Rainfall data, skewed with zeros

Question

I would love some insight on how to treat daily rainfall data that is highly skewed with many zeros. I would like to use the rainfall data as a regressor of a logistic outcome. I do plan on categorizing the data but would also like to investigate linear associations and keep the rainfall data continuous. I would appreciate any thoughts on the best way to treat this data.

Answer 1

There is no rule against using the data as they come; you just have to see what works.

Historically, some people have used cube roots with rainfalls to make distributions more symmetric. Manifestly, zeros go to zeros with cube roots, so that fits. (The obvious contrast is the difficulty of what to do with logarithms when zeros are presented.) More statistically, the use of cube roots can be motivated by the idea that rainfall distributions can be approximately gamma-like.

However, the main reason for transforming would, or should, be to match the best functional form for your problem, not because the logistic model assumes anything about the marginal distribution of any regressor.

It's difficult to say more in the absence of any information on what your response variable is, what the other regressors might be, and what the scientific or practical problem is.

Possible complications include

1. Whether there is a qualitative difference between days without rain (or, days without "substantial" rain, for some definition of "substantial") and days with (same qualification) that is not captured by treating rainfall quantitatively. (I can't see any case for categorising rainfall otherwise; that strikes me as completely unphysical unless you have independent scientific grounds for expecting thresholds to be affecting your system.)

2. Whether there are memory or carry-over effects that are, or are not, captured in your model. For example, are you assuming that rain has an instantaneous and transient effect? That wouldn't fit many systems influenced by rainfall.