Using the output from the initial logit regression (the one not in odds ratio form), calculate the marginal effect of being female on the probability of reporting YES to the question. Do this in each of the three ways we have discussed, and be sure to think about how the interaction term affects your calculation.
Here is the output from the logit:
char literacy[omit] 3 char location[omit] 3 xi: logit part1con1 age female i.location femeduc educ i.literacy
Logit estimates Number of obs = 1739
LR chi2(8) = 615.77
Prob > chi2 = 0.0000
Log likelihood = -831.79169 Pseudo R2 = 0.2702
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part1con1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.1287028 .0071621 -17.97 0.000 -.1427402 -.1146655
female | -1.33864 .3525716 -3.80 0.000 -2.029667 -.6476121
_Ilocation_1 | .1567167 .1425106 1.10 0.271 -.1225989 .4360323
_Ilocation_2 | .1860074 .158996 1.17 0.242 -.125619 .4976338
femeduc | .0934957 .036732 2.55 0.011 .0215024 .1654891
educ | .0273958 .0254095 1.08 0.281 -.022406 .0771975
_Iliteracy_1 | 1.271578 .4779464 2.66 0.008 .3348202 2.208336
_Iliteracy_2 | .7676351 .4840312 1.59 0.113 -.1810485 1.716319
_cons | 3.422056 .5161311 6.63 0.000 2.410457 4.433654
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Calculating the marginal effect of being female is a little more tricky in this case, because female enters additively and multiplicatively with education. Intuitively, what this means is that the effect of being female will be different, at different levels of education. Since the interaction term is positive but the female coefficient is negative, we will expect females with no education to be more likely to report NO to the question than men with no education, and we will expect females with lots of education to be less likely to report NO than females with much lower levels of education. (This is a long sentence, but think of it like this: a woman with 12 years of education will be less likely to report NO than a woman with 0 years of education, even though both of them may still be more likely to report NO than an otherwise similar man with the same education).
The formula we will use is an adaptation of the one in the module:
dY/d(fem)
= F(Xb)(1-F(Xb))*btotal female effect
= F(Xb)(1-F(Xb))*(bfemale + bfemeduc*education)
{Note: if you are comfortable with calculus, you can compute this derivative the same way as we did before}
Already, you can see in this formula that the marginal effect of being female is different for different levels of education.
1. Using the sample mean for F(Xb) and for educ.
summ part1con1 /*here, we need the mean of part1con1 for our calculation*/ summ educ /*from this command, we get the mean of years of school*/
We ask Stata to do the relevant calculation for us, by using the di command (this is for display). Anything in quotation marks after this command is given will be displayed on the screen directly, and anything not in quotation marks will be evaluated to an expression, and the answer is displayed on the screen, as in the following syntax:
di "the marginal effect using sample means is " .5754625*(1-.5754625)*(-1.33864+.0934957*8.078016)
The output is:
the marginal effect using sample means is -.14252295
Thus, the marginal effect using sample means is -.14252285: this means that women with an average level of education are about 14% less likely to report YES than men with the same characteristics.
2. Using the average of the predicted probabilities for F(Xb), and the sample mean for educ.
summ part1con1hat /*again, we need the mean for our calculations*/
di "the marginal effect using mean of predictions is " .7289634*(1-.7289634)*(-1.33864+.0934957*8.078016)
the marginal effect using mean of predictions is -.1152618
The answer here is -.11526173, which is a fair amount smaller than the previous marginal effect. The difference in means between the actual observations and the predicted probabilities drives this 3 percentage point difference.
3. Exponentiating to get the odds ratio interpretation
To exponentiate, we need to use the function exp:
di "the marginal effect on the odds ratio of answering YES is " exp(-1.33864+.0934957*8.078016)
the marginal effect on the odds ratio of answering YES is .55800897
The answer is .55800919: this means that women with an average number of years of education are just more than half as likely to report YES as they are to report NO (that is, they are LESS likely to report yes).