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

[Stas Kolenikov <skolenik@gmail.com>]

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
>
> Factor loadings (pattern matrix) and unique variances
>
>    -----------------------------------------------------------
>        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
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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