Tobit model refers to a kind of model in which the dependent variable is approximately continuously distributed in a positive value, but contains some observations with a positive probability of 0.

For example, in any year, a considerable number of families' medical insurance costs are zero. Therefore, although the overall distribution of annual family medical insurance expenses is scattered in a larger positive range, it is quite concentrated on the number 0. Also called censored regression model or censored regression model, it belongs to a finite dependent variable regression. Restricted dependent variable means that the observed value of the dependent variable is continuous, but subject to some restrictions, the observed value obtained can not fully reflect the actual state of the dependent variable. It mainly includes truncated regression model, tobit model and sample selection model.

The classic Tobit model is james tobin's generalization of Probit regression when analyzing household durable goods expenditure (the word Tobit comes from Tobin's Probit), and then it is extended to many situations, and Amelia classifies it into I-type to V-type Tobit models.