Logistic Regression Modeling with Dichotomous Dependent Variables

A New Type of Model… • Dichotomous Dependent Variable: – Why did someone vote for Bush or Kerry? – Why did residents own or rent their houses? – Why do some people drink alcohol and others don’t? – What determined if a household owned a car?

Dependent Variable… • Is binary, with a yes or a no answer • Can be coded, 1 for yes and 0 for no. • There are no other valid responses. 0510152025 V2-0.3 0.0 0.3 0.6 0.9 1.2 1.5 V A R 0 0 0 0 1

Problem: OLS Regression does not model the relationship well 0510152025 V2-0.3 0.3 0.9 1.5 V A R 0 0 0 0 1

Solution:Use a Different Functional Form • The properties we need: – The model should be bounded by 0 and 1 – The model should estimate a value for the dependent variable in terms of the probability of being in one category or the other, e.g., a owner or renter; or a Bush voter or Kerry voter

Solution, cont. • We want to know the probability, p, that a particular case falls in the 0 or the 1 category. • We want to derive a model which gives good estimates of 0 and 1, or put another way, that a particular case is likely to be a 0 or a 1.

Solution:A Logistic Curve -5-4-3-2-1012345 V50.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

The Logistic Function • Probabilitythat a case is a 0 or a 1 is distributed according to the logistic function.

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