skewed continuous outcome with negative values

[Robbie Dembo]

Hi all --

I am hoping to get some advice on analyzing continuous outcomes which are very right-skewed and have negative values. The outcomes are standardized which is why there are values below zero. I know that log-transforming or doing something like a Poisson with robust variance won't work due to the negative values. I would appreciate any other suggestions. Thanks in advance.

[Nick Cox]

Don't standardize before trying to transform. If you're interested in Poisson regression you need data on the original scale any way, not a transformation.

[Robbie Dembo]

Hi Nick, thanks for your response. Unfortunately, these are secondary data and the particular outcomes I am working with are already standardized. So my challenge is to try to figure out a regression approach that can help address the skewness, while also allowing for negative values. I am not sure if there are good options, though...

[Nick Cox]

I can't see a way to proceed without the mean and SD to reverse the standardization (or equivalently the original minimum and maximum). Denote mean and SD by m and s. Then you want

either log(m + s y) if you are going to transform

or m + sy if you are going to use logarithmic link (in generalized linear model jargon)

for some standardized y, Minimum and maximum would do it as

original SD = original range / standardized range

and so forth.

[Robbie Dembo]

I hadn't thought of reversing the standardization, I should be able to do that. Thanks!