I have a simple linear regression model and am trying to locate structural breaks in the relationship between the two variables. The data are cross-sectional, not time-series.
I've been using Wald tests on pairs of dummies (1 if X is above some threshold, zero otherwise) & interaction terms (of the dummy and X) and found quite a few "candidate" points. But after reading up on the topic, it seems this method is frowned upon. That is, testing multiple points in hopes of finding something rather than testing a "known" point.
The estat sbsingle command in Stata shows some promise, but requires a gapless time series. Is it advisable/reasonable/defensible to assign ranks to the observations based on each's X value, and then treat the rank as a time-series variable in order to meet the estat command's requirements?
--Edit in response to GeoMatt22--