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In one paper I read that the researchers used OLS model (considered well-known, simple and robust to misspecification) but they admitted to have not tested whether its assumptions were met. However, they added that the OLS results were consistent with probit model.

My question is: is this a right way to procede? Can I use and report OLS model results (since they have the advantage of being widely known and easy to interpret also by persons with low statistical literacy) whithout testing its assumptions if its results are consistent with those of other type of models?

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1) I assume that by "OLS model" you mean (ordinary) least squares regression, which is in fact a method and not a model; people sometimes call the a "model" because it is (in theory) based on a model with certain assumptions. However, I can imagine also other things being meant by "OLS model". Also note that although the OLS regression theory depends on certain model assumptions, this doesn't necessarily mean that it is useless or meaningless if the model assumptions are not met. It still has some kind of interpretation as line/hyperplane/function (depending on what OLS method you are exactly talking about) approximating the data, and even statistical inference may (or may not) be approximately correct, depending on in which way assumptions are violated.

2) The OLS regression is not in fact robust against misspecification. There is a big literature on how particularly outliers will cause trouble.

3) "Is it OK to report...?" That's a weird kind of question. I'd certainly say it is not a good way to find out something valid from the data. This would require some more inspection and maybe testing (surely it is sensible to assess problems with the model assumptions, although this doesn't necessarily have to take the form of a hypothesis test). Whether it is "OK to report" something depends on what you write around it, what audience this is for etc. One could argue it is OK in the sense that it is correct to just say "I applied OLS regression without model checking and the result was this". The reader then knows a rather weakly justified approach was used and can make up their own mind (assuming they're competent enough). However, chances are I wouldn't put too much trust into any subject-matter interpretation or conclusion from this.

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  • $\begingroup$ Yes, I intend "ordinary least squares regression". It seems that, instead of validate the accuracy of their OLS results by testing the assumptions, they used the results of the other method as a validation. Since they should know how to test OLS assumptions and there is no reason not to test them, I would conclude they were not met! This is surprising because the paper was published in a important journal. Anyway, I found also other cases where (social) researchers report results of different methods to support the robusteness of their outputs, instead of saying the assumptions were met $\endgroup$
    – kk68
    Mar 6, 2020 at 11:39
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    $\begingroup$ I was thinking about writing something about "validating results of method A by similarity to results of method B", but it's hard to comment on that. Obviously this would assume that method B is fine, but if we knew that, why would we need method A? But then I can see why two methods pointing in the same direction give some more assurance than just one. However from my point of view it depends heavily on the details, what exactly was done and how exactly it was presented, whether I can imagine this to be a sensible thing to say/do. $\endgroup$ Mar 6, 2020 at 11:46
  • $\begingroup$ You are right and probably what the reseachers did was the right thing to do also for the reviewers, considered the importance of the journal. If you want to take a look you can find here the paper $\endgroup$
    – kk68
    Mar 6, 2020 at 11:59
  • $\begingroup$ Thanks... well, that's probably too much to read for me right now. $\endgroup$ Mar 6, 2020 at 12:08

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