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I have two sets of real-valued data and I am interested in their correlation. From my perspective, there appear to be errors both variables, so I am inclined to perform a regression with TLS (Total Least Squares). Other analysts (perhaps because of lack of comfort with error-in-variables regression) prefer OLS.

I would like to compare the likelihoods of the two models, or use some principled model selection criterion. However, it occurs to me that if the TLS regressed slope is non-zero, then the residual variance of the TLS solution will be strictly less than the OLS solution. If so, it seems like TLS will always "win". (I guess that last statement assumes that both models have equal prior probability.)

Is there a good way to compare these two models?

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    $\begingroup$ I guess it was answered here - stats.stackexchange.com/questions/184341/… (I could not answer and googled)... $\endgroup$
    – German Demidov
    Feb 9, 2016 at 15:34
  • $\begingroup$ The question and answer referenced by @GermanDemidov are very interesting (essentially: if you use Pearson correlation, your answer is independent of model), but I don't think it quite answers my question. I want to know which model is better! $\endgroup$
    – Bill Bradley
    Feb 12, 2016 at 20:27
  • $\begingroup$ Can Bland-Altman plots solve your problem?) As for me, in case if I expect errors in both variables, I have to use TLS. IMHO - I would not think of using OLS in your case. $\endgroup$
    – German Demidov
    Feb 12, 2016 at 21:39

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