Heteroscedastic Tobit Regression

Gaussian regression models with a response variable left-censored at zero and both distribution parameters (the latent location $\mu_i$ and scale $\sigma_i$) can depend on covariates, e.g.,

$y_i^* \sim \mathcal{N}(\mu_i = 0.0 + 1.0 \cdot x_i, \sigma_i = \exp(0.0 - 1.0 \cdot x_i))$

$y_i = \max(0, y_i^*)$