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I'm going to do a multiple regression analysis with two continuous IVs and their interaction. I've centered the IVs and then multiplied one with another for interaction. My problem is that the interaction variable is severely kurtotic (kurtosis 7,731, standard error=0,127, z=60.87). How should I deal with this? Removal of the most extreme cases of course helps, but what would be the most recommended way to define outliers?

N=1479 with all cases, the range of centered IVs is around 50 and the range of interaction variable around 700. The two IVs are normally distributed.

Let me know if any additional info or exact numbers would help.

Sanna Jaakkonen
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  • Hi Sanna and welcome to the site! Can you explain why you think that the kurtosis of the interaction variable may be a problem? How do the residuals of your regression look? – COOLSerdash Jul 10 '13 at 07:57
  • Thanks for the welcoming! The residuals are about normally and linearly distributed, but heteroscedastic. The errors of prediction increase as the size of the prediction increases. I think the kurtosis might be a problem because regression is sensitive to outliers. Is my reasoning on completely wrong tracks? – Sanna Jaakkonen Jul 10 '13 at 08:27
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    First, linear regression does not assume that the independent variables or their interaction are normally distributed. The heteroscedasticity may be a problem. [Here](http://stats.stackexchange.com/questions/175/how-should-outliers-be-dealt-with-in-linear-regression-analysis) is a good post about how to deal with outliers. [This post](http://stats.stackexchange.com/questions/23887/linear-model-heteroscedasticity) may be informative regarding the heteroscedasticity. One proposal is to use robust standard errors or to respecify the model (or transform he variables). – COOLSerdash Jul 10 '13 at 08:35
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    +1. Numerous different strategies could make sense here. Broadly speaking, dropping outliers because some of the data make analysis more challenging is about the worst. Identifying a better scale for your predictors is a better strategy. – Nick Cox Jul 10 '13 at 08:44
  • Thank you COOLSerdash for the links, I'll familiarize myself with them. – Sanna Jaakkonen Jul 10 '13 at 08:52
  • Nick Cox: I agree that there's no reason to throw out data just because an inexperienced analysist is a bit lost with it. :) What do you mean by "identifying a better scale" -variable transformations? – Sanna Jaakkonen Jul 10 '13 at 08:59
  • Indeed: transformations, in the most general sense. – Nick Cox Jul 10 '13 at 10:18

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