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Re: st: Identifying the best scale without a "gold standard"


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Identifying the best scale without a "gold standard"
Date   Wed, 16 Nov 2011 18:56:01 -0500

Oops... I thought the full data matrix (all individual scale items) was being analyzed, not just the six scale scores (guess I should learn to scroll down). However, this raises concerns about parceling the individual items into the six summary scores:

Bandalos, D.L. (2008). Is Parceling Really Necessary? A Comparison of Results from Item Parceling and Categorical Variable Methodology. Structural Equation Modeling, 15(2), 211-240.

But I guess with only N = 103, analyzing the full inter-item correlation matrix might be intractable. 

Cam

> Date: Wed, 16 Nov 2011 17:46:58 -0500
> Subject: Re: st: Identifying the best scale without a "gold standard"
> From: skolenik@gmail.com
> To: statalist@hsphsun2.harvard.edu
> 
> On Mon, Nov 14, 2011 at 3:53 PM, Seed, Paul <paul.seed@kcl.ac.uk> wrote:
> > Dear Cameron,
> >
> > Thank you for all this information. áI may have given the wrong impression.
> > In the real data (results below), áthere is only one factor with eigenvalue > 1,
> > made up of six highly correlated measurements of breathlessness.
> > There is no space (as I understand it) for a second order factor analysis.
> >
> > The six individual measurements are all well-established and validated scales,
> > and are treated as single measurements for the purposes of the analysis.
> > It is therefore not entirely surprising that they agree so well.
> >
> > The research problem is to identify the best single scale for measuring breathlessness
> > from the six candidates. áI was therefore interested in a valid test for
> > identifying agreement of individual measures with a latent factor
> > to which they all contributed.
> >
> > *********************************************************************************
> >
> > . local vars overallNRSave overallMRC overallBorgave overalldyspnoea12 overallCRQMastery overallCRQDyspnoea
> >
> > . factor `vars'
> > (obs=103)
> >
> > Factor analysis/correlation á á á á á á á á á á á áNumber of obs á á= á á á103
> > á áMethod: principal factors á á á á á á á á á á áRetained factors = á á á á3
> > á áRotation: (unrotated) á á á á á á á á á á á á áNumber of params = á á á 15
> >
> > á á--------------------------------------------------------------------------
> > á á á á Factor á| á Eigenvalue á Difference á á á áProportion á Cumulative
> > á á-------------+------------------------------------------------------------
> > á á á áFactor1 á| á á á2.68006 á á á2.52737 á á á á á á1.0799 á á á 1.0799
> > á á á áFactor2 á| á á á0.15269 á á á0.02393 á á á á á á0.0615 á á á 1.1414
> > á á á áFactor3 á| á á á0.12876 á á á0.22397 á á á á á á0.0519 á á á 1.1933
> > á á á áFactor4 á| á á -0.09520 á á á0.08428 á á á á á -0.0384 á á á 1.1549
> > á á á áFactor5 á| á á -0.17948 á á á0.02553 á á á á á -0.0723 á á á 1.0826
> > á á á áFactor6 á| á á -0.20501 á á á á á á. á á á á á -0.0826 á á á 1.0000
> > á á--------------------------------------------------------------------------
> > á áLR test: independent vs. saturated: áchi2(15) = á206.74 Prob>chi2 = 0.0000
> >
> > Factor loadings (pattern matrix) and unique variances
> >
> > á á-----------------------------------------------------------
> > á á á áVariable | áFactor1 á Factor2 á Factor3 | á Uniqueness
> > á á-------------+------------------------------+--------------
> > á áoverallNRS~e | á 0.6421 á á0.2124 á á0.0122 | á á á0.5424
> > á á áoverallMRC | á 0.6465 á -0.1168 á á0.1992 | á á á0.5288
> > á áoverallBor~e | á 0.5869 á á0.1940 á á0.1212 | á á á0.6033
> > á áoveralldy~12 | á 0.7569 á á0.0510 á -0.1620 | á á á0.3982
> > á áoverallCRQ~y | á-0.6479 á á0.0963 á á0.2079 | á á á0.5277
> > á áoverallCRQ~a | á-0.7160 á á0.2108 á -0.0692 | á á á0.4381
> > á á-----------------------------------------------------------
> >
> 
> It looks like the first four variables measure the factor with about
> equal positive weights, while the last two, with the negative weights
> of about the same magnitude. So your ad hoc unit weighted scaled
> should be
> 
> gen unit_weighted = overallNRSave + overallMRC + overallBorgave +
> overalldyspnoea12 - overallCRQMastery - overallCRQDyspnoea
> 
> See if this makes substantive sense though. If it does not, there is
> something grossly wrong with your data.
> 
> -- 
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
> 
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