Estimation Of Generalized Linear Models With A Mixture Of Classical And Berkson Errors

Variable error model has been applied in many fields such as medicine,biostatistics and sociology.For example,in medicine and biostatistics,when the independent variables are measured,the results often have measurement errors,so the traditional methods of estimation such as the least squares estimation and maximum likelihood are not applicable,because the parameter estimation using these methods are usually biased and inconsistent.In general,there are three types of variable errors,classical,Berkson,and a mixture of Berkson and classical variable error.In this paper,we mainly study the parameter estimation of generalized linear model with mixed variable error.At the beginning of the paper,firstly we give parameter estimation methods--instrumental variable method and corrected likelihood method in the model with classical variable error.The numerical simulation method is used to compare the two kinds of estimation results.Secondly,the parameter estimation methods--the least squares method in the model with Berkson variable model is given,and this method is verified by numerical simulation.Finally,the parametric estimation methods--factor scores method and corrected likelihood method in generalized linear model with mixed variable error is given.Factor scores method is to estimate parameter by estimating the true variable,so it has low requirement for the model,but it also has limitation,which has high requirement for distribution of variable error.The corrected likelihood method is only for the generalized linear model,but it has low requirement for distribution of variable error.Then R software is used to simulate the data with different error variance and sample size,and a good simulation result is obtained.Therefore,for the generalized linear model with mixed variable error,the result of the parameter estimation can be obtained by factor scores method and corrected likelihood method.