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I have the following data: Predictor X: positive count data (range 0 to 43), in this case the number of symptoms present out of a total of 43. Outcome Y: binary

I want to test, whether (or to what extend) the predictor (i.e. the number of symptoms present) is associated with the binary outcome in a logistic regression.

The predictor variable obviously is not normal and it is zero-inflated.

If I treat X as a linear predictor, I feel I would lose information as I won't be able to discriminate between the lower values of X (which are most of them). Larger values (higher number of symptoms) possibly are due to reporting bias rather than due to a much worse symptomatology. From a clinical perspective it would make sense to give more weight to 1 point increases in the lower end than in the upper end.

How do I incorporate this information into my regression model? How should I transform the X variable for this type of data?

Thank you for your help.

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First off, predictors do not need to be normally distributed. And whether there are many zeros does not make any difference at all.

You want to model possible nonlinearity in the relationship between the predictor and the outcome (a stronger response as we move from 0 to 1 point than as we move from 42 to 43 points). The method of choice would be to transform the predictor using . Frank Harrell's Regression Modeling Strategies has a very good introduction to splines.

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