The UCLA IDRE website has an article on -intreg- to estimate models with interval dependent variables. It seems interesting, but I can't find any theoretical discussion of it. No wikipedia article. No sources when I google. It always just re-routes to the stata package. The R equivalent is survreg(), which is based on something in survival analysis. However survreg() and -intreg- seem different. For instance, the former estimates log-odds and the latter standard OLS coefficients.

I guess I'm trying to learn more about "interval regressions," but I can't find any info on it outside these two packages. So I'm wary to use them.