Re: st: Simulate and corr2data

[Richard Williams <Richard.A.Williams.5@nd.edu>]

At 09:48 PM 1/20/2004 +0000, Allan Reese wrote:
> Followed example for simulate except to use corr2data rather than gen to
> create the dataset.  Imagine my chagrin when each repetition gave the same
> answer!  So tried corr2data from the command prompt and found it gives the
> same sample time after time, regardless of any setting of seed.  Does
> anyone have a fix please?  Is this an unintended bug?  Looks counter
> intuitive and ought to happen only if "set seed" used to restart the
> sequence.
Given corr2data's intended purpose, I don't think this is really a 
bug.  corr2data is meant to generate data where only the means, 
correlations, sds and N are required for the analysis -- if any other 
feature of the data is required, corr2data will not handle it.  Hence, it 
doesn't matter what the data is, so long as it produces the desired 
correlations, etc.  As the online docs say,

    "corr2data is designed to enable analyses of correlation (covariance) 
matrices by commands that expect variables rather than a correlation 
(covariance) matrix.  corr2data creates variables with exactly the 
correlation (covariance) that you want to analyze.  Apart from means and 
covariances, all aspects of the data are meaningless.  Only analyses that 
depend on the     correlations (covariances) and means produce meaningful 
results.  Thus, you may perform a principal components analysis pca, a 
factor analysis factor, or an ordinary regression analysis regress, etc.

    "If you are not sure that a statistical result only depends on the 
specified matrices and not on meaningless aspects of the representation of 
the data, you can generate different datasets, each having the same 
correlation (covariance) matrix and means, by specifying different seed() 
values.  If the statistical result differs beyond what is attributable to 
roundoff error, the     statistical result is meaningless."

corr2data is great if, say, you want to replicate a published regression 
analysis where the means, sds and correlations are in the paper.  It is 
pretty obvious that the data are fake though, when you see that something 
that was a dummy variable in the original data takes on values like .432987 
in your corr2data pseudo-replication.  In SPSS, you achieve the same goal 
via various matrix commands where you just input the correlations, etc.; in 
Stata you create fake data with the desired structure.  I discuss this on 
pp. 7-9 of this handout:

http://www.nd.edu/~rwilliam/xsoc593/lectures/OLS-Stata.pdf



> If corr2data can not produce independent samples, can I have comments
> please on whather it is equivalent to use bootstrap with a large N and
> relatively small sample size.  I am interested in sample statistics that
> depend on the overall distribution of points, and the default use of
> bootstrap to select multiple samples of size N from N points must rely
> upon random points being used once, twice or more - or have I completely
> misunderstood?
Again, not clear on the goal -- but if corr2data with the seed option does 
not give you what you want (and I suspect it doesn't) you could create a 
large data set or data sets with corr2data and then draw random samples 
from them.  That might be easier than figuring out the gen commands that 
would be required to create a data set drawn from a population with certain 
desired characteristics.

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Richard Williams, Notre Dame Dept of Sociology
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