I have been using the crch
package for modelling censored data with the tobit model. I noticed early on that the errors (by far) are not normally distributed by means of QQ-plot. Furthermore, I know from earlier posts on cross-validated that the Breusch-Pagan test was not option to test for heteroscedasticity. So I chose to employ two models (one with conditional heteroscedasticity, and the other without). After that I looked to see if there is a big difference in AIC to see if conditional heteroscedasticity is statistically present.
Now, I would like to fully understand what a conditional heteroscedasticity tobit model really is? Does it assume that if X (explonatory variables) increases, the scale (sigma) of heteroscedasticity increases as well? Does the crch model impose a linear scaling between X and sigma?