Bayesian Analysis Of Longitudinal Proportion Data

Longitudinal proportional data is a kind of data with repeated observation values between [0,1] and widely exists in the fields of economics and medicine.In this paper,three models(based on Beta distribution,logistic-normal distribution and Simplex distribution respectively)were used to analyze the longitudinal proportional data by Bayesian method.Besides,BIC(Bayesian information Criterion)and DIC(deviation information criterion)were used to compare and obtain the optimal mode for the purpose of improving the efficiency and effect of statistical inference.Using numerical simulation and example analysis to verify the feasibility of the model and method proposed by this paper.First,Calling WinBUGS to fit the simulation data based on three distributions and generated in R.Checking the convergence of parameters,comparing the fitted value and true value and verifying the rationality of the model in the WinBUGS.Determining the models that different types of data are relatively suitable for by comparing the values of BIC(Bayesian information criterion)and DIC(deviation information criterion)of different models.Then,an exploratory analysis was conducted on a group of ophthalmic treatment data.Using R language to draw its nuclear density distribution.It was assumed that optimal model was based on Beta distribution with its nuclear density distribution is similar with Beta(1,0.5).Then,Analyzing the ophthalmology data through WinBUGS and fitting it in three models respectively,comparing the fitted values of the parameters and standard deviation,BIC(Bayesian information criterion),DIC(deviation information criterion).Eventually,the conclusion that the optimal model was a model based on Beta distribution were drawn,which is the same as the expected assumption and shows the feasibility of this method.In sum up,Different distribution models can be used to obtain better analysis results for different types of longitudinal ratio data.Among the three existing models,the optimal model is selected for statistical inference based on the analysis of the data.