standard error of geometric mean of estimates

[Barbro Widerstedt]

Hi,

I want to calculate a geometric mean of estimates in separate regressions.

I have n binomial variables, for which I want to calculate composite indices for combinations of probabilities for different groups.
I do a logistic regression on each of these n variables , and compute margins for a categorial variable (at a type observation)
I want to calculate the geometric mean of the n estimates for each value of the categorial variable - and get a sense of the variation of this derived variable

probit var1 x1 x2 x3 i.x4
margins i.x4 , at(x1=1 x2=0 x3=21) coeflegend post
estimates store v1estimate

probit var2 x1 x2 x3 i.x4
margins i.x4 , at(x1=1 x2=0 x3=21) coeflegend post
estimates store v2estimate

Then for each level of x4, I want to calculate the product of the margins. My instinct is to try something like (for level 1 of x4)

nlcom  ({v1estimate}_b[1.bransch] *{v2_estimate} _b[1.bransch])^(1/2)

Which does not work. Calculating the mean is simple, but how would I get a standard error for this composite measure? In the worst one, I have four variables in the composite index.

Can I use nlcom, and how do I reference the different results, or how would I calculate this (if possible)

Grateful for any help!

[Dimitriy V. Masterov]

My first idea was to use -suest- to combine the margins estimation results, but that would not work since the variance is funky.

I wonder if you can use -biprobit- (or user-written -cmp-) to fit a SUP. This allows for correlation between the errors in the two outcome equations, so it is not quite equivalent to the two separate probits, but it makes everything else a lot easier

Here's an example:

set more off
webuse school, clear
biprobit private vote logptax loginc years i.school
margins school, expression(sqrt(predict(pmarg1)*predict(pmarg2))) at(logptax=7 loginc=10)

[Barbro Widerstedt]

Thanks, that worked a treat for the two-variable case. Now I have to go think deeply about the four-variabel indices...

[Dimitriy V. Masterov]

The -cmp- command I suggested may be able to do that.

[Barbro Widerstedt]

I had to do some hard thinking, but in the end I managed to get output.
Only crinkle was that option svy made the margins command throw a varlist missing (r(100)) error. Strange. And I didn't understand which variable list was missing... Still, without svy it worked. Happy days .

[Barbro Widerstedt]

Ok, for general productivity purposes (if I or anybody else should need this again)

cmp (Y1 = i.X1 i.X2 X3  X4) (Y2 = i.X1 i.X2 X3  X4) (Y3 = i.X1 i.X2 X3  X4) (Y4 = i.X1 i.X2 X3  X4) , ind($cmp_probit $cmp_probit $cmp_probit $cmp_probit)

margins i.X1, expression((predict(pr eq(#1))*predict(pr eq(#2))*predict(pr eq(#3))*predict(pr eq(#4)))^(1/4))  at(X3=12.43 X4=100 X2=0)