Hello,
I would like to conduct a logistic regression, however, I have an independent variable that is not normally distributed and some values seem to be a bit extreme.
Shall I be worried about the effect of potential outliers in an independent variable that is not normally distributed or it will not impact the results of the logistic regression?
If yes, any advice on how to deal with these outliers would be very much appreciated.
Many thanks.
Regards,
You need to say more about your DV which I assume is binary. My recommendations are contained in the protocol that is contained in the attached paper. Best wishes David Booth
Agree with David Eugene Booth
The basis of the logit model is the binomial function, not the Gauss curve.
In practice this has little to do with distributional assumptions and is about where the observations lie in the multidimensional space of Y and the Xs. Outliers can wreck an analysis; especially observations that are extreme in both X and Y:
https://stattrek.com/regression/influential-points.aspx
https://www.theopeneducator.com/doe/Regression/outlier-leverage-influential-points
There are various residual diagnostics for logit models that you can use to identify the effects of outliers in the predictor variables eg Dbeta will give you the change in a particular regression coefficient if that observation was dropped. This will tell you how sensitive your model is to particular observations. You can then investigate these observations further to understand what is going on. There is an example in this paper in which I plot the Dbeta against the case number of two variables I am most concerned about:Article Death and deprivation: an exploratory analysis of deaths in ...
[ Note: I am careful to say that observations should not be routinely dropped, they may be telling you that the model is wrong.]
See the section on influential observations in this
https://stats.oarc.ucla.edu/stata/webbooks/logistic/chapter3/lesson-3-logistic-regression-diagnostics/
The original development was by Pregibon, D. (1981) Logistic Regression Diagnostics, Annals of Statistics, Vol. 9, 705-724.
see also
Neil Wrigley (1983) Quantitative methods: on data and diagnostics https://doi.org/10.1177/030913258300700405
Neil Wrigley (1984) Quantitative Methods: Diagnostics Revisited
https://doi.org/10.1177/030913258400800404
and
http://web.pdx.edu/~newsomj/cdaclass/ho_diagnostics.pdf
These diagnostics are quite widely implemented in software.
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