Built-in models_Tobit regression

Model (Edit)

The Tobit model is a model proposed by James Tobin (Tobin, 1958) to describe the relationship between a limited dependent variable \(y_{i}\) and independent variables \(\mathbf{x}_{i}\). This model is widely used in econometrics and biometrics. To better understand the model, we can assume there is a latent (unobservable) variable \(y^{*}\) underlying

the observed variable \(y\). The relationship between \(y^{*}\) and \(y\) is given by

\[ y_{i}=\begin{cases} y_{i}^{*} & \text{if }y_{i}^{*}>\tau \ \tau & \text{otherwise} \end{cases}. \]

In Tobin (1958), the threshold \(\tau=0\). The latent variable can

be predicted using the independent variables as in

\[ y_{i}^{*}=\beta_{0}+\beta_{1}x_{1i}+\ldots+\beta_{q}x_{qi}+e_{i} \]

with \(e_{i}\sim N(0,\sigma^{2})\).

Code(Edit)