Logit Confidence Intervals

[Anja Heimann]

Hi,

I was wondering whether someone could help me get less confused.
I have run a logit model , where the dependent variable is binary and the independent variable is a country dummy. It is conditioned on a subsample of people aged 16-24.
Specifically, I have run the following code:

svy: logit Learning i.country if Agegroup==1

margins, dydx(country)

I get the following results:

Number of strata   =        10                  Number of obs     =     37,109
Number of PSUs     =    37,109                  Population size   =  7,554,754
                                                Design df         =     37,099
                                                F(   1,  37099)   =       1.87
                                                Prob > F          =     0.1710

------------------------------------------------------------------------------
             |             Linearized
    Learning |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   1.country |   .0546632   .0399255     1.37   0.171     -.023592    .1329184
       _cons |  -1.160101   .0146527   -79.17   0.000    -1.188821   -1.131381
------------------------------------------------------------------------------



Conditional marginal effects

Number of strata   =        10                  Number of obs     =     37,109
Number of PSUs     =    37,109                  Population size   =  7,554,754
Model VCE    : Linearized                       Design df         =     37,099

Expression   : Pr(Learning), predict()
dy/dx w.r.t. : 1.country


------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   1.country |   .0100735    .007433     1.36   0.175    -.0044955    .0246424
------------------------------------------------------------------------------

My question is: How can the confidence interval include a negative number, when I am running a logit regression? They shouldn't be odds ratios as I didn't specify that option in the command? Should it not be bounded by 0 and 1 like the coefficient?

[Maarten Buis]

You asked for marginal effects, i.e. change in predicted proportion. A change can be positive or negative. So the confidence interval is not incompatible with what you asked for.

In general the confidence intervals from margins use the delta method approximation, so assumes that the sampling distribution is normal. As a consequence it will not respect any bounds that you know must exist. As I said above, that is not a problem in your case, but may come up later.

As an aside, you do not want to use if in combination with the svy: prefix, instead you want to use the subpop() option within svy instead, see help svy

[Anja Heimann]

Thanks Maarten, that makes sense. As to not using an if in combination with svy, thank you for pointing that out, I had overlooked it in the manual.

If I wanted to get a binomial CI for the marginal effect out of this estimation process however, how would I go about doing that?
I tried

bys country: ci proportion, exact

but that did not provide me with the result I need.

[Maarten Buis]

It looks like you don't want a marginal effect (change in proportion), but just a predicted proportion. Is that correct?

[Anja Heimann]

I am trying to test whether the difference in the people in age group 1 in two countries that are in Learning establishments is significant.
From previous year's results I know that the coefficient of 0.0100735 multiplied by 100 should be the percentage difference between the two countries. So I need the margins command.
But what I am trying to get to is how I can make my CI follow a binomial distribution.

[Leonardo Guizzetti]

Edit: crossed with #5.

Perhaps this will illustrate using -margins- for estimating predicted proportions:

webuse nhanes2f
svyset psuid [pweight=finalwgt], strata(stratid)
svy: logit diabetes i.sex
margins i.sex
margins, dydx(sex)

and selected output:

. margins i.sex

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         sex |
       Male  |   .0291678   .0026414    11.04   0.000     .0237807     .034555
     Female  |   .0390031   .0026753    14.58   0.000     .0335469    .0444594
------------------------------------------------------------------------------

. margins, dydx(sex)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         sex |
     Female  |   .0098353   .0038657     2.54   0.016     .0019511    .0177194
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

[Leonardo Guizzetti]

I believe -proportion- is what you're after. See the documentation for different CI types and a useful -percent- option. Continuing from the example in #6.

svy: proportion 1.diabetes, citype(exact) over(sex)

[Maarten Buis]

I am trying to test whether the difference in the people in age group 1 in two countries that are in Learning establishments is significant.
But what I am trying to get to is how I can make my CI follow a binomial distribution.

That is impossible. A single confidence interval for a proportion can be based on a binomial (it is often a bad idea, but that is a different question). A confidence interval for a difference between proportions cannot be based a a binomial.

I suspect we are dealing with an xy-problem (https://en.m.wikipedia.org/wiki/XY_problem). So we need to find out what the real question is that you want answered. Let's start with why you think you need a binomial confidence interval for a difference between proportions, what is that going to do for you that margins cannot?

[Anja Heimann]

Thanks for all your answers.
I think running the logit command before margins has made me wrongly believe I need a binomial CI for results from the margins command too. I realise now that asking for a binomial CI for a difference in proportions, which is not binary by definition, is impossible and doesn't make sense.

[mahfuz rahman]

Hi Maarten Buis,
Could you please tell me when we run the code: svy: logit d002 i.post i.p01, or
It gives us confidence interval of odds ratio, then what method (such as the standard maximum likelihood method, or the method of endpoint transformations, or the delta method, or bootstrapping) does the logit use to calculate confidence interval by default? I really desperately need this information.

[Maarten Buis]

https://www.stata.com/support/faqs/s...cs/delta-rule/