Logistic regression with probabilities instead of binary values

[Clara Daru]

Hi everyone,

I would like to run a logistic regression of a certain variable distance to get the probability of a certain outcome valid, but instead of rows in the format

distance	valid
500	1
500	1
500	0
1000	1
1000	0

I have counts, for ex

distance	valid_count	total_count
500	2	3
1000	1	2

I reasoned it should be possible to run the logistic regression with the data as it is, using frequency weights. I generated a new variable valid_ratio with

. gen valid_ratio = valid_count/total_count

but when running the regression I get the following error:

. logistic valid_ratio distance [fweight = total_count]
outcome does not vary; remember:
                                  0 = negative outcome,
        all other nonmissing values = positive outcome

Which I assume means Stata is interpreting all my ratios as positive outcomes.

My first question is: is it possible to run this logistic regression with the data as it is? If so, how?

If not, what is the best way to process the data to make this regression possible? The two options that come to my mind are:

1. generate, for every currently existing observation, two rows: one with valid=1 and count=valid_count, and the other with valid=0 and count=total_count-valid_count, and then run the regression with

   . logistic valid distance [fweight = count]

   . In this case, the variables would look like

   distance	valid	count
   500	1	2
   500	0	1
   1000	1	1
   1000	0	1

2. generate, for each currently existing observation, total_count rows, being valid_count of them with valid=1 and total_count-valid_count of the with valid=0. In this case, the variables would be exactly in the format of the first table and I would run the regression without any weights:

   . logistic valid distance

   .

I prefer option 1 because it looks cleaner, but maybe that won't work with the frequency weights?

Thanks in advance.

[Jeff Wooldridge]

Clara: You want to use fracreg logit. It is intended precisely for fractional responses. Be sure to use the margins command.

Alternatively, you could use binomial regression and implement it using the glm command.

JW

[Bruce Weaver]

Hello Clara Daru. I wonder if -fracreg logit- is what you are looking for. E.g.,

fracreg logit valid_ratio distance

HTH

[Clara Daru]

Thanks Jeff Wooldridge and Bruce Weaver , fracreg was exactly what I needed!

[Bruce Weaver]

No worries, Clara, and welcome to Statalist. (I failed to notice last time that it was your first post.)