[R] Specifying Path Model in SEM for CFA

[Rick Bilonick]

On Wed, 2006-08-16 at 17:01 -0400, John Fox wrote:
> Dear Rick,
> 
> It's unclear to me what you mean by constraining "each column of the factor
> matrix to sum to one." If you intend to constrain the loadings on each
> factor to sum to one, sem() won't do that, since it supports only equality
> constraints, not general linear constraints on parameters of the model, but
> why such a constraint would be reasonable in the first place escapes me.
> More common in confirmatory factor analysis would be to constrain more of
> the loadings to zero. Of course, one would do this only if it made
> substantive sense in the context of the research.
> 
> Regards,
>  John
> 
> --------------------------------
> John Fox
> Department of Sociology
> McMaster University
> Hamilton, Ontario
> Canada L8S 4M4
> 905-525-9140x23604
> http://socserv.mcmaster.ca/jfox 
> -------------------------------- 

I'm trying to build a multivariate receptor model as described by
Christensen and Sain (Technometrics, vol 44 (4) pp. 328-337). The model
is

x_t = Af_t + e_t

where A is the matrix of nonnegative source compositions, x_t are the
observed pollutant concentrations at time t, and f_t are the unobserved
factors. The columns of A are supposed to sum to no more than 100%. They
say they are using a latent variable model. If sem can't handle this, do
you know of another R package that could?

Rick B.