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

 From Stas Kolenikov To statalist@hsphsun2.harvard.edu Subject Re: st: Identifying the best scale without a "gold standard" Date Wed, 16 Nov 2011 17:46:58 -0500

```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.  I may have given the wrong impression.
> In the real data (results below),  there 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.  I 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                        Number of obs    =      103
>    Method: principal factors                      Retained factors =        3
>    Rotation: (unrotated)                          Number of params =       15
>
>    --------------------------------------------------------------------------
>         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
>    -------------+------------------------------------------------------------
>        Factor1  |      2.68006      2.52737            1.0799       1.0799
>        Factor2  |      0.15269      0.02393            0.0615       1.1414
>        Factor3  |      0.12876      0.22397            0.0519       1.1933
>        Factor4  |     -0.09520      0.08428           -0.0384       1.1549
>        Factor5  |     -0.17948      0.02553           -0.0723       1.0826
>        Factor6  |     -0.20501            .           -0.0826       1.0000
>    --------------------------------------------------------------------------
>    LR test: independent vs. saturated:  chi2(15) =  206.74 Prob>chi2 = 0.0000
>
>
>    -----------------------------------------------------------
>        Variable |  Factor1   Factor2   Factor3 |   Uniqueness
>    -------------+------------------------------+--------------
>    overallNRS~e |   0.6421    0.2124    0.0122 |      0.5424
>      overallMRC |   0.6465   -0.1168    0.1992 |      0.5288
>    overallBor~e |   0.5869    0.1940    0.1212 |      0.6033
>    overalldy~12 |   0.7569    0.0510   -0.1620 |      0.3982
>    overallCRQ~y |  -0.6479    0.0963    0.2079 |      0.5277
>    overallCRQ~a |  -0.7160    0.2108   -0.0692 |      0.4381
>    -----------------------------------------------------------
>

It looks like the first four variables measure the factor with about
equal positive weights, while the last two, with the negative weights
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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```