Sibling fixed effect model including children with no siblings at all?

[Sylvie Rod]

I am analysing a sample of children to examine the effect of breastfeeding (bf) on mental health (mh). The sample includes both children with no siblings (only children) and those with siblings. The variable "sib" identifies individuals as part of sibling groups, which may consist of children with one, two, or more siblings, or just one child in cases where they have no siblings. I believe I am employing a Sibling Fixed Effects Model for this analysis in the following form:



xtset sib

xtreg mh bf, vce(robust) fe



However, I am uncertain about whether to include children with no siblings in the sample or not.

When I exclude children with no siblings, breastfeeding is no longer significant, possibly due to the reduced sample size, although I am unsure if other factors are at play?

Would it be valid to use a Sibling Fixed Effects Model while retaining children with no siblings in the sample?

Any guidance on this issue would be greatly appreciated!

[Clyde Schechter]

Singletons in fixed-effect models have very little effect on the regression results. They do affect the constant term, and they do affect the value of sigma_u and rho and R² between. Another thing that they effect is the calculation of the robust (actually, clustered on sib) VCE matrix. If you scrutnize the output and focus on the actual coefficient of bf instead of the p-value, you should see that it is the same either way. The change in significance would be due to the change in the standard error. Had you not used -vce(robust)- there would have been no change in the standard error, t-statistic or p-value. And I suspect also that the change in significance you see is just a small change from p slightly below to p slightly above 0.05.

But I think there is a bigger problem here. Fixed-effects models estimate within-group effects, not between group. In particular, any sib-ship where all of the siblings were breast fed, or where all of the siblings were not breast fed, will contribute nothing to the estimation of the breast feeding effect, because they contain no variation in the bf variable. I don't know what population you are working in, but in my environment, I think most mothers who breast feed one of their children breast feed them all, and other mothers do not breast feed any. So you may be doing your effect estimation on an atypical subset of sibships where the mother changed her breast feeding behavior. Often this will be the result of some event or illness affecting the mother or the baby(ies) and one has to wonder whether this extraneous event/illness may not itself have mental health effects. So I'd be cautious about using this design--I suspect it is inherently biased, and perhaps strongly so.

[Andrew Musau]

'Sibling fixed effects' is not the correct terminology. You should refer to your model as a linear regression model with sibling dummies. There is nothing wrong with including sibling dummies in a model. The variable will equal zero for individuals with no siblings, who simply function as the reference group.

regress mh bf i.sib, robust

With only two right-hand-side variables, you will likely encounter omitted variable bias, as it is probable that several factors predict the outcome that your model fails to account for.

[Clyde Schechter]

I'm not sure "sibling fixed effects" is incorrect. My understanding of #1 is that she has a variable that identifies distinct sibships. If I have that right, she has sibship (OK, not sibling) fixed effects. If she just has an indicator for who has siblings and who is an only child, then, no, that wouldn't be a fixed effect in the usual sense of the term--but I don't think that's what she has.

[Andrew Musau]

Okay, if each level defines a distinct group of siblings, that’s fine. I had imagined it was a binary variable coded as 0/1.