Different approaches to censored or truncated regression with conditional heteroscedasticity are provided. First, continuous distributions can be used for the (right and/or left censored or truncated) response with separate linear predictors for the mean and variance. Second, cumulative link models for ordinal data (obtained by interval-censoring continuous data) can be employed for heteroscedastic extended logistic regression (HXLR). In the latter type of models, the intercepts depend on the thresholds that define the intervals.
