Logit, Probit and Tobit: Models for Categorical and Limited ...

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Introduction • In social science research research, categorical data are often collected through surveys. – Categorical g Nominal and Ordinal variables – They take only a few values that do NOT have a metric. • A) ) Binary yCase • Many dependent variables of interest take only two values (a dichotomous variable), denoting an event or non-event and coded as 1 and 0 respectively. Some examples: – The labor force status of a person. – Voting behavior of a person (in favor of a new policy). – Whether a person got married or divorced. – Whether a person involved in criminal behaviour, etc.
Introduction • With such variables variables, we can build models that describe the response probabilities, say P(yi = 1), of the dependent p variable y yi. i – For a sample of N independently and identically distributed observations i = 1, ... ,N and a (K+1)-dimensional vector x′ i of f explanatory l t variables, i bl the th probability b bilit th that t y tk takes value l 1 is modeled as P ( yi = 1| xi ) = F ( xi′ β ) = F ( zi where β is a (K + 1)-dimensional column vector of parameters. • The transformation function F is crucial. It maps the linear combination into [0,1] and satisfies in general F(−∞) =0 = 0, F(+∞) = =1 1, and andδF(z)/δz δF(z)/δz > 0 [that is is, it is a cumulative distribution function]. )
Page 1: Logit, Probit and Tobit: Models for
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 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

Logit, Probit and Tobit: Models for Categorical and Limited ...

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