''TYPOLOGY'' from factor analysis

[Rich Ulrich]

The most common way to score factors in social science research is
to take, for instance,  Factor1= mean(var1 to var5, var7, var15, v21).
You do your factor scoring by simple Compute statements, which are
entirely portable to research by everyone else.

That gives you a score that is anchored to the original labels, easing
interpretation and discussion.

When you score several factors this way, they will end up correlated
regardless of whether the factor analysis you are referencing used
oblique or orthogonal rotations.  In practice, using oblique tends to
produce an excessive amount of inter-correlation.  Also, an oblique
rotation is not likely to give you the convenient use of cut-offs for the
loadings -- there will be many more items that load on multiple factors.

Your cluster analysis will be /much/ more robust if you base it on five
factors than if you use 40 or 80 items.

"Iterate on the communalities" is the default option for most factor analyses.
If you keep 1's on the diagonal, the result is a Principal-Components analysis;
this is desirable when distinct items are assumed to have "unique" variance
which should be preserved.  Those are (by far) the most common choices.

The communality for a variable shows how much of the items variance (R2)
is accounted for by the factors that have been derived.  When the sample N
is barely above the number of variables, that R2 will be too high, because of
capitalization on chance.  Factoring is not very robust when the N is not at
least 4 to 10 to 20 times the number of variables; for small N, you can help
the robustness by putting a fixed value like 0.7  as the communality.

--
Rich Ulrich

> Date: Thu, 2 Jun 2016 12:24:08 -0700

> From: [hidden email]
> Subject: Re: ''TYPOLOGY'' from factor analysis
> To: [hidden email]
>
> Thanks Rich.
>
> Actually some initial data analysis now done and form initial factor
> analysis looks like there are about 5 'worthwhile' factors, using scree plot
> to judge cut off. Oblique rotation was used as no reason to think factors
> should not be correlated. These five factors seems to replicate patterns in
> the literature broadly. So if proceeding along this path then one question
> would be how do they take this 'model' to classify new cases (to 'score' a
> datset).
>
> E.g. person x fills in questionnaire (same as the one used to generate the
> data for the factor analysis) and the researchers would like to determine
> which factor/s would best explain that person's responses. Perhaps this can
> be done using the factor scores, though I don't immediately see how.
>
> In SPSS cluster analysis models can be exported in XML and applied to an
> unscored dataset but this doe snot seem possible for factor analysis, at
> least not in the same way.
>
> It is cases that they wish to score ultimately, not variables so that may
> mean cluster analysis makes more sense.
>
>
> Could you elaborate just a little on ''Iterate on the communalities ''. I
> understand what communalities are (just about) but not sure how one iterates
> on them in SPSS>
>
> Thanks

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[John F Hall]

An early example of typology construction was generated (from a survey of academic staff in universities in the late 1950s) by the late “Chelly” Halsey. [https://en.wikipedia.org/wiki/A._H._Halsey]   From memory, he and his colleagues divided academics into something like this:

 

                                    Elitist                 Expansionist

                              _________________________

Teachers              |                            |                            |

                              |___________   |___________   |            

Researchers        |                            |                            |

                              |___________   |___________   |

 

The typology was developed, not from factor or cluster analysis, but from previous knowledge, experience, sociological and political theory, and eyeballing frequency counts and contingency tables, plus a bit of brain power and intuition.

 

I think the original authors were Halsey. Floud and Martin, but that could have been for a journal article.  One book title is:

Education, Economy, and Society: A Reader in the Sociology of Education (1961)

[https://books.google.fr/books/about/Education_economy_and_society.html?id=E2UXAAAAIAAJ&redir_esc=y]

Other references can be found on:

[https://books.google.fr/books?id=szimMC01FWwC&pg=PA65&lpg=PA65&dq=floud+halsey+martin+education&source=bl&ots=J31VoXen64&sig=fLqSZj4Ksr5znF3wrKNScZRbPf0&hl=en&sa=X&ved=0ahUKEwiGmdOVg4vNAhXBfhoKHZY1Ad8Q6AEIPjAG#v=onepage&q=floud%20halsey%20martin%20education&f=false]

 

John F Hall (Mr)

[Retired academic survey researcher]

 

Email:   [hidden email] 

Website: www.surveyresearch.weebly.com

SPSS start page:  www.surveyresearch.weebly.com/1-survey-analysis-workshop

 

 

 

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[Art Kendall]

The kaiser criterion rarely (if ever) the best number of factors to retain.
The eigenvalue of one is used for programming convenience. it tells teh computer the maximum number of dimensions to extract. Mathematically there could be as many factors as there are input variables, but it is a lot of work for a computer to extract factors, so programmers say if the purpose is to reduce the number of dimensions, it would be unreasonable to extract dimensions that account for less than the average input variable.

Was the factor analysis done by earlier researchers? How many cases were used?  How many variables were factored?

Varimax rotation  maximizes divergent validity.  



Do you have access to the data that was used?  If you do, I suggest that you check the archives for this list for "parallel analysis".   I had done many factor analyses for a couple of decades before parallel analyses came out (early 90's?).  I used several then current ways of ball-parking the number of factors to retain.  When I went back, the number of factors retained corresponded to about 1.00 more than the eigenvalues from the parallel analysis.

When you have ball-parked the number of factors to retain, it becomes a matter of interpretation as to whether you can make sense of why items appear to be measuring the same thing and what that "same thing" (construct) might be.  If you cannot make sense of what the pile/heap/bunch of items have in common, then you would not want to create a scale score with that set/pile.

Rich gave you some good advice on scores.