Regression Analysis Of Joint Model With Latent Variables And Unordered Categorical Variables

In psychological and medical studies,the joint model with latent variables is often used to analyze data with highly correlated variables.In the existing literature of joint model with latent variables,the response variables of interest are continuous variables or censored survival time.The research is still lacking in the case of unordered categorical response variables.Joint models with unordered categorical response and latent variables are proposed in this dissertation,including binary classification and multi-classification cases.The joint models include two or three models,the first one of the proposed joint model in this dissertation is used to extract the information of latent variables from observed variables;the second one is a binary logistic regression model or a multinomial logistic regression model,which is used to investigate the observable and latent factors that affect the response variables of interest.When the missing data mechanism of the variables is nonignorable,the third one is a model of missing data mechanism in the binary classification.A joint logistic regression model with latent variables is established based on binary classification and multi-classification cases respectively.A weighted score function is corrected based on the borrow-strength idea.The corrected weighted score function is used to conduct the statistical inference on the parameters.The asymptotic properties of the proposed estimators are established and proved in this dissertation which perform well.Statistical simulation studies show that the proposed method performs satisfactorily with limited samples.The proposed joint model and inference method are applied to investigating the effects of social-psychological factors on the onset of depression and the influencing factors of multiple complications in Type 2 diabetic patients respectively,and constructive results are obtained.In the case of missing data exists in the observed variables in factor analysis model,a model of missing not at random mechanism is added to the joint logistic regression model with latent variables.Bayesian approach coupled with Hamiltonian Monte Carlo method is developed to conduct statistical inference.The performance of the proposed method is demonstrated through statistical simulation.The case where the missing data is missing at blocks is further considered in the practical applications.The proposed model and method are applied to depression data with missing variables.One of the main contributions of this dissertation is the innovation in the model.The three types of joint model are all motivated by the real data analysis in the psychological and medical studies.The observed or latent variables influencing the unordered categorical response are analyzed.The observed variables related to the latent variables with missing data are also analyzed.The second contribution is the innovation in the inference method,which solves the problem that the score function of the logistic regression joint model with latent variables cannot be corrected.The parameter estimates with asymptotic properties are obtained based on the weighted score function.