# Grid analysis

Tim A. Connor (connort@pacificu.edu)
Sat, 10 Feb 1996 14:03:00 -0800 (PST)

Chris Evans pointed out that I made an error typing the grid into the
mailer (constructs 2 and 3 were identical--a slip of the eye. There was
one other error as well). This is the corrected version:

I've been playing around with a grid I administered to a client a couple
of months ago. It's been useful therapeutically, but being something of
a novice to this I've been trying out different things just to see what I
can squeeze out of it. It's a 9x9 grid; the elements are the self in
various situations. I'm not sure how much information one would need to
give useful feedback, so I'll err on the side of too much.

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 -1 1 0 2 2 -2
2 -2 -2 2 2 1 -2 2 1
2 -2 -1 2 2 1 -2 2 2
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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