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Science Forum Index » Statistics - Education Forum » Bootstrap method for comparing correlations
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Message |
| Artur Matos |
 Posted: Sat Feb 10, 2007 8:25 pm |
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Guest
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Hi,
I have 2 multivariate data samples, and I want to compare their
correlation matrices: that is, for a set of variables (X, Y, Z...), I
want to find out
which correlations X-Y, X-Z,..., are different between the 2 samples.
The pairs (X,Y) are definitely not bivariate normal, so a standard
Fisher transformation will not work. I thought of applying a bootstrap
method for this, but I could not find any reference for this specific
test. I have only started studying bootstrap methods recently, so I am
not sure of how to proceed. My naive take on it would be to do
something as follows:
1) From the first sample, generate a new data set (X1,Y1) of the same
size, by sampling (X,Y) values with replacement. Pairs are sampled
together, so whenever a specific X is chosen, its corresponding Y
value is also sampled.
2) Compute the correlation of this bootstrap sample, rho1
3) Apply the same procedure for the second sample, and compute rho2
4) Compute their difference d*1 = rho1 - rho2,
5) Repeat this procedure R times, yielding d* = d*1, d*2, ... d*r
6) (Assuming alpha = 0.05) compute the 2.5 and 97.5 percentiles of
d*. The confidence interval of d* will be between these percentiles
7) if 0 belongs to the confidence interval of d* then reject the
hypothesis that the (X,Y) correlation is significantly different
between the two samples
 Proceed like this for all the remaning variable pairs (X,Z),
(Y,Z)... in the correlation matrix.
Is this approach correct, or is there any better way to solve it?
Thanks in advance,
Artur Matos |
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| Jeff Miller |
| Posted: Mon Feb 12, 2007 7:55 pm |
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On Feb 11, 1:25 pm, "Artur Matos" <arturmato...@gmail.com> wrote:
Quote: I have 2 multivariate data samples, and I want to compare their
correlation matrices..
The pairs (X,Y) are definitely not bivariate normal, so ...
I thought of applying a bootstrap
Sounds reasonable to me, but...
Quote: 1) From the first sample, generate a new data set (X1,Y1) of the same
size, by sampling (X,Y) values with replacement. Pairs are sampled
together, so whenever a specific X is chosen, its corresponding Y
value is also sampled.
2) Compute the correlation of this bootstrap sample, rho1
3) Apply the same procedure for the second sample, and compute rho2
4) Compute their difference d*1 = rho1 - rho2,
Step 4 doesn't seem like the right way to go, since rho1 and rho2
aren't
paired in any meaningful sense.
Suppose instead you repeat steps 1 & 2 many times to build up a
bootstrap
distribution of rho1 values, from which you can compute a bootstrap
confidence
interval (BCI) for correlation 1. Then, repeat the same steps many
times
for the second sample to get a BCI for correlation 2. Now, the issue
reduces to deciding whether these two BCIs overlap. |
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