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  • alternative to interaction term in regression

    Hi all,

    I am examining the interaction effect between X and Y (outcome var is Z) using fixed effects model. However, I have reason to suspect that simply adding an interaction term may not well capture the real picture of how the effect of X on Z varies across the level of Y. So I am wondering if there is any statistical methods (and Stata package) that can determine if there is any cutoff points (in terms of, for instance, percentile i of Y) along the range of Y, around which the effect of X on Z is statistically significantly different from each other below and above the cutoff point?

    Thank you very much!

  • #2
    If you do not have an a priori hypothesis about such cutoff points and you want a program that will estimate them, then I am unaware of any existing code to do that. As far as I know, you would have to write your own maximum likelihood estimator for that--it's a big deal.

    If, however, you have specific cutoffs in mind, you could use the -mkspline- command to partition Y into a series of variables and then use the interactions of the spline variables with X.

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    • #3
      Thank you very much Clyde!

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      • #4
        If you don't have an immense data set, you can also simply run a loop over cutoff points. I believe Simonsohn, U. (2018). Two Lines: A Valid Alternative to the Invalid Testing of U-Shaped Relationships
        With Quadratic Regressions. Advances in Methods and Practices in Psychological Science, 1(4), 538–555.
        https://doi.org/10.1177/2515245918805755

        addresses a similar problem and offers a strategy for finding cutpoints.

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        • #5
          Thank you Phil! The paper is very interesting.

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          • #6
            the is a user-written routine that finds a breakpoint in linear or logistic regression - sometimes called 'hockey stick' regresson.
            this might be of interest?
            see https://personalpages.manchester.ac....loghockey.html

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            • #7
              Hi George,

              Thank you! I will check it out! Do you know if this trick applies to fixed effects model?

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