Timeline for Omitted variable bias vs. Multicollinearity
Current License: CC BY-SA 4.0
23 events
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| May 5, 2020 at 8:46 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| May 5, 2020 at 8:35 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| May 3, 2020 at 20:07 | comment | added | LSC | My point is that, to less technical readers, your point may be lost because they're asking the question in the first place and it may not necessarily follow what I have mentioned, but others can't necessarily pick that up, otherwise the question from OP wouldn't arise in the first place. 2/2 | |
| May 3, 2020 at 20:06 | comment | added | LSC | OVB is more of an econometrics term. In traditional statistics, not many use "omitted variable bias" but talk about biased estimation and how omitting a relevant variable (nonzero beta and nonzero correlation with something else in the model) could cause this. I think your explanation of "this sounds the same but it's not" is lacking, but if you don't feel further explanation is needed, that's okay! I think we agreed on the important points of what MC or biased estimation can mean, just maybe some vocabulary differences. 1/2 | |
| May 3, 2020 at 13:51 | comment | added | markowitz | @RichardHardy I agree with you reply about prediction side. However I fear that your reply conflated causation and description role. I writed a related question here (stats.stackexchange.com/questions/464261/…) I would appreciate you reply there. | |
| May 3, 2020 at 11:05 | comment | added | Richard Hardy | @LSC, Thank you for your comments! I have tried honestly to explain myself to a degree of sufficient detail. I think the best one can do now is carefully read what I have written and be extra careful about deriving implications. The ones you mention were not meant and do not follow from my statements. I have by now provided a definition of the OVB, and I have elaborated below on the tangential point which is not about OVB but about the effect of omitting variables on prediction. The confusion should clear up if one pays sufficient attention to definitions and my precise wording. | |
| May 3, 2020 at 10:56 | comment | added | LSC | And your original text was "For prediction, omitted variable bias is largely irrelevant as you are not interested in model's coefficients per se, only in predictions. " Which reads a lot like "biased estimation is irrelevant for predictions, so OVB doesn't matter if you're trying to get predictions." which would be not a great statement. This is mostly what I was commenting on at the origin of this discussion. | |
| May 3, 2020 at 10:51 | comment | added | LSC | You definitely implied the effects of OVB on predictions by your verbiage, so please clarify your wording. If you're conceding OVB has an implication for prediction, then certainly it matters for prediction but to know how much is more challenging in any particular case because it depends on the degree of bias. This feels more like a word game to me, but so I think clarifying your point further would be helpful rather than just saying "these things aren't the same." 2/2 | |
| May 3, 2020 at 10:48 | comment | added | LSC | Maybe we're saying the same thing in different language, but I'm sure confused by your post. "For prediction, multicollinearity and omitted variable bias are largely irrelevant as you are not interested in model's coefficients per se, only in predictions." But you claim "This is tangential to my points because I did not discuss the effect of omitting a variable on prediction. I only discussed the relevance of omitted variable bias for prediction. The two are not the same." I think you should elaborate on how you are using these differently, because it's not clear to me here. 1/n | |
| May 3, 2020 at 8:18 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| May 3, 2020 at 8:03 | vote | accept | Maverick Meerkat | ||
| May 3, 2020 at 7:55 | comment | added | Richard Hardy | @LSC, thank you for your elaboration. Let me try to explain my points in more detail. (1) I do not see how I might have implied prediction to deal with interpreting betas or making inferences on betas, because I specifically stated the opposite: you are not interested in model's coefficients per se. (2) I believe my statement For prediction, omitted variable bias is largely irrelevant as you are not interested in model's coefficients per se, only in predictions is also correct; I have elaborated on it by appending my post. | |
| May 3, 2020 at 7:54 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| May 3, 2020 at 7:18 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| May 3, 2020 at 2:04 | comment | added | LSC | 2/2 I also think your comment that for "For prediction, omitted variable bias is largely irrelevant as you are not interested in model's coefficients per se, only in predictions. " is wrong because OVB will necessarily introduce bias into the estimation process and can screw with predictions because the linear predictor is no longer unbiased. | |
| May 3, 2020 at 2:02 | comment | added | LSC | I'm not trying to be funny, but the feedback I gave is in my post. Prediction is unaffected because multicollinearity doesn't introduce bias and allows for the use of whatever variables are useful for prediction even if information is redundant. "Prediction" as you were using it seemed more imprecise and to imply interpreting betas or making inferences on betas which isn't really prediction in a statistical sense. My use of "confusion" was more of an oblique way to say I think the word is used wrong and this context warrants correct usage of the term. 1/n | |
| May 2, 2020 at 14:09 | comment | added | Richard Hardy | Why the downvote? I would appreciate some constructive feedback so that I can improve my answer. Thank you. | |
| May 2, 2020 at 11:55 | comment | added | Richard Hardy | @LSC, you mentioned confusion regarding prediction in a comment above and stressed the 99%... bit, but I do not see any confusion. While none of us has specified the notion of prediction explicitly, we seem to agree well on the implications of multicollinearity w.r.t. it. | |
| May 2, 2020 at 10:55 | comment | added | Richard Hardy | @LSC, (continued) Meanwhile, omitted variables cause not only finite-sample, but also asymptotic bias (hence also inconsistency w.r.t. to the true parameter), except when the omitted variables are orthogonal to the space of the included regressors. | |
| May 2, 2020 at 10:53 | comment | added | Richard Hardy | @LSC, multicollinearity does not cause bias, but this applies equally to prediction and inference. Importantly, while multicollinearity causes high variance, some combinations of parameters have low variance, e.g. the linear combination that is used for prediction in linear regression. That is why multicollinearity does not matter much for prediction. Meanwhile, the high variance of individual parameters is a problem in inference, as the high uncertainty of the point estimates is undesirable. | |
| May 2, 2020 at 10:43 | comment | added | LSC | "Prediction" as used by 99.9999% of statisticians would be a case where multicollinearity is generally irrelevant. "Inference" or even just describing the relationships estimated with beta coefficients is when multicollinearity matters more. Multicollinearity does not cause bias in the estimation process and therefore, prediction (predicted Y values or model performance) is almost always considered unaffected by multicollinearity. Omitting pertinent variables, though, causes misspecification and can introduce at least bias but possibly inconsistency into the estimation procedure. | |
| May 2, 2020 at 10:38 | history | edited | Richard Hardy | CC BY-SA 4.0 |
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| Mar 15, 2020 at 8:27 | history | answered | Richard Hardy | CC BY-SA 4.0 |