[R] Specifying Path Model in SEM for CFA

[John Fox]

Dear Rick,


> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Rick Bilonick
> Sent: Thursday, August 17, 2006 7:07 AM
> To: John Fox
> Cc: 'R Help'; 'Rick Bilonick'
> Subject: Re: [R] Specifying Path Model in SEM for CFA
> 

. . .

> 
> 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?
> 

sem() handles only equality constraints among parameters, and this model
requires linear inequality constraints. 

I'm aware of SEM software that handles inequality constraints, but I'm not
aware of anything in R that will do it "out of the box." One possibility is
to write out the likelihood (or "fitting function") for your model and
perform a bounded optimization using optim(). It would probably be a fair
amount of work setting up the problem.

Finally, there are tricks that permit the imposition of general constraints
and inequality constraints using software, like sem(), that handles only
equality constraints. It's probably possible to do what you want using such
a trick, but it would be awkward. See the references given in Bollen,
Structural Equations with Latent Variables (Wiley, 1989), pp. 401-403.

I'm sorry that I can't be of more direct help.
 John