Interpretation of coefficient of binary outcome variabel using xtreg ..., fe

[Lena Buettner]

Hey everyone,

Using the following code:

xtreg enrollment birth_order sex i.age, fe cluster(hh_idn)

I obtain this outcome:


The outcome variable is "enrollment", which is a dummy / binary variable. I didn't use the logistic regression but the xtreg command for a regression with fixed effects. If it had been odds ratio, I would have known how to interpret them, but here I see a coefficient of 0,0896. Can someone tell me what exactly this number means?

I have tried to find that question in the forum, but without success, so I would be super grateful for help!

Lena

[Clyde Schechter]

So, you have fit a linear probability model. The interpretation of the coefficient of birth_order, 0.0896477, is that each 1-unit increase in the value of the birth_order variable is associated with an increase of 0.0896477 in the probability of enrollment. You did not explain what the birth_order variable is, so only you can truly understand the meaning of this. If it is 1, 2, 3, 4, ... etc. then it means, for example, that, on average, the probability of enrolling the 3rd child in a household is 0.0896447 higher than the probability of enrolling the 2nd child in the same household, holding constant age and sex. (Restriction to the same household arises because a fixed-effects model was used.) If birth_order is a more coarse-grained category, such as 1 = birth orders 1-3, and 2 = birth orders 4 +, then the interpretation would be about the difference in probability of enrollment for an early vs late born child in the same household.

Put very briefly: it is an expected difference in probability, not a ratio of anything.

Added: I am a bit troubled by this model. The "holding constant age" part is quite problematic. As multiple births are uncommon, it will seldom be the case that children of different birth orders in the same household will be of the same age. So the meaning of this coefficient (and you would face the same difficulty had you used a logistic regression) is about circumstances that are rare in the real world. To make this more meaningful as an effect of birth order, you would really want to be able to compare enrollment probabilities of children of different birth orders across all households, so that the same-age constraint would be more realistic. The problem is even worse if whatever "enrollment" means is, itself, something that might differ between children of a multiple gestation versus singletons--in which case the estimates you are getting are not only restricted to an uncommon situation, but that uncommon situation may actually be very unrepresentative of the usual situation.

Fixed-effects estimators can only estimate marginal effects within the grouping variable. I know that in some disciplines, fixed-effects models are strongly preferred, but this is a situation where fixed-effects can only answer a question that is largely irrelevant in real life, and could be misleading as to what is going on among singleton births. I think you need a random effects model here, and you may have to deal with issues of possible inconsistency of estimates by getting a fuller range of covariates to include.

[Lena Buettner]

Thank you so much for you helpful answer!