Raw grid (elements in columns):
2 1 -2 2 2 -2 2 2 1
2 -2 -2 2 2 0 -1 2 -1
2 -2 -2 2 2 0 -1 2 -1
2 -2 -2 2 2 1 -2 2 1
2 -2 -1 2 2 1 -2 2 -1
1 -2 -1 2 2 0 -2 2 -1
2 -1 -1 2 2 0 1 1 2
2 -1 -2 1 1 1 -2 2 1
1 -2 -2 1 0 -1 2 2 -1
Correlation matrix (from OMNIGRID):
C1 C2 C3 C4 C5 C6 C7 C8 C9
C1 .55 .49 .37 .27 .35 .69 .34 .7
C2 .62 .9 .8 .94 .73 .81 .66
C3 .37 .23 .41 .44 .35 .83
C4 .97 .89 .76 .95 .42
C5 .83 .75 .92 .31
C6 .59 .78 .47
C7 .64 .62
C8 .35
PCA (from NCSS):
Component 1:
Value 6.031759 Percent 67.01959
Asociated Eigenvector
1 Construct 1 .2502107
2 Construct 2 .3931041
3 Construct 3 .2475273
4 Construct 4 .3807792
5 Construct 5 .3535509
6 Construct 6 .3583258
7 Construct 7 .3446303
8 Construct 8 .3537053
9 Construct 9 .2816513
Component 2:
Value 1.660841 Percent 18.4538
Associated Eigenvector
1 Construct 1 -.4332807
2 Construct 2 .005710154
3 Construct 3 -.4751942
4 Construct 4 .267817
5 Construct 5 .3580443
6 Construct 6 .1899857
7 Construct 7 -.08576919
8 Construct 8 .2850366
9 Construct 9 -.511671
The first two components account for 85% of the variance, so I won't take
up bandwidth with the others. My main question is, is the first component
interpretable as it stands? All the constructs load positively, none very
heavily, and all within a fairly narrow range. NCSS doesn't do rotation,
so I may have just hit the limits of my not-terribly-sophisticated
software.
Another question is how the subjects-to-variables ratio affects PCA with
grids. All the grids I've seen violate the rule of thumb that the STV
ratio should be >5; this one, in addition, has fewer than 100
observations. Does this limit the value of PCA with smaller grids?
All suggestions are welcome. As I said, I'm fairly new to this, so there
may be (almost certainly are) questions I haven't thought to ask.
Thanks,
Tim Connor, M.S.
Pacific University
School of Professional Psychology
<connort@pacificu.edu>
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