[R] Re: Factor analysis of categorical or mixed categorical/continuousdata in [R]

[Prof Brian Ripley]

On Thu, 21 Feb 2002, John Fox wrote:

> At 11:18 AM 2/21/2002 +0000, Dr Stuart Leask wrote:
> >I am looking to fit one or more latent categorical variables to data that is
> >a mixture of categorical and continuous variables. Factor analysis would
> >work for continuous data, latent class analysis for categorical data. I
> >understand that in a package such as MPlus I could perform a single analysis
> >of both data types. Are there similar routines available in R?
>
> Dear Stuart,
>
> If memory serves me, a common approach is to use tetrachoric correlations
> (for dichotomous data), polychoric correlations (for ordered-category
> data), and point-biserial and polyserial correlations (for mixed data). If
> you want to do inference, then this approach gets complicated (requiring
> asymptotic sampling covariances for the correlations), but for a
> descriptive factor analysis, it should be reasonably straightforward.

Well, I'm confused.  Stuart said he wanted a latent *categorical*
variable, although that is not what factor analysis assumes, and John's
approach is presumably to do factor analysis and get continuous latent
variables out.

There really are tens of possible approaches even for continuous latent
variables and ordered categorical manifest variables.  All seem to boil
down to some algebra, some integration (perhaps numerical) and a good
constrained optimizer.  Given that the latent variable must affect the
manifest variable non-linearly, there are many possible links.
(Consider for example voter agreement variables, where `folding' can
occur.)

That's why I asked for *precise* details ....

> I'm not aware of any facility for calculating these kinds of correlations
> in R, but programming them shouldn't be too hard. I may add this at some
> point to the sem package.

Like factor analysis, finding good estimates is not an easy task, and
there are usually myriad local optima.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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