Dear community,
I am analyzing a dataset where the outcome variables has a lower-bound of zero, approximately 50% of the values are actually 0, and the other 50% is skewed. In the end, I would like to use a censored model with a lower bound of 0, but I need to take the skewed distribution into account.
For the non-zero values, a log transformation would do the trick to achieve a approx. normal distribution, but (a) I cannot log-transform the 0-values, and (b) if I only log-transformed the values above 0, those values between 0 and 1 would result in negative values and would then be below the lower bound.
The variable is numeric, not a count variable, so no Poisson or negative binomial model can be applied.
Do you have any suggestion?
Thank you!
Someone recently asked a question that sounded quite similar on SEMNET. A tweedie distribution was mentioned. If that's helpful at all, then credit Holger Steinmetz
Hello Mirka,
The first consideration is, are the cases having a recorded value of zero pertinent to your research question? If not, then omit them (e.g., as might be the case if one is investigating persons having non-zero HIV viral loads).
If the zero case values are pertinent, then there will, in all likelihood, be no transformation which somehow makes the full distribution symmetric, let alone Gaussian in shape. (As an aside, you can always add a constant to the values in a data set prior to trying a nonlinear transform such as root or log.)
So, an option here, if you're convinced that the scores are indeed continuous in form, would be to use exact/permutation or resampling/bootstrap methods for running comparisons or estimating parameters of interest. Doing so frees you from having to make specific distributional assumptions. Dropping to rank-based methods could be another option, depending on your specific analytic aims.
Finally, as Carl Falk noted, the tweedie distribution could potentially be useful, especially as it can mimic (and therefore be replaced by proxy) for a number of better-known distributions: see this link: https://www.statisticshowto.com/tweedie-distribution/
Good luck with your work.
Have you considered hurdle models? Depends on your research question(s) and why you think the zeroes are inflated and if you have specific research questions about the zeroes.
Thank you all for your responses. I totally agree that a censored/hurdle model in combination with a lognormal model for the non-zeros would be optimal, and that the Bayesian approach can be useful to account for non-gaussian distribution. I did not know the tweedie distribution, thank you for pointing it out!
Because the application in which I wanted to use the model is in the clinical area, we aimed at keeping the analysis very simple. So I think, we will use a completely non-parametric approach in the end.
- Badges
- Science topic
- Similar topics
- Linguistics
- Composition Studies
- Publication