Date: Mon, 19 Nov 2001 13:07:47 -0800
Reply-To: Dale McLerran <dmclerra@MY-DEJA.COM>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Dale McLerran <dmclerra@MY-DEJA.COM>
Subject: Re: Three questions about factor analysis (scree, Bartlett,
cumulative over 1.0)
Content-Type: text/plain
>Date: Sun, 18 Nov 2001 11:44:24 +0100
>Reply-To: "Christian F.G. Schendera" <schendera@NIKOCITY.DE>
> "Christian F.G. Schendera" <schendera@NIKOCITY.DE> SAS-L@LISTSERV.UGA.EDU
>(1) Why does the scree plot of PROC FACTOR describe the eigenvalues based on
>the inital
>communalities? Is this correct? I would have expected eigenvalues based on
>the final communalities.
The final communalities are dependent upon the number of factors
which you have selected. Under the model for the selected factors,
the eigenvalues of excluded factors will be zero.
>(2) Is Bartlett's ChiČ in SAS synonymous to Barlett's sphericity test in
>SPSS?
Don't know.
>(3) I found cumulative over 1.0 in the results from a prinicpal factor
>analysis (see below). What does this mean?
>I read that the negative eigenvalues are meaningless. Anyway, cumulative
>goes beyond 1.0 before them. What is to be done? One of the final
>ccommunality esitimates for one var reaches 1.002, two only 0.35. Is this
>the possible cause?
What is your prior communality specification? If it is not one (i.e.,
you are not extracting principal components and rotating them), then
your correlation matrix is not positive semi-definite and you will
get some negative eigenvalues. The question is, what is the
interpretation of the eigenvalues which you compute? Of course, you
know that the eigenvalues are supposed to represent the variance
explained by a given linear combination of the variables. Well,
when we employ the correlation matrix, the variance being represented
is the total variance in the data. But, if you analyze a correlation
matrix where you place something other than 1 along the diagonal as
prior communalities, then the eigenvalues are constructed with
regard to those prior commonalities. Now, those prior communalities
are representative of the common variance in the data. This is less
than the total variance in the data. When we construct the eigenvalues
with respect to the common variance in the data, then the eigenvalues
of the first few factors should total to the "common variance".
The sum of all eigenvalues must total to the prior communality (common
variance). Because the sum of the eigenvalues for the "significant"
factors should approximate the total prior communality, and the sum
of the eigenvalues for all factors must equal the total prior
communality, the eigenvalues of the "nonsignificant" factors will
tend to be near zero, with some positive and some negative.
>Thanks in advance,
>Chris
>
>Eigenvalues of the Reduced Correlation Matrix: Total = 10.2169128 Average =
>0.72977948
>
>
> Eigenvalue Difference Proportion
>Cumulative
>
> 1 4.04496579 0.14190274 0.3959
>0.3959
> 2 3.90306305 2.67170554 0.3820
>0.7779
> 3 1.23135751 0.65423951 0.1205
>0.8985
> 4 0.57711800 0.11555809 0.0565
>0.9549
> 5 0.46155991 0.29883109 0.0452
>1.0001
> 6 0.16272882 0.07236559 0.0159
>1.0160
> 7 0.09036323 0.05838027 0.0088
>1.0249
> 8 0.03198296 0.01971677 0.0031
>1.0280
> 9 0.01226619 0.01727564 0.0012
>1.0292
> 10 -.00500945 0.02007918 -0.0005
>1.0287
> 11 -.02508863 0.01572435 -0.0025
>1.0263
> 12 -.04081298 0.05335051 -0.0040
>1.0223
> 13 -.09416348 0.03925466 -0.0092
>1.0131
> 14 -.13341815 -0.0131
>1.0000
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@fhcrc.org
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------
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