The partial observability probit model is a statistical model for discrete outcomes caused by a complex combination of multiple latent factors. It is useful for political science research because political scientists often study interactions of unobservable decision making by several actors or survey responses resulted from a mixture of psychological factors, and because outcomes are recorded as a discrete variable in many cases of political science. I introduce this model as well as its underlying models, and its application and extension in political science literature. In addition, I developed an applied model with partial observability for the study of the survey responses on ideological self-identification. Ideological self-identification is measured by where a respondent place oneself on a discrete ideological scale, and can be decomposed into three latent factors: recognition, extremity, and direction. The new model can be estimated by Markov chain Monte Carlo methods. I applied my model to Japanese opinion poll data. An information criteria judged my model was superior to the previous ones, and I found some results that could not be led by the previous models.
