[R] Factor Analysis?

John Maindonald john.maindonald at anu.edu.au
Fri Feb 4 01:33:37 CET 2000

John Fox wrote

> Dear John,

> At 10:01 AM 2/3/2000 +1100, you wrote:

> >One could easily get the impression that these sorts of use are
> >almost the only ways in which factor analysis that goes beyond
> >principal components kinds of uses, and structural equation
> >modelling, are used.  It is very hard to find examples of the use
> >of these techniques where there is some genuine and plausible
> >attempt at model validation.  It is also very hard to devise and
> >implement good diagnostic statistics and plots.  Such concerns are
> >well articulated in David Freedman's paper (with extensive
> >following discussion) "As Others See Us; A Case Study in Path
> >Analysis", in J. Educ. Statistics 12: 101-223

> I think that Freedman's point is more general, and extends, for
  example, to regression analysis, even supported by good diagnostics
  -- he argues generally against drawing causal conclusions from
  nonexperimental data. Although many of his points are well taken, I
  find his argument extreme.

Thanks for that comment.

The arrow surely goes in the other direction.  The points which
Freedman makes on regression in his "Statistical Analysis and Shoe
Leather" paper (Sociological Methodology 1991, pp. 291-358) apply also
to Path Analysis, Structural Equation Modelling, etc.  There are
however additional points to be made, which have to do with the near
impossibility of checking empirically the hidden relationships that
are assumed.  

Freedman does sometimes get extreme.  I do not think it is fair to say
that he rules out the drawing of causal conclusions from
non-experimental data.  Rather I understand his argument to be that
the data on its own, however analysed, are not enough.  There is
extensive contextual information which, as he illustrates from John
Snow's work on the spread of cholera in the mid-19th C in London, has
to come together with the data.  In Path Analysis, Structural Equation
Modelling etc., one has to be very sure of the contextual information
(what are are paths?  what direction do they go?) for the analytic
results to have any credence.  This is in a context where the
statistical assumptions, on variables that are mostly hidden, readily
get out of hand.

> >I'd very much like to learn of published examples of the use of
> >these methods which do address these concerns.  If these can be
> >found, they would be good references to include when and if these
> >techniques are implemented.

> I don't generally think of myself as an advocate of either factor
  analysis or of structural-equation models, but I recognize that the
  better practitioners of these methods pay some attention to the
  descriptive adequacy of their models. Take a look, for example, at
  Bollen, Structural Equations With Latent Variables (Wiley, 1989) and
  Bollen and Long, eds., Testing Structural Equation Models (Sage,

> John
> |----------------------------------------------------|
> | John Fox                          jfox at McMaster.ca |
> | Department of Sociology        McMaster University |
> |----------------------------------------------------|
> -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-

I guess if this discussion is to continue, it might be well for it to
continue off-list.  It is well for list members to be aware that there
are issues here to consider.  One service that R may perform is to bring
together communities of statisticians and statistical users which have
become too largely separate.

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