We consider an ordinal regression model with latent variables to investigate the effects of observable and latent explanatory variables on the ordinal responses of interest. Each latent variable is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a Bayesian adaptive lasso procedure to conduct simultaneous estimation and variable selection. Nice features including empirical performance of the proposed methodology are demonstrated by simulation studies. The model is applied to a study on happiness and its potential determinants from the Inter-university Consortium for Political and Social Research.