Bayesian Latent Regression Model And Variable Selection

This article focuses on the Bayesian variable selection problem of latent regression model coefficients under the three-parameter logistic item response model.Firstly,a latent regression model is established by nesting the three-parameter logistic item response model in a linear model.The model takes the latent traits of individuals as dependent variables and observed variables such as gender and socio-economic status as independent variables.Secondly,the Pólya-Gamma distribution-based data augmentation method is introduced to introduce latent variables.Three types of compressed priors(Laplace,horseshoe,and horseshoe+)are then used to perform Bayesian parameter estimation and variable selection on the latent regression coefficients.Thirdly,the performance of the proposed Gibbs sampling method is evaluated by comparing it with the traditional Metropolis-Hasting algorithm through simulation studies.The results demonstrate that the Gibbs estimation method is more efficient and flexible than the Metropolis-Hasting algorithm.Finally,the effectiveness and practicality of the proposed latent regression model and estimation method are verified by analyzing the data from the 2018 PISA mathematics assessment test.