Is there a nonparametric equivalent to multiple regression? I have
three predictors which correlate (using Spearman's rho) with my
outcome measure of interest. I can't do a multiple regression because
the assumptions are violated, but is there a way to find out how much
variance the three predictors contribute to the outcome?

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Request for Question Clarification by jeremymiles-ga on 20 Mar 2003 04:58 PST

Why can't you use OLS regression - do you have ordered categorical
(ordinal) dependent variables, or do you have non-normal
distributions?  (Or some other reason).

If the former, the variance doesn't really exist, because the variance
is a parametric statistic.  However, there are ways around this.

Also, what program do you use / would you be able to use?  (If any.)

jeremymiles-ga

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Request for Question Clarification by jeremymiles-ga on 21 Mar 2003 03:05 PST

Also, what is your sample size?

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Clarification of Question by gareth981-ga on 21 Mar 2003 09:01 PST

Hi

I have non-normal distributions on the DV (highly skewed)

I'm using SPSS

I am going to give you three possible solutions to your problem, if
none of these work, then get back to me and we will find another.

1.  First, you might be surprised to hear that regression does not
assume that either the DV or the IVs are normally distributed. 
Rather, it assumes that the residuals are normally distributed.  The
easiest way to check this is to click on plots from the main
regression dialog, and ask for a histogram or a normal probability
plot.  This might show that you don't have a problem.

2. If you still have a problem, you might be able to transform your
DV.  If you have positive skew (i.e. lots of low values, not many
high, common in reaction time, or finance) then try a log transform -
this might solve the problem.  If you have negative skew, try a square
transform.

3.  If your skew is very serious, you could consider recoding into a
series of values, e.g. if it is salaries, you might split into 10
groups.

4.  If we are desperate, we could try bootstrapping, although this is
a bit tricky.

5.  If we are more desperate and you have a large sample, we could try
a technique that doesn't require normality, or is robust against it. 
We probably want to avoid this though.

That was more than three, wasn't it?  Let me know if that works, or
doesn't work, and we will have another go.

jeremymiles-ga

p.s.  I can provide some links or recommendations for further reading.
Are you based in a university where you have access to a library?

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Request for Answer Clarification by gareth981-ga on 26 May 2003 09:07 PDT

Where can I read about bootstrapping?

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Clarification of Answer by jeremymiles-ga on 27 May 2003 03:14 PDT

There are some syntax files for bootstrapping in SPSS here:

http://pages.infinit.net/rlevesqu/SampleSyntax.htm#Bootstrap

Two books that I like, which are not too technical are:

An introduction to the bootstrap, by Efron and Tibshirani,
http://www.amazon.com/exec/obidos/ASIN/0412042312/qid=1054030275/sr=2-1/ref=sr_2_1/002-7345361-6416803

And 
Bootstrapping, by Mooney and Duval,
http://www.amazon.com/exec/obidos/tg/detail/-/080395381X/qid=1054030275/sr=1-10/ref=sr_1_10/002-7345361-6416803?v=glance&s=books