Finally,the R-efficiency of the fixed-interval logistic regression model is given.In the random intercept logistic regression model,only the single factor case is considered.The quasi-information matrix is constructed using the covariance matrix based on the parameters of the PQL1 estimation,and the R-optimal criterion function is written.Since the single-layer random intercept model is equivalent to the fixed intercept model,similar to the fixed intercept model,the initial parameters?₁ are set for the single-factor model,the distribution of the random coefficients is set,and the initial design of the two design points is given.An iterative algorithm is used to solve the R-optimal design under the initial design and to verify the reliability and accuracy of the results.The results show that the R-optimal of fixed-intercept and random intercept logistic regression models are both present,and the calculated single-factor model and the R-efficiency of the two-factor model all show that the R-optimal design is better than the initial design.