Your CIOS file request: Q-METHOD/06089124.521 hotline item

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Received:  by CIOS Mailer; Monday 8 Jun 2009 12:45:21
Date:         Mon, 8 Jun 2009 09:43:59 -0700
From:         Daniel Ozer 
Subject: Re: Analysis?
To:           Q-METHOD@LISTSERV.KENT.EDU
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Regardless of how many are rotated, the=20
cumulative proportion of variance accounted for=20
by the first k rotated components will never be=20
greater than the proportion of variance explained=20
by the first k unrotated components.  That's what=20
makes the components "principal".

At 12:06 AM 6/8/2009, you wrote:

>There seems to be something definitely amiss=20
>about this situation.  It is impossible, as=20
>Peter Schmolck notes, to rotate the first four=20
>unrotated factors and end up explaining more=20
>variance (or even explaining less variance).  If=20
>only the first four unrotated factors are=20
>admitted into the varimax phase, then the=20
>rotated factors should explain exactly 72.55% of=20
>the variance, just as the unrotated factors=20
>did.  However, I do agree with Bob Braswell that=20
>if (say) all eight principal components were=20
>allowed into the varimax rotation, that it would=20
>then be possible that four of those rotated=20
>factors could account for more variability than=20
>the first four unrotated factors by virtue of=20
>gaining some of the variance from those factors=20
>not retained in the final four.  But Sam Hopper=20
>claims to have kept only four factors for the=20
>varimax phase.  This doesn=92t add up and I would=20
>be inclined to re-run the analysis.
>
>Even without this problem, however, Sam Hopper=92s=20
>rotated solution looks problematic.  Factors 3=20
>and 4, for example, are only defined by a single=20
>Q sort and should therefore probably not be=20
>retained unless there is something special about=20
>those two individuals.  (The two sets of factor=20
>scores for these two factors will be nothing=20
>more than the Q sorts for those two=20
>persons.)  Moreover, the defining Q sort for=20
>factor 4 carries a negative loading, so that=20
>factor should probably be reflected.  In=20
>addition, it very much looks like factors 1 and=20
>2 are highly correlated with one another.  This=20
>may be one of those rare cases in which the=20
>unrotated solution might be the best final=20
>solution.  It might be helpful if Sam Hopper=20
>could provide us with more information about the=20
>nature of the study and perhaps the Q sample=20
>that is being used.  This might provide a key=20
>that would help explain these unusual results.
>
>As to Sam Hopper=92s desire =93to look at subgroups=20
>within my data,=94 this is generally not a good=20
>idea.  For one thing, males-females,=20
>Republicans-Democrats, and like divisions are=20
>mere categories which are supplanted by the=20
>operant categories represented by the Q=20
>factors.  Conventional categories are not=20
>accurate guides as to the way nature actually=20
>operates and ought to be replaced by more=20
>precise designations (such as Q factors) when=20
>these reveal themselves.  Conventional=20
>categories are only useful in designing P sets,=20
>and to return to categories once the Q factors=20
>have been revealed is to place the lever in the=20
>wrong location.  Moreover, given that P samples=20
>are neither large nor randomly selected means=20
>that the categories that comprise them are ill=20
>suited for inferential purposes.  That said, it=20
>is always possible to keep the Q factors intact=20
>and then compare subcategories of persons using=20
>t, F, or other tests of this kind.  For=20
>instance, a t-test could be used to determine=20
>whether the average factor-1 loadings for males=20
>is significantly greater than the average=20
>factor-1 loadings for females.  Or quantitative=20
>variables (such as IQ) could be correlated with=20
>the loadings for the various factors.  Such test=20
>results would still be on shaky ground given the=20
>small and probably unrepresentative character of=20
