Bayesian Analysis Of Mixed Models With Different Type Of Data

Transformation linear mixed model is a generalization of mixed model,the biological medicine,environmental science,education,and many other areas of widely used in the recent years.Transformation mixed model is a powerful tool for studying longitudinal data.Mixed model,which has both fixed effect and random effect,it can reflect the difference between individual or space position;and transformation model can be solve this problem that real data does not meet the normal distribution assumption,so based on longitudinal data and a large scale of spatial data transformation linear mixed model can describe many practical problems,it is a kind of flexible model,it can be applied to different model analysis in the future.This article adopts the method of bayesian penalize spline estimation transformaiton function,using the method of Dirichlet process prior to estimate the distribution of the random effects in transformation linear mixed model under longitudinal data,using multi-resolution wavelet analysis method to estimate non-stationary spatial process in transformation linear mixed model under a large scale of spatial data,in combination with the MCMC calculation method to estimate the parameters in the model,both the simulation results and instance analysis show that transformation linear mixed model is better than the traditional Cox-Box transformation in the accuracy of the model parameter estimation,transformation linear mixed model under longitudinal data Bayesian statistical diagnostic method is studied based on the data deletion model and the local influence analysis model,bayesian model comparison method is studied based on a large scale of spatial data transformation linear mixed model.Both the simulation results and instance analysis show that bayesian statistical diagnosis method can well identify outlier in the data,and the bayesian model comparison method can well select true model.Mixed structural equation model is a generalization of the structural equation model.Hidden markov mixed structural equation model can solve many practical problems with large scale data,especially in psychology and environmental science.In this paper,an hidden markov model is used to process the a large scale of spatio-temporal data set and estimate the structural equation model in different states,and the non-stationary spatial process is estimated by multi-resolution wavelet analysis,the relationship between the transition probability of the state is described by using the continuous ratio logit mixed model,in combination with the MCMC calculation method to estimate the parameters and the value of hidden state in the model,both the simulation results and instance analysis show that Bayesian analysis method can well estimate parameter of model.