The function receives the model information, as well as the variable response and the predicted theta values and calculates the model's pseudo.r.squared, using the formula proposed by Cribarri-Neto and Ferrari.
pseudo.r.squared(x)an object of the class bayesbr, containing the list returned from the bayesbr function.
A number containing the pseudo r squared of the adjusted model, this value can be used to assess the quality of the model.
Ferarri and Cribari-Neto (2004) defined the pseudo.r.squared as the square of the correlation between the theta estimated by the maximum likelihood and the logis of the variable response of the model. But as we are in the context of Bayesian statistics, the estimated theta is given by the mean of the posterior distribution of the parameter. So the informed pseudo.r.squared is a Bayesian adaptation to what was suggested by Ferarri and Cribari-Neto (2004).
10.1080/0266476042000214501 Ferrari, S., & Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of applied statistics, 31(7), 799-815.