Tobit with non-zero truncation is a statistical model used to analyze data where the dependent variable is censored or truncated at a certain value, typically zero. This model is often used in economics and social sciences to account for situations where a variable of interest cannot be directly observed or measured.
Regular Tobit model assumes that the dependent variable is either fully observed or fully censored at a specific threshold, while Tobit with non-zero truncation allows for a non-zero threshold and accounts for observations that are only partially censored. This makes it a more flexible and realistic model for many real-world situations.
Tobit with non-zero truncation should be used when the dependent variable has a non-normal distribution and is censored or truncated at a specific value, but not necessarily at zero. This model is particularly useful when analyzing data with a large number of observations at the threshold value, as in the case of income or expenditure data.
Tobit with non-zero truncation is typically estimated using maximum likelihood estimation, where the likelihood function is derived based on the censored and uncensored portions of the data. This method takes into account the censoring mechanism and provides consistent estimates of the model parameters.
One limitation of Tobit with non-zero truncation is that it assumes a linear relationship between the dependent variable and the explanatory variables. This may not always be the case in real-world data. Additionally, the model relies on the assumption that the censoring mechanism is independent of the outcome variable, which may not always hold true.
