Hello everyone,
Re. Factor Analysis: Covariance based
I have received a reply from SPSS which details why the order of factors
in an SPSS solution (Covariance based) aren't necessarily the same as
the order of the factors in Minitab.
In SPSS, in an analysis based on covariances, the rotations are done in
the *rescaled* metric, and the rotated results are sorted in *descending
order of sums of squared loadings in that metric*. [The rescaled
component loading matrix (which is subjected to rotation) is the raw
component loading matrix rescaled by dividing each coefficient related
to a particular variable by that variable's standard deviation.]
In Minitab, we do not work such 'rescaled loadings' merely the 'raw
loadings'.
Many thanks,
Kim.
Dr Kim Pearce,
Industrial Statistics Research Unit (ISRU),
Stephenson Centre,
Stephenson Building,
Newcastle University,
Newcastle upon Tyne,
United Kingdom,
NE1 7RU.
Tel: +44 (0)191 222 6281,
Fax: +44 (0)191 222 7365
>-----Original Message-----
>From: K F Pearce
>Sent: 16 June 2005 12:28
>To: [log in to unmask]
>Subject: SPSS and Mintab comparisons
>
>Hello everyone,
>
>I was comparing the results of a Factor Analysis in Minitab
>and SPSS [v11 & v12] (covariance based with Varimax rotation)
>and I noticed that SPSS printed Factors 2 and 3 in the
>opposite order. Has anyone noticed this too? I think it must
>be a bug in SPSS as the factors should be arranged in
>decreasing order of the variance explained, and as we can see
>from the output below this is not the case for the SPSS
>solution. The Minitab solution does, however, appear to be correct.
>
>Many thanks,
>Kim
>
>Minitab Output
>
>Rotated Factor Loadings and Communalities Varimax Rotation
>
>Variable Factor1 Factor2 Factor3 Factor4 Communality
>var1 1.103 0.520 -0.287 -0.085 1.577
>var2 0.160 0.168 -0.894 0.061 0.857
>var3 0.001 0.082 -0.044 -1.001 1.010
>var4 0.916 0.835 -0.296 -0.046 1.625
>var5 1.027 0.497 -0.296 -0.043 1.392
>var6 1.249 0.307 -0.278 -0.112 1.743
>var7 -0.193 -0.371 0.297 0.284 0.344
>var8 1.059 0.088 -0.396 -0.043 1.288
>var9 0.438 0.868 -0.357 -0.109 1.085
>var10 0.274 0.249 -0.640 -0.099 0.556
>var11 0.393 0.153 -0.566 -0.337 0.611
>
>Variance 6.2750 2.3286 2.2385 1.2470 12.0890
>% Var 0.445 0.165 0.159 0.088 0.857
>
>
>SPSS OUTPUT
>
>
>Rotated Component Matrix
> Raw
> Component
> 1 2 3 4
>VAR00001 1.103 .287 .520 .085
>VAR00002 .160 .894 .168 -.061
>VAR00003 .000 .044 .082 1.001
>VAR00004 .916 .296 .835 .046
>VAR00005 1.027 .296 .497 .043
>VAR00006 1.249 .278 .307 .112
>VAR00007 -.193 -.297 -.371 -.284
>VAR00009 1.059 .396 .088 .043
>VAR00010 .438 .357 .868 .109
>VAR00011 .274 .640 .249 .099
>VAR00012 .393 .566 .153 .337
>
>Extraction Method: Principal Component Analysis. Rotation
>Method: Varimax with Kaiser Normalization.
>a Rotation converged in 5 iterations.
>
>Total Variance Explained
>
> Component % of Var Cumulative %
> 1 44.486 44.486
> 2 15.870 60.356
> 3 16.511 76.867
> 4 8.840 85.707
>
>
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