[R] Simple simulation in R

[Liaw, Andy]

I believe simple math stat calculations should be sufficient for this.

For simplicity, assume X1 through X4 are iid with mean m and variance v.

Note that

  var1 = (3*var2 + x4) / 4

so
 
  cov(var1, var2) = cov(var2, (3*var2 + x4)/4)

and since var2 and x4 are independent, this covariance can be simplified.
Carry this through and substituting in m and v in the appropriate places
should give you the covariance (and hence correlation) in terms of m and
v.

Andy



> -----Original Message-----
> From: Peter Flom [mailto:flom at ndri.org] 
> Sent: Tuesday, August 26, 2003 10:31 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Simple simulation in R
> 
> 
> Hello all
> 
> I have a feeling this is very simple......but I am not sure 
> how to do it
> 
> My boss has two variables, one is an average of 4 numbers, 
> the other is an average of 3 of those numbers i.e
> 
> var1 = (X1 + X2 + X3 + X4)/4
> var2 = (X1 + X2 + X3)/3
> 
> all of the X variables are supposed to be measuring similar constructs
> 
> not surprisingly, these are highly correlated (r = .98), the 
> question is how much of  this correlation is due to the fact 
> that the X's are related, and how much to the fact that the 
> two VARs are similarly constructed
> 
> What I want to do is simulate this with normally distributed 
> data for the X's.  That is, generate (say) 1000 sets of X1 
> through X4, use those to caluculate 1000 var1 and var2, and 
> then 1000 correlations between var1 and var2, and then plot 
> those results.
> 
> Any help appreciated
> 
> Peter Flom
> 
> Peter L. Flom, PhD
> Assistant Director, Statistics and Data Analysis Core
> Center for Drug Use and HIV Research
> National Development and Research Institutes
> 71 W. 23rd St
> www.peterflom.com
> New York, NY 10010
> (212) 845-4485 (voice)
> (917) 438-0894 (fax)
> 
> ______________________________________________
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> 

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