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  • Compare two models with different dependent variables

    Hello

    I want to choose between two linear models describing some data in my dataset. In the field that I am studying, an independent variable, say X1, is conventionally used to predict some dependent variable, say Y1:

    model 1: Y1 = a1*X1 + b

    I have hypothesised that X1 is a better predictor of a different variable, say Y2

    model 2: Y2 = a1*X1+b

    Furthermore, I propose that if a second predictor, say X2, is taken into account, the model becomes even better

    model 3: Y2 = a1*X1 + a2*X2 + b

    The importance of this lies in the fact, that Y1 and Y2 are calculated measures based on some raw data. So if model 2 and 3 are shown to be better than model 1, one may prefer to calculate Y2 based on the raw data, rather than Y1 for future experiments.

    Now, I know that models 2 and 3 may be compared using the Akaikes information criterion (AIC). But the core argument for me is to compare model 2 to model 1 - and importantly, compare the final model, i.e. model 3, to the reference model that is conventionally used, i.e. model 1

    To compare 3 to 1, the AIC does not apply, because I am looking at different dependent variables. But any suggestions on alternative methods ?

    I have limited knowledge about statistics, so please explain in simple terms and please include an example with Stata commands if possible

    Thanks in advance

  • #2
    No luck so far - I will try Cross Validated.

    Comment


    • #3
      It sounds like you want "seemingly unlrelated regression"; try -help sureg-

      hth,
      Jeph

      Comment


      • #4
        Also, you can compare AIC and BIC of Models 1 & 2; the model with smaller values is preferred. But I endorse Jeph's suggestion of sureg, as you can compare the coefficients of X1 directly. If you do take this to Cross Validated, then cross reference the two discussions: http://www.statalist.org/forums/help#crossposting.
        Steve Samuels
        Statistical Consulting
        [email protected]

        Stata 14.2

        Comment


        • #5
          Dear Rozh,

          I believe that what you need is the MacKinnon-White-Davidson (1983) Pe test. This is very easy to implement and is described in some textbooks; you can also look at the original paper. Apologies for not providing the full reference but this should be easy to google.

          Joao

          Comment


          • #6
            Thank you everyone for the fine suggestions.

            Just to make sure I understand things correctly, I have a couple of followup questions:

            Jeph: thanks for suggesting sureg. I have tried that now and did some googling efterwards. Is it correct, as Steve also suggests, that the method allows comparison of the coefficients of X1 ? My problem is that Y1 and Y2 are have different scales, so the coefficient will probably reflect this difference in scaling rather than superiority of one model to the other. Am I correct ? And will calculating standardised coefficients, if possible, solve this issue ?

            Steve: I read somewhere that AIC only applies when the same dependant variable is used in all models - since I only have limited knowledge in the area I do not know if that is correct or not ? And as you suggest here is the link to the discussion at CV: http://stats.stackexchange.com/quest.../178434#178434

            Joao: thank you for the suggestion, I will try to look that up


            Comment


            • #7
              You right about AIC and BIC

              Since you used the constant to describe the coefficient of X1 in both equations, I assumed that scaling was comparable. If not, then you have to define what you mean by a "better predictor" for your purpose. One possibility is to compare r-squares.

              This discussion assumes that each model fits the data: that a single linear term in X1 is sufficient; that, in the case of Model 3, no interaction is present; and that outliers or high leverage points have not obscured the "best" model. In other words, you have the same obligation to check models as you would in any other regression analysis.
              Steve Samuels
              Statistical Consulting
              [email protected]

              Stata 14.2

              Comment

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