>the person sample.  In Q studies, it is best=20
>(and certainly safest) to focus on the factor=20
>arrays=ADwhich is where the subjectivity is=ADand to=20
>play down the matrix of factor loadings and the=20
>objective demographic characteristics of the=20
>respondents that are associated with the=20
>loadings.  To focus on the latter is to move=20
>back toward R methodology and all its logic,=20
>which Q methodology is ill suited to do.
>___________________________________________
>*  _____  ______  ____  __ __  ____  ___ _  *  Steven R. Brown
>| |  ___||_    _||  _ ||  |  ||  _ ||   | | |  Political Science
>| |___  |  |  |  |  _| |  |  ||  _| |     | |  Kent State University
>| |_____|  |__|  |____| \___/ |____||_|___|=20
>|  (sbrown@kent.edu)
>*___________________________________________*_________________________
>Economists have forecasted nine out of the past five recessions.
>
>
>
>
>On 6/5/09 9:37 AM, "Sam Hopper"=20
><hopper_sam@HOTMAIL.COM> wrote:
>
>Dear all
>I just have a couple of questions regarding my results and I wondered if
>
>anyone could help. The first is regarding eigenvalue's/% of variance
>explained - the prerotation values are:
>Factor  Eigenvalue      As Percentage   Cumulative percentage
>1       20.78                61.12      61.12
>2       1.74                 5.13       66.26
>3       1.13                 3.34       69.60
>4       1.00                 2.95       72.55
>
>ect...
>
>but the post rotation ones are higher (see below), why is this, I'm going
>
>to have to explain it in a viva potentially.
>
>  QSORT             1         2         3         4
>
>   1 1            0.4356    0.6995X   0.1473   -0.1207
>   2 2            0.6738X   0.4643   -0.0180    0.1879
>   3 3            0.7053X   0.5243    0.0358    0.0964
>   4 4            0.5475    0.6437X  -0.1134   -0.1321
>   5 5            0.1918    0.6030X   0.3802   -0.0802
>   6 6            0.5815    0.6357X   0.0655    0.0106
>   7 7            0.8032X   0.3382    0.0457    0.2553
>   8 8            0.5793X   0.5234   -0.0133    0.0006
>   9 9            0.7499X   0.3172   -0.0290    0.3484
>  10 10           0.6242X   0.5898    0.0382    0.0342
>  11 11           0.6167X   0.4980    0.1298   -0.0137
>  12 12           0.7740X   0.3658    0.0986    0.2421
>  13 13           0.3465    0.4923X  -0.0391    0.2337
>  14 14           0.6139X   0.5119   -0.0139    0.0914
>  15 15           0.5519    0.6386X   0.2492   -0.1189
>  16 16           0.7346X   0.4022    0.1266    0.2470
>  17 17           0.8324X   0.2080    0.1408    0.4370
>  18 18           0.8249X   0.3016    0.1740    0.3439
>  19 19           0.7487X   0.4959    0.1330    0.0894
>  20 2800         0.6644X   0.4046    0.1106    0.2713
>  21 2809         0.0840    0.2934X   0.9208X   0.0424
>  22 2830         0.8255X   0.2794    0.0717    0.3035
>  23 2876         0.7728X   0.4232    0.1197    0.1627
>  24 2878         0.6264X   0.4768    0.1398    0.0909
>  25 2880         0.2799    0.7442X   0.2099   -0.1633
>  26 2884         0.6981X   0.5118    0.0937    0.0570
>  27 29 21        0.3420    0.7810X   0.1600   -0.2195
>  28 30 74        0.6144X   0.6092    0.0311    0.0211
>  29 3120         0.7232X   0.4899    0.0517    0.0845
>  30 3357         0.6375X   0.5772    0.1268   -0.0659
>  31 3371         0.6214X   0.4536    0.2503   -0.0161
>  32 3380        -0.5689X   0.4873    0.0069   -0.8105X
>  33 3382         0.7587X   0.3588   -0.0038    0.2617
>  34 3383         0.6317X   0.4697    0.2232    0.2220
>
>  % expl.Var.         41        26         4         5
>
>
>
>Secondly, I would like to look at subgroups within my data, but dont want
>
>to delete sorts from the file to do this. Is there a way of "ignoring"
>
>certain participants sorts or making a new file (with copied data) so I c
>an
>delete the unwanted sorts?
>
>Thank you very much for any help!
>Sam


Daniel Ozer
Department of Psychology
University of California, Riverside
Riverside CA  92521

http://www.psych.ucr.edu/faculty/ozer/index.html

Voice:  (951) 827-5211
Fax:  (951) 827-3985
e-mail:  daniel.ozer@ucr.edu