Research On Parameter Estimation And Application Of Generarlized Linear Model Based On INLA Algorithm

The Nested Laplace Approximation(INLA)algorithm is a method that combines Laplace approximation and modern numerical integration to achieve fast calculations under the Bayesian framework.Because of the obvious advantages of computing speed,it has been applied in many fields.Generalized linear models are widely used in the fields of social science and epidemiology,especially the logistic model and Poisson model.The INLA algorithm is used to estimate the parameters of the two generalized linear models,and the application of this estimation method to the actual field is worth studying.Based on the Bayesian-INLA estimation of the logistic model and the Poisson model,this paper will study the application of the estimation methods of these two generalized linear models.First,according to the Bayesian-INLA estimation idea of the logistic model,the Bayesian-INLA estimation of the multi-parameter logistic model is realized,including Rasch model and 2-parameter logistic model.The multi-parameter logistic model is an important type of model in item response theory,and it plays an important role in the field of education measurement.The Bayesian-INLA estimation of this model is divided into two parts:known and unknown ability parameters.When the ability parameters are known,the parameter estimation process of the two models is transformed into a logistic regression process,and then the INLA algorithm is used to estimate the project parameters in the model;When the ability parameter is unknown,for the Rasch model,a method similar to the spatial-temporal model is adopted,and both the ability parameter and the difficulty parameter are regarded as random effect items,and then the INLA algorithm is used to intervene to obtain the Bayesian-INLA estimator of the Rasch model;For the 2-parameter logistic model,the iterative method is adopted.First,the initial value of the ability is given,and then the project parameters are estimated according to the logistic regression and the INLA algorithm,and then the variable slope model and the INLA algorithm are used to estimate the ability parameters,and iterate repeatedly until the iteration condition is satisfied.Since both logistic regression process and variable slope model can use INLA algorithm to obtain parameter estimators,the estimation is feasible.Through simulation experiments,it can be seen that the accuracy of the Bayesian-INLA estimation of the Rasch model and 2PLM under the known ability parameters is high,but the effect of the Bayesian-INLA estimation under the unknown capacity parameters is not ideal,and further improvements are needed.Second,according to the Bayesian-INLA estimation of the Poisson model,a spatio-temporal disease mapping model was constructed to realize the analysis of the spatiotemporal distribution characteristics of tuberculosis.The Gauss Markov random field required in the INLA algorithm has a good explanation for the neighboring relationship of spatial geographic locations.Using the INLA algorithm can speed up the parameter estimation,effectively solve the problem of high dimensionality and time-consuming,and get the disease characteristics faster.First,the q-statistic is used to detect the spatial stratified heterogeneity of various influencing factors and the interaction between spatial and temporal effects.Then,according to the Poisson model and various influencing factors of tuberculosis,and taking into account the temporal effect,spatial effect and spatial-temporal effect,a spatio-temporal disease mapping model is established,and the parameters of the model are estimated using the INLA algorithm.Finally,according to the parameter estimation results of different effects,the influencing factors and spatialtemporal distribution of tuberculosis are specifically analyzed to provide a scientific basis for formulating prevention and control measures.