[R] Specifying Path Model in SEM for CFA

[Rick Bilonick]

On Wed, 2006-08-16 at 08:47 -0400, John Fox wrote:
> Dear Rick,
> 
> There are a couple of problems here:
> 
> (1) You've fixed the error variance parameters for each of the observed
> variables to 1 rather than defining each as a free parameter to estimate.
> For example, use 
> 
> X1 <-> X1, theta1, NA
> 
> Rather than 
> 
> X1 <-> X1, NA, 1
> 
> The general principle is that if you give a parameter a name, it's a free
> parameter to be estimated; if you give the name as NA, then the parameter is
> given a fixed value (here, 1). (There is some more information on this and
> on error-variance parameters in ?sem.)
> 
> (2) I believe that the model you're trying to specify -- in which all
> variables but X6 load on F1, and all variables but X1 load on F2 -- is
> underidentified.
> 
> In addition, you've set the metric of the factors by fixing one loading to
> 0.20 and another to 0.25. That should work but strikes me as unusual, and
> makes me wonder whether this was what you really intended. It would be more
> common in a CFA to fix the variance of each factor to 1, and let the factor
> loadings be free parameters. Then the factor covariance would be their
> correlation. 
> 
> You should not have to specify start values for free parameters (such as
> g11, g22, and g12 in your model), though it is not wrong to do so. I would
> not, however, specify start values that imply a singular covariance matrix
> among the factors, as you've done; I'm surprised that the program was able
> to get by the start values to produce a solution.
> 
> BTW, the Thurstone example in ?sem is for a confirmatory factor analysis
> (albeit a slightly more complicated one with a second-order factor). There's
> also an example of a one-factor CFA in the paper at
> <http://socserv.socsci.mcmaster.ca/jfox/Misc/sem/SEM-paper.pdf>, though this
> is for ordinal observed variables.
> 
> I hope this helps,
>  John
> 
> --------------------------------
> John Fox
> Department of Sociology
> McMaster University
> Hamilton, Ontario
> Canada L8S 4M4
> 905-525-9140x23604
> http://socserv.mcmaster.ca/jfox 
> -------------------------------- 

Thanks for the information. I think I understand how to handle the
residual variance after reading the sem help file more carefully. Now I
have to figure out how to constrain each column of the factor matrix to
sum to one. Maybe this will fix the problem with being under-identified.

Rick B.