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lect15_103_2010_Compatibility_Mode_

# lect15_103_2010_Compatibility_Mode_ - Interpreting Results...

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5/26/2010 1 Interpreting Results - I How do we interpret results in Probit and Logit models? The estimated Probit regression line is: Since the Bought i is binary, the predicted/expected value of Bought i is equal to the probability that Bought i = 1 (given any value of Price i ). So if Price i =0.70, the results say that the probability of purchase is Φ (-1.37-1.26*0.7) = Φ (-2.25) = 0.012, or 1.2% If Price i =0.60, the probability of purchase is Φ (-1.37-1.26*0.6) = Φ (-2.13) = 0.017, or 1.7% If Price i =1.00, the probability of purchase is Φ (-1.37-1.26*1) = Φ (-2.63) = 0.004, or 0.4% (Note: this is not less than zero like in the LPM!) circumflexnosp4char ( 29 Bought = 1.37 1.26Price i i Φ - - Interpreting Results - II The estimated Logit regression line is: So if Price i =0.70, this says that the probability of purchase is 1/(1+exp(-(-1.91-3.44*0.7))) = 1/(1+exp(4.32)) = 0.013, or 1.3% If Price i =0.60, the probability of purchase is 1/(1+exp(-(-1.91- 3.44*0.6))) = 1/(1+exp(3.97)) = 0.019, or 1.9% If Price i =1.00, the probability of purchase is 1/(1+exp(-(-1.91- 3.44*1))) = 1/(1+exp(5.35)) = 0.005, or 0.5% circumflexnosp4char ( 29 ( 29 1 Bought = 1 exp 1.91 3.44Price i i + - - -

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5/26/2010 2 Interpreting Results - III Note that since both the Probit and Logit models are non-linear (in contrast to the linear probability model, which is linear): 1) The estimated “slope” coefficient β 1 does not directly measure the effect of changing X i on Pr( Y i =1| X i ) (recall that Z i = Pr( Y i =1| X i )) 2) The effect of changing X i on Pr( Y i =1| X i ) varies depending on what X i is. For example, in the above Probit model:
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lect15_103_2010_Compatibility_Mode_ - Interpreting Results...

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