[R] sem: incorrect parameter estimates

[John Fox]

Dear Baxter,

I suspect that there's a numerical problem here in nlm (the minimizer that 
sem uses) because of the different magnitudes of the parameters. I found 
that sem required 7 iterations even when it is started at the correct solution.

When I tried fitting the model to standardized variables, I got the correct 
solution immediately:

     > p.sd <- sqrt(diag(p.cov))
     > p.cor <- p.cov/outer(p.sd, p.sd)
     > p.ram.cor <- matrix(c( 'A->B', 'p1', NA,
     +                    'B->C', 'p2', NA,
     +                    'B<>B', 'p3', NA,
     +                    'D->B', 'p4', NA,
     +                    'C<>C', 'p5', NA
     +                   ), ncol=3, byrow=T)
     >
     > p.sem.cor <- sem(p.ram.cor, p.cor, 293, fixed.x=c('A','D'))
     > p.sem.cor

     Model Chisquare =  69.73743   Df =  2

             p1         p2         p3         p4         p5
     0.78408275 0.76667339 0.30200657 0.06088651 0.41221191

     Iterations =  0

This is as it should be, since for this model, the OLS estimates computed 
for the start values are the FIML estimates.

It seems to me that there are two issues here: (1) The different magnitudes 
of the parameters are causing problems. I may be able to improve the way 
sem passes the optimization problem to nlm. I'll take a look at this. (2) 
In some cases the start values produced by sem are not good, particularly 
for models with unstandardized variables. I've fiddled with this problem a 
bit without much success, which is primarily why I've kept sem below 
version 1.0. When I have a chance, I'll take another look at the start values.

Thanks for this example,
  John

At 10:57 PM 7/17/2002 -0500, Baxter Rogers wrote:
>Hello.
>
>I am getting results from sem that are not correct (that's assuming
>that the results from my AMOS 4.0 software are correct).  sem does not
>vary some of the parameters substantially from their starting values,
>and the final estimates of those parameters as well as the model
>chisquare value are incorrect.  I've attached some code that
>replicates the problem.  The parameters in question are the residual
>variances of the endogenous variables B and C.
>
>A couple of things: the coefficents for the one-headed paths are on a
>much different scale than those for the two-headed paths (1e-1 vs
>1e6).  I had to supply starting values, because the automatic ones
>were not reasonable (1e19) and caused a "singular matrix" error.  Is
>this possibly just a numerical issue?
>
>Thanks for any help!
>
>Baxter Rogers
>
>
>
>
>======= begin R code =======
>
># 071702 Baxter P. Rogers (rogers at mr.radiology.wisc.edu)
>#
># Self-contained demonstration of the sem package's failure to modify
># covariances from their starting values.  (This happens for numerical
># or analytic gradient calculation.)  Starting values are supplied
># because the default ones cause a "singular matrix" error.
>
># covariance matrix
>p.cov <- matrix(c( 6330357, 3398673, 3547333, 4764233,
>                    3398673, 2618468, 2194462, 2626567,
>                    3547333, 2194462, 3128874, 2869895,
>                    4764233, 2626567, 2869895, 5171829
>                   ), ncol=4, byrow=T)
>rownames(p.cov) <- colnames(p.cov) <- c('A','B','C','D')
>
># RAM specification
>p.ram <- matrix(c( 'A->B', 'p1', 0.2,
>                    'B->C', 'p2', 0.2,
>                    'B<>B', 'p3', 1e6,
>                    'D->B', 'p4', 0.2,
>                    'C<>C', 'p5', 1e6
>                   ), ncol=3, byrow=T)
>
>p.sem <- sem(p.ram, p.cov, 293, fixed.x=c('A','D'), debug=T,
>analytic.gradient=F)
>
>print(summary(p.sem))
>
>cat('\n\nFinal parameter values:\n')
>print(p.sem$coeff,digits=2)
>
>cat('\nExpected final values (from AMOS software):\n')
>cat('5.0e-01 8.4e-01 7.9e+05 4.3e-02 1.3e+06\n\n')
>
>cat('\n\nThe chisquare value from the AMOS fit is 69.7.\n')
>
>====== end R code =======
>
>
>--
>Baxter Rogers (rogers at mr.radiology.wisc.edu)
>UW Madison Medical Physics Department, fMRI
>Madison, Wisconsin, USA
>http://zoot.radiology.wisc.edu/~rogers/
>
>
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-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
-----------------------------------------------------

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