**From:** Lucke, Joseph F (*LUCKE@uthscsa.edu*)

**Date:** Thu 13 May 2004 - 23:19:29 EST

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Message-id: <C4A57662D47C7B44B781D39E4C8F06940E31EE@SAIGA.win.uthscsa.edu>

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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