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Subject:

Re: Multiple regression where heavy positive skew?

From:

Ben Gardner <[log in to unmask]>

Reply-To:

Ben Gardner <[log in to unmask]>

Date:

Mon, 23 Nov 2009 12:21:08 +0000

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

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Thanks to everyone who replied to my message about multiple regression for 
skewed outcomes. Iíve summarised responses below:

Assess skew using residuals, not raw data:
- In regression, skew (or non-normality, or even inconstancy of
variance) is only an issue in the residuals.  Different patterns of predictors can 
create very skewed patterns, but that's part of the systematic effects, not 
the random variation.  Testing the raw data set is irrelevant.

Use a different log transformation for multiple regression?
- Instead of log(x) try using log(x-1) or log(x-10) ... try different values, and 
find the one that minimizes the skew. No guarantee you'll get the really low 
skew you're after, but you should definitely get a better value than 14 when 
you find the optimum section of the curve. You can also extend the linear 
transformation to something like log(0.1(x-1)). Essentially you're moving your 
data range to the region of the curve that is most similar to the skewness to 
neutralize it. 

Binary logistic regression?
- Use binary logistic regression to model the probability of choosing option B 
(any B vs no B), as a function of the various factors that are presumed to 
affect the choice



Original message:
Quick summary:
(How) can I perform multiple regression analysis with a very strongly positively 
skewed variable, ideally using SPSS?

Details:
I have a dataset comprised of 206 participants been recruited on the basis 
that, where faced with a choice between Option A or Option B only, they 
almost always choose Option A not B. The study aims to predict why they 
might (occasionally) choose Option B not A. The outcome variable is the % of 
times over a 2-week period that Option B not A was chosen (i.e. % = number 
of option B choices / number of choice opportunities).

Frequencies indicate that 87% of participants chose Option A on 100% of 
occasions. 5% of participants chose Option B not A on 10% of occasions.
Only
1% chose Option B not A on the majority of occasions.

I have a number of potential predictor/explanatory variables that I would like 
to test as predictors of participants' deviation from using Option A all of the 
time. Can such an analysis be meaningfully conducted (using SPSS) with such 
heavy positive skew? If so, how?

(NB - using base 10 logarithm doesn't work - the skewness Z score, which I 
understand should be less than 1.96, is 35.21, and the base 10 log reduces it 
only to 14.55.)

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