negative constant value for binary outcome

[Tracy Lam]

I am using the xtivreg command for a binary outcome, but the constant that Stata is producing is negative. Is this possible? How can I check what is going on?

[Richard Williams]

Sure, why not? The constant is the predicted value for a case when all Xs = 0. But, that is often impossible, e.g. a scale may only run from 400 to 1200.

If it really bothers you you center the Xs. Then 0 is possible -- it represents a person with the average score on a variable.

Also, why use xtivreg with a binary outcome? If you have Stata 16, consider using the xteprobit command. https://www.stata.com/manuals/xtxteprobit.pdf

[Tracy Lam]

Richard, thanks for the suggestion for xteprobit. Could you say a little more about the example you gave of a scale only running from 400 to 1200? I thought that because the outcome is a predicted probability that the constant cannot be negative.

[Richard Williams]

First off, the constant by itself is not the predicted probability. But even if some cases did have negative predicted probabilities, that can happen with a linear regression technique. That is one of the reasons people prefer logit or probit when analyzing binary DVs -- the predicted probabilities must range between 0 and 1.

This handout says more about centering:

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

[Tracy Lam]

Richard, thanks for this very helpful resource. Let's say I use xtlogit (instead of xtivreg in my first post) for a dichotomous outcome. Is it still possible to get a negative constant?

[Richard Williams]

Sure, it is possible. But a negative constant does not mean a negative probability. It would mean that, when all Xs = 0, the probability of the event occurring is less than 50%