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Built-in models_Tobit regression
!Model 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 \(e_{i}\sim N(0,\sigma^{2})\).
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. Last changed: 2024/12/10 23:04
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