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I want to conduct a mediational analyses with three variables:

  • Predictor: it is the result of a memory test with range -1 to 1.
  • Mediator: it is the absolute error made by the participant when estimating a magnitude that goes from -1 to 1. Thus, it is a variable that can only take positive values, because it is the absolute deviation from a fixed value. Also, most errors are small so the distribution is skewed (lots of small values).
  • Dependent Variable: it is another absolute error made by the participant when estimating a different magnitude. Again, this is a variable with a skewed distribution, all positive values.

My prediction is that the Predictor will affect the Dependent variable through the Mediator. However, I don't think the usual OSL regression with normal functions that most software produces will work here, because of the skewed distributions.

Which approach should I use in this case? I haven't tried but I guess there are a couple things to do: transformations, non-nomral functions (Gamma?)... Still, I prefer receiving input from experts rather than trying things alone.

References are welcome.

EDIT: Thanks to one commenter, I know that I have to look at the residuals. Thus, I have examined the q-q plots for the normal model and the Gamma model (which I think would make sense given my variable).

These are the q-q plots from the Gaussian model – Identity link: Predictor + Mediator on dependent var. Residuals from Gaussian model Outcome~Predictor+Mediator

Predictor on mediator: Residuals from Gaussian model Mediator~Predictor

If I try a Gamma function instead: Predictor + Mediator on dependent var. Residuals from Gamma model Outcome~Predictor+Mediator

Predictor on mediator: Residuals from Gamma model Mediator~Predictor

So, I am no expert on q-q plots but these don’t look OK to me. What would you conclude from these plots?

Also: does it make sense to use one distribution for modelling one of the steps of the mediational analysis, and a different one for the others? (I mean, it seems that the residuals look better for Gamma when predicting the mediator, but Gaussian is better when predicting the outcome variable). Prehaps what I am asking makes no sense, sorry.

Experimental Psychologist
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1 Answers1

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First, OLS regression does not assume the variables are normally distributed. It assumes the errors are normally distributed. You can look at this by examining the residuals.

Second, the type of regression generally depends on the nature of the dependent variable. You have one that is always positive. This was discussed in this thread.

Peter Flom
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  • Thank you for your quick answer! I have added the q-q plots to the main post, but still no clue as to what I should do. They do not look good so maybe I should try a different thing. – Experimental Psychologist Jul 02 '23 at 16:54
  • You could try quantile regression. It makes no assumptions about the distribution of the residuals. – Peter Flom Jul 02 '23 at 17:07