Regression analysis of logistic model with latent variables

We propose a joint modeling approach to investigating the effects of social-psychological factors on the onset of depression. The proposed model comprises two components. The first one is a confirmatory factor analysis model that summarizes latent factors through multiple correlated observed variables. The second one is a logistic regression model that investigates the effects of observed and latent influence factors on the occurrence of depression. We develop a hybrid procedure based on the borrow-strength estimation procedure and the weighted score function to estimate the model parameters. The asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the method we proposed performs well. An application to a study concerning the social-psychological factors of depression is provided.