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I've come across SMA (Standard Major Axis) regression recently and was wondering if it would be appropriate to compare SMA and OLS models with AIC? When I use the aicc function from the package bbmle, I've stuck both SMA and OLS regressions into the function and have not had any issues running the command. However, I'm a little wary about doing this because AIC is based off of some elements of likelihood. I'm not sure if these two types of regressions calculate likelihood the same way.

Does anyone have any information regarding this?

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  • $\begingroup$ I take it you refer to Standard Major Axis regression? $\endgroup$
    – usεr11852
    Oct 24, 2018 at 20:37
  • $\begingroup$ Curiosity: What is the likelihood function for SMA? Joint distribution of X and Y? $\endgroup$
    – user158565
    Oct 24, 2018 at 21:44

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I'm fairly confident that the mathematics of SMA regression is equivalent to OLS regression, so the joint distribution of X & Y will have equal likelihoods under these three models (OLS Y ~ X)*P(X)==(OLS X ~ Y)*P(Y)==SMA(X, Y). However I'm not 100% certain of this.

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