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 ...
The Tobit Model • The estimated tobit coefficients are the marginal effects of a change in xj on y*, the unobservable latent variable and can be interpreted p in the same way y as in a linear regression model. • But such an interpretation may not be useful since we are interested in the effect of X on the observable y (or change in the censored outcome). – It can bbe shown h th that t change h iin y iis found f d by b multiplying lti l i the coefficient with Pr(a
Illustrations for logit, probit and tobit models, using womenwk.dta from Baum available at http://www.stata-press.com/data/imeus/womenwk.dta Descriptive Statistics N Minimum Maximum Mean Std. Deviation age 2000 20 59 36.21 8.287 education 2000 10 20 13.08 3.046 married 2000 0 1 .67 .470 children 2000 0 5 1.64 1.399 wagefull 2000 -1.68 45.81 21.3118 7.01204 wage 1343 5.88 45.81 23.6922 6.30537 lw 1343 1.77 3.82 3.1267 .28651 work 2000 0 1 .67 .470 lwf 2000 .00 3.82 2.0996 1.48752 Valid N (listwise) 1343 Binary Logistic Regression Step -2 Log likelihood Model Summary Cox & Snell R Square Nagelkerke R Square 1 2055.829 a .212 .295 a. Estimation terminated at iteration number 5 because parameter estimates changed by less than .001. Hosmer and Lemeshow Test Step Chi-square df Sig. 1 6.491 8 .592 Variables in the Equation B S.E. Wald df Sig. Exp(B) Step 1 a age .058 .007 64.359 1 .000 1.060 education .098 .019 27.747 1 .000 1.103 married .742 .126 34.401 1 .000 2.100 children .764 .052 220.110 1 .000 2.148 Constant -4.159 .332 156.909 1 .000 .016 a. Variable(s) entered on step 1: age, education, married, children.
- 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 and 12: Ordinal Logistic - a a11, a a22, a
- Page 13 and 14: The Tobit Model • The model is ca
- Page 15: The Tobit Model • The Tobit model
- Page 19: Tobit regression Number of obs = 20
Illustrations <strong>for</strong> logit, probit <strong>and</strong> tobit models, using womenwk.dta from Baum available at<br />
http://www.stata-press.com/data/imeus/womenwk.dta<br />
Descriptive Statistics<br />
N Minimum Maximum Mean Std. Deviation<br />
age 2000 20 59 36.21 8.287<br />
education 2000 10 20 13.08 3.046<br />
married 2000 0 1 .67 .470<br />
children 2000 0 5 1.64 1.399<br />
wagefull 2000 -1.68 45.81 21.3118 7.01204<br />
wage 1343 5.88 45.81 23.6922 6.30537<br />
lw 1343 1.77 3.82 3.1267 .28651<br />
work 2000 0 1 .67 .470<br />
lwf 2000 .00 3.82 2.0996 1.48752<br />
Valid N (listwise) 1343<br />
Binary Logistic Regression<br />
Step<br />
-2 Log likelihood<br />
Model Summary<br />
Cox & Snell R<br />
Square<br />
Nagelkerke R<br />
Square<br />
1 2055.829 a .212 .295<br />
a. Estimation terminated at iteration number 5 because<br />
parameter estimates changed by less than .001.<br />
Hosmer <strong>and</strong> Lemeshow Test<br />
Step Chi-square df Sig.<br />
1 6.491 8 .592<br />
Variables in the Equation<br />
B S.E. Wald df Sig. Exp(B)<br />
Step 1 a age .058 .007 64.359 1 .000 1.060<br />
education .098 .019 27.747 1 .000 1.103<br />
married .742 .126 34.401 1 .000 2.100<br />
children .764 .052 220.110 1 .000 2.148<br />
Constant -4.159 .332 156.909 1 .000 .016<br />
a. Variable(s) entered on step 1: age, education, married, children.
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