R help - May 2004 - please help with estimation of true correlations and reliabilities

Can someone point me to literature and/or R software to solve the following
problem:

Assume n true scores t measured as x with uncorrelated errors e , i.e. 
x = t + e 
and assume each true score to a have a certain amount of correlation with
some of the other true scores.

The correlation matrix cx of x will have its off-diagonal entries reduced by
measurement error compared to the true correlation matrix ct of t, however
the diagonal entries remain without attenuation. Consequently the
correlation matrix of observed variables has different things on- and
off-diagonal. 

I would like to estimate 
1) the true correlation matrix ct
2) the measurement reliabilities rxx, i.e. the correlation of a score with
itself attenuated by its measurement error (as if we had two measurements of
the same score).
but I don't have predefined asumptions about structure in the variable set
as I guess would be needed for SEM.

Is R software available to do this?

Best regards


Jens Oehlschl??gel

--

Dear Jens,

It sounds as if you're postulating a single-factor model underlying the
x's
(which is an assumption about the structure of the variables). If that's the
case, then you could either use the factanal function in the stats package
or the sem function in the sem package to estimate the model. The former
would be simpler. 

I hope this helps,
 John
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Jens 
> Oehlschl??gel
> Sent: Thursday, May 13, 2004 4:06 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] please help with estimation of true correlations 
> andreliabilities
> 
> 
> Can someone point me to literature and/or R software to solve 
> the following
> problem:
> 
> Assume n true scores t measured as x with uncorrelated errors 
> e , i.e. 
> x = t + e
> and assume each true score to a have a certain amount of 
> correlation with some of the other true scores.
> 
> The correlation matrix cx of x will have its off-diagonal 
> entries reduced by measurement error compared to the true 
> correlation matrix ct of t, however the diagonal entries 
> remain without attenuation. Consequently the correlation 
> matrix of observed variables has different things on- and 
> off-diagonal. 
> 
> I would like to estimate
> 1) the true correlation matrix ct
> 2) the measurement reliabilities rxx, i.e. the correlation of 
> a score with itself attenuated by its measurement error (as 
> if we had two measurements of the same score).
> but I don't have predefined asumptions about structure in the 
> variable set as I guess would be needed for SEM.
> 
> Is R software available to do this?
> 
> Best regards
> 
> 
> Jens Oehlschl??gel
> 
> --
> 
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Dear John,

I checked for the uniquenesses from factanal() and found out that these
estimates need an a priori assumption about the number of latent factors
(and they depend strongly on that assumption). What I want is an estimate of
reliablity independent of such an assumption.  Is it possible to specify
such "structure" to sem or another SEM software? (no assumption about
number
of factors, no assumptions about which variables group together).

Best regards


Jens Oehlschl??gel

--