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06-27-2017 01:59 AM

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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Solution

06-27-2017
07:56 PM

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06-27-2017 05:35 PM

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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06-27-2017 05:00 AM - edited 06-27-2017 08:23 AM

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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06-27-2017 07:44 AM

Hi Rick,

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

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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06-27-2017 08:25 AM

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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06-27-2017 09:29 AM

Rick, so if I want to model this response variable in the most natural way, ie I can have some cases with Casi/100 equal to 0 or 1, what would be the most appropriate distribution?

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06-27-2017 08:12 AM - edited 06-27-2017 08:50 AM

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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06-27-2017 09:27 AM

Hi Ksharp,

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.

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.

Solution

06-27-2017
07:56 PM

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06-27-2017 05:35 PM

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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06-27-2017 08:07 PM

Hi sld,

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,

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,