R help - Aug 2003 - 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)

> 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
Hello Peter, try the following:

####################################
nsim  <- 100
nsamp <- 100

r <- numeric(nsim)

for (i in 1:nsim) {
   dat <- matrix(rnorm(4 * nsamp), ncol=4)
   v1 <- rowSums(dat)/4
   v2 <- rowSums(dat[,1:3])/3
   r[i] <- cor(v1,v2)
}

plot(sort(r))
####################################

Hope it helps!

Thomas P.

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)
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list 
> https://www.stat.math.ethz.ch/mailman/listinfo> /r-help
> 
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