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Hi all,
My response variable is cognitive function (CASI) which is scored from 0 to 100.
I want to model the relationship between CASI and some predictors.
One reccommendation is to transform CASI to CASI/100 and fit a logistic model.
So here CASI/100 ranges from 0 to 1.
I plan to use PROC GLIMMIX in this case. But I'm not sure which distribution should I specify for this special response variable.
Is it beta distribution? I read somewhere that beta distribution doesn't accept value 0 or 1.
I would love to hear from your experience.
Thank you,
Trang
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One approach is to gently rescale the data to lie strictly in (0, 1); see
https://www.ncbi.nlm.nih.gov/pubmed/16594767
A more elegant approach is the zero one inflated beta model; see
http://support.sas.com/resources/papers/proceedings12/325-2012.pdf
and an example
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Yes, beta distribution. Unless responses are 0 or 100, you won't need to worry about whether the beta distribution "accepts values 0 or 1."
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If I choose beta distribution and I have some case that Casi/100 equals 0 or 1, although they are extremely rare, would SAS omit these cases from the analysis?
Thank you for your reply,
Trang
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Yes, you are correct. The procedure will drop observations for which the response is not in (0,1) and will display the NOTE
NOTE: Some observations are not used in the analysis because of: not a
proportion, zero or negative response.
If you have 0 and 1 responses, perhaps beta is not the best model.
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I could suggest using GAMMA distribution for CASI variable.
and if you have many zero , try tweedie distribution.
OR
Try Poisson distribution + offset= option. Make an offset variable which is 100 .
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Thank you for your suggestion.
However, CASI is skewed, so I'm not sure that gamma distribution works here.
maybe it's the reason that I need to transform CASI to CASI/100, which ranges from 0 to 1.
I'm thinking of beta distribution, but it doesn't allow 0 and 1.
I want to find the most appropriate distribution that can accept value of 0 and 1.
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One approach is to gently rescale the data to lie strictly in (0, 1); see
https://www.ncbi.nlm.nih.gov/pubmed/16594767
A more elegant approach is the zero one inflated beta model; see
http://support.sas.com/resources/papers/proceedings12/325-2012.pdf
and an example
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Thank you so much for your reference with one-zero inflated beta regression!
I know something about beta regression, but never thought of one- zero inflated one.
This is exactly I want.
The illustration of SAS used similar type of response variable (a score from 0 to 100) like mine.
They also divided it by 100 and gave detailed guidance of the Macro for this analysis.
Best,