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

John Fox <jfox at mcmaster.ca> writes:

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.

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.

On the face of it (which is as far as I am able to see), it would seem
fairly easy to set up an MLE procedure if you treat all discrete
variables as obtained by setting cutpoints on continuous latent
variables. I suspect this is what MPlus is doing. The requisite normal
integrals should be available through library(mvtnorm).