# RE: [R] please help with estimation of true correlations and reli abilities

From: Lucke, Joseph F (LUCKE@uthscsa.edu)
Date: Thu 13 May 2004 - 23:19:29 EST

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Jens
I'm not sure what you intend by "predefined assumptions".

1. If you merely want to conduct an exploratory rather than confirmatory
analysis for the relevant paths, there are ways within SEM to do this. (In
this case you could use John Fox's SEM package).
2. If you do not wish to assume multivariate normality, then you may use a
variety of alternative (to maximum likelihood) estimation algorithms
available in most SEM programs.
3. If you do not wish to assume either the outcome variable or the latent
variable is continuous, there are SEM programs for this (Mplus being the
most prominent.)
4. If you do not wish to assume the true score is a linear function (or
generalized linear function for categorical variables) of the attribute
being measured, then you have a more difficult problem.

If presume you are familiar with SEMnet at
http://www.gsu.edu/~mkteer/semnet.html.
Joe

-----Original Message-----
From: "Jens Oehlschlägel" [mailto:joehl@gmx.de]
Sent: Thursday, May 13, 2004 4:06 AM
To: r-help@stat.math.ethz.ch
Subject: [R] 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 Oehlschlägel

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