plot, summarize changes in h2 per people-varibale per additional PC extracted

[maxheld83]

This is another idea to inform a decision on how many factors should be extracted (in addition to #68).

Ideally, in a Q analysis, we'd like all respondents to be somewhat represented in the resulting factor interpretation. Of course, if you retain fewer, rather than more PCs (as may be suggested by a parallel analysis), it is possible that the h2 communality for some people will drop precipitously, as you drop a PC.

This may be unacceptable.

Furthermore, if the researcher has substantive reasons for believing that the h2-depressed participants actually do share a real common subjectivity, the additional PC may be retained even if the parallel analysis suggests otherwise. In this case, the researcher would effectively be saying "yeah, actually, I know these people, they're viewpoint is really not random", even if parallel analysis offers no such support.

The plot and summary will make these kinds of judgements easier.

It's probably most useful in marginal decisions; should retain one more/less borderline factor/PC.

[maxheld83]

Something like this.

Here the slightly disorienting plot over all possible components.

Here the more tightly concentrated plot only up to the 5th PC, with initials as labels.

[maxheld83]

I'm still looking for a name for this plot. It's actually the opposite to a scree plot, both in terms of the data (it's the communalities, not the eigenvalues), and the interpretation: we're looking for that spot in the slope(s), where there is no longer a systematic/parallel/dramatic upward movement. In this case, I'd argue, it's between Ncomps 3 and 4.

So basically, I'm looking for the geological, or otherwise, opposite of scree.

• "Ridgeplot"?
• "Plateauplot"?

[maxheld83]

Some words on interpretation, too, to illustrate the point of this all:

I'd argue that, even though the parallel analysis doesn't bear this out (EVs, do, however), 3 PCs should be retained, because there is a dramatic, and parallel (!) movement of several people from the 2, to the 3-factor model: Su, He and Sa, in particular. I also happen to know that these people share some socio-demographic markers, and, from my interactions with them, it seems plausible that these women (!) might share a substantial viewpoint, and that their correlation isn't merely an artefact of random chance.

That might lead me to retain 3 factors, even though I can't support that by statistical criteria (under a parallel analysis).

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And the same stuff with the actual data:

  Christian Claus Frank Gisela Guenther Helga Horst Ingrid Juergen Karin Monika Petra Renate Sabine Stefan Susanne Ursula
2      0.50  0.64  0.66   0.59     0.50  0.25  0.52   0.65    0.45  0.42   0.54  0.67   0.55   0.34   0.42    0.12   0.46
3      0.62  0.65  0.66   0.60     0.56  0.40  0.52   0.65    0.56  0.47   0.59  0.70   0.58   0.64   0.50    0.47   0.46
4      0.63  0.71  0.74   0.62     0.60  0.49  0.55   0.82    0.64  0.54   0.60  0.70   0.58   0.73   0.61    0.60   0.48

According to parallel analysis, I should retain only 2 principal components. However, on closer inspection, three people's communalities drop quite dramatically between extracting 2 or 3 PCs, effectively making a 2-factor solution utterly irrelevant for them. I happen to know that these three women, Susanne, Sabine and Helga, share a) sociodemographic variables to some extent and b) might well really share some common viewpoint (I talked to them at length). This is less so for the change between a 3 and 4 component solution: the changes in communality are not as precipitous here, and the people who gain most, Helga and Ingrid, do not strike me as obviously sharing a viewpoint. Maybe then, adding a 4th component would move me into the realm of spurious factors.

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Makes sense?

[maxheld83]

done.