Logit, Probit and Tobit: Models for Categorical and Limited ...
Logit, Probit and Tobit: Models for Categorical and Limited ... Logit, Probit and Tobit: Models for Categorical and Limited ...
Model for Limited Dependent Variable • C) Tobit Model • This model is for metric dependent variable and when it is “limited” limited in the sense we observe it only if it is above or below some cut off level. For example, – the wages g may ybe limited from below by y the minimum wage – The donation amount give to charity – “Top coding” income at, say, at $300,000 – Time use and leisure activity of individuals – Extramarital affairs • It is also called censored regression model. Censoring can be from below or from above, also called left and right censoring. [Do not confuse the term “censoring” with the one used in dynamic modeling.]
The Tobit Model • The model is called Tobit because it was first proposed by Tobin (1958), and involves aspects of Probit analysis – a term coined by Goldberger for Tobin’s Probit. • Reasoning behind: – If we include the censored observations as y = 0, the censored d observations b i on the h lleft f will ill pull ll down d the h end d of f the line, resulting in underestimates of the intercept and overestimates of the slope. p – If we exclude the censored observations and just use the observations for which y>0 (that is, truncating the sample), it will overestimate the intercept and underestimate the slope. – The degree g of bias in both will increase as the number of observations that take on the value of zero increases. (see Figure next slide)
- Page 1 and 2: Logit, Probit and Tobit: Models for
- Page 3 and 4: Introduction • With such variable
- Page 5 and 6: Source: J.S. Long, 1997
- Page 7 and 8: The Logit and Probit Models • Not
- Page 9 and 10: Models for Polytomous Data • B) P
- Page 11: Ordinal Logistic - a a11, a a22, a
- Page 15 and 16: The Tobit Model • The Tobit model
- Page 17 and 18: Illustrations for logit, probit and
- Page 19: Tobit regression Number of obs = 20
Model <strong>for</strong> <strong>Limited</strong> Dependent Variable<br />
• C) <strong>Tobit</strong> Model<br />
• This model is <strong>for</strong> metric dependent variable <strong>and</strong><br />
when it is “limited” limited in the sense we observe it only if<br />
it is above or below some cut off level. For example,<br />
– the wages g may ybe limited from below by y the minimum<br />
wage<br />
– The donation amount give to charity<br />
– “Top coding” income at, say, at $300,000<br />
– Time use <strong>and</strong> leisure activity of individuals<br />
– Extramarital affairs<br />
• It is also called censored regression model. Censoring<br />
can be from below or from above, also called left <strong>and</strong><br />
right censoring. [Do not confuse the term “censoring”<br />
with the one used in dynamic modeling.]
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