After estimating a logit model for the likelihood of a website visitor clicking through conditional on if the visit occurred on a weekday or not, you get the following results: ClickThrough_i = -1.2(0.4) + 0.8(0.2)WeekDay_i, where standard errors are reported in parenthesis. What would be the calculation that yields the marginal effect of a visit moving from a weekend to a weekday on click-throughs? A) -1.2 + 0.8 = -0.4 B) 0.8 C) $\frac { 1 } { 1 + e ^ { - 1.2 + 0.8 } }$ D) $$\frac { 1 } { 1 + e ^ { - 1.2 + 0.8 } }$$ - $$\frac { 1 } { 1 + e ^ { - 1.2 } }$$

Question

Quizplus · Accepted Answer

The marginal effect of a visit moving from a weekend to a weekday on click-throughs is given by the equation: $$\frac { ∂P(Y = 1|Weekday = 1) } { ∂Weekday }$$ This can be calculated using the following formula: $$\hat { β }_{ Weekday }\hat { P }(Y = 1|Weekday = 1)\hat { (1 - \hat { P }(Y = 1|Weekday = 1)) }$$ where $$\hat { β }_{ Weekday }$$ is the coefficient estimate for the Weekday variable from the logit model, $$\hat { P }(Y = 1|Weekday = 1)$$ is the predicted probability of a click-through given that the visit occurred on a weekday (calculated using the logit model), and $$\hat { (1 - \hat { P }(Y = 1|Weekday = 1)) }$$ is the predicted probability of no click-through given that the visit occurred on a weekday. Plugging in the given values, we get: $$\hat { β }_{ Weekday }\hat { P }(Y = 1|Weekday = 1)\hat { (1 - \hat { P }(Y = 1|Weekday = 1)) }$$ = (0.8)($$\frac { 1 } { 1 + e ^ { -1.2 + 0.8 } }]\)(\[\frac { e ^ { -1.2 } } { 1 + e ^ { -1.2 } }$$) = 0.165 Therefore, the answer is D, which calculates the above formula and simplifies it.

After Estimating a Logit Model for the Likelihood of a Website