Dear all,
I hope everything is going well with you.
I am going to downscale GCM models using Statistical Downscaling. For conditional downscaling your predictand (precipitation) should be transformed to a normal distribution as I see in the leiterature. So I have a statistical problem which is related to hydrology.
I tried someroutine transforamtions such as root 4, root 3, binomial, one parameter Box Cox which failed to normalize my data.
Now I am looking for a recommended solution for transforming the data to normal distribution.
My precipitation data has a great deal of zero as I am working on an arid area so I think this should be the main problem.
As I have the pressure of time in my PhD, I prefer to use some availabe methods in SPSS or prepared platforms such as MATLAB or R available packages.
In addition, it is important that the data can inversely denormalized with a reliable results.
I would appreciate your comments and advice.
Best Regards,
FARZAD
I don't think you can. Say you have a distribution like in the attached histogram; that 'spike' of zeros all have the same value, so no matter what transformation you apply they are always going to have the same value, they are always going to be a 'spike' sticking out from the rest of the distribution.
One option would be to do separate analyses. First you recode this variable as binary (e.g., "WasThereRainfall", with values 'yes' or 'no') and do a binomial (logistic) analysis predicting whether or not there was rainfall at all (as a function of whatever predictors you have). Then you do a separate analysis on only the nonzero data to predict how much rainfall there was, contingent on there being rain at all, as a function of your predictors.
I don't think you can. Say you have a distribution like in the attached histogram; that 'spike' of zeros all have the same value, so no matter what transformation you apply they are always going to have the same value, they are always going to be a 'spike' sticking out from the rest of the distribution.
One option would be to do separate analyses. First you recode this variable as binary (e.g., "WasThereRainfall", with values 'yes' or 'no') and do a binomial (logistic) analysis predicting whether or not there was rainfall at all (as a function of whatever predictors you have). Then you do a separate analysis on only the nonzero data to predict how much rainfall there was, contingent on there being rain at all, as a function of your predictors.
I have done some literature review on the subject latelly and the usual approach is the one that Stephe Politzer-Ahles broadly described. You can search for "weather generators" or "rainfall generators". These will lead you to the methods and hopefully some prebacked routine.
Thanks for the info, Rafael. I don't know this field, but this method is also what is used in eye-tracking research about reading, which is what I am familiar with. We often have this kind of problem with 0s (for example, one measure we might look at is how much time someone spends re-reading a word in a sentence after they have passed it once... so there is maybe a regular distribution of reading times, but then also a ton of 0s since a lot of the time the person never did re-read the word at all) and the method I described is how we often deal with it, i.e., instead of doing one analysis of "re-reading times", we instead do one analysis of "proportion of re-reads" [in our jargon this is usually called "percent regressions"] and a second analysis of the re-reading times just for the datapoints that actually were re-read.
Interesting Stephen. I am always amazed by how somethings in science evolve in paralell.
I think that Stephen hit the mark.
You may find these papers helpful:
http://www.stat.ufl.edu/~aa/articles/min_agresti_2002.pdf
http://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-10-55
https://theses.lib.vt.edu/theses/available/etd-23098-6054/unrestricted/ch2.pdf
http://seananderson.ca/2014/05/18/gamma-hurdle.html
http://www.ncbi.nlm.nih.gov/pubmed/17885875
Dear Rafael,
Thank you for your comment on my question.
I would appreciate if you can share with me some of the publications that you mentioned.
Thank you for your cooperation in advance.
Best Regards,
Here are a couple, if you do not find what you are looking for tell me.
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