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Deming regressions have some serious drawbacks compared to OLS, most importantly that it's not scale/unit-invariant: if you rescale your (e.g. use house area in
by em500 6y ago
Deming regressions have some serious drawbacks compared to OLS, most importantly that it's not scale/unit-invariant: if you rescale your (e.g. use house area in square metres instead of square feet to predict house prices) you get different results.
This may be less of an issue for the machine leaner who's only interested in point predictions, but it's a serious concern for us old fashioned statisticians who are more interested in inference.
- autokad 6y agoi wouldn't dare to say its a 'serious drawback'. as soon as you add ridge to regression (something very common for statisticians to do), it's also no longer scale/unit-invariant. Edit: this is also not just true for ridge, but lasso as well
- em500 6y agoPersonally I consider the lack of scale-invariance one of the main drawbacks of most common regularizers too. Again, not a big deal if all you're after are y-hat, a bit more concerning if you're interested in beta-hat.
- pps43 6y agoI would not call it a drawback. In regular regression you make an assumption that x is known exactly, and all errors are in y. In Deming regression you make another assumption, about the ratio of their variances (δ). If you change units, you need to change δ as well, and then there's no difference.