Dear John,

Thank you for your reply.  My data is actually simulated under the model X
= Lambda*F + E.

Since my post, I've simplified the simulation of my data and I still get
the error.  This is what I've done since my last post.

I constructed Lambda apriori (so I know exactly which observed variables
load onto which factors), E follows a Gaussian with mean 0 and var-cov
matrix given by the Identity matrix.

For my particular model, I sample the factor scores F_i (for sample i) from
a multivariate normal

F_i ~ N(mu_i, Phi).

mu_i is fixed to Phi*z_i, where z_i is a 5x1 vector.

Thinking I could have an ill-conditioned var-cov matrix, I looked at the
condition number of Phi (the factor var-cov matrix).  I recently adjusted
Phi to ensure that the condition number was indeed small (it is now about
2).

I then sample Y_i ~ N(Lambda*F_i, Psi).

If the data I'm simulating is ill conditioned, I'm not even sure how to fix
it because the simulation itself is pretty straightforward.  Even with a
well conditioned factor var-cov matrix Phi that I used to sample my factor
scores, I still get that same problem.

In any case, I am so grateful for your help- I've been working on this all
day and I can't seem to figure out where I go wrong.  I made Lambda pretty
sparse and with 150 samples, I certainly don't have too many parameters...
besides identifiability, I'm not sure what to check for if its not a
problem with my coding.  Your post has already helped me to think about
this problem a little differently.

Sincerely,
Lisa


On Tue, Nov 8, 2011 at 9:32 PM, John Fox <jfox@mcmaster.ca> wrote:

> Dear Lisa,
>
> There doesn't seem to be anything logically wrong with your model.
>
> I don't have much time today to look into it, but trying different
> optimizers in version 2.0-0 of sem, using the correlation matrix in place
> of the covariance matrix, and setting the par.size parameter, I was unable
> to obtain an admissible solution. I also was unable using factanal() to fit
> an exploratory factor analysis for five factors to your data. I expect that
> the problem is ill-conditioned.
>
> Best,
>  John
>
> ------------------------------------------------
> John Fox
> Sen. William McMaster Prof. of Social Statistics
> Department of Sociology
> McMaster University
> Hamilton, Ontario, Canada
> http://socserv.mcmaster.ca/jfox/
> On Tue, 8 Nov 2011 08:18:28 -0800 (PST)
>  lisamp85 <lisamlpham@gmail.com> wrote:
> > Hello.
> >
> > I started using the sem package in R and after a lot of searching and
> trying
> > things I am still having difficulty.  I get the following error message
> when
> > I use the sem() function:
> >
> > Warning message:
> > In sem.default(ram = ram, S = S, N = N, param.names = pars, var.names =
> > vars,  :
> >   Could not compute QR decomposition of Hessian.
> > Optimization probably did not converge.
> >
> > I started with a simple example using the specify.model() function, but
> it
> > is really straight forward.  I uploaded my specify.model script and my
> data
> > covariance matrix here too so I wouldn't clutter this email with the
> entire
> > model (20 observed variables, 5 factors).  Could this error message be
> from
> > the data itself and not from my path model?
> >
> > I have my observed variables X and my unobserved variables F.  I have
> ONLY
> > exogenous latent variables (i.e. they never appear on the right side of
> the
> > single head arrow ->).  I include all possible factor covariances FjFk,
> and
> > the only constraints I've made was to restrict the Factor variances to 1.
> > My model follows in this basic format (as you can see from my uploaded
> > file):
> >
> > # Factors (where I specify which observed variables load on to which
> > factors)
> > # I have only exogenous latent variables
> > F.i -> X.j, lamj.i, NA
> > .
> > .
> > .
> > # Observed variable variances
> > X.j <-> X.j, ej, NA
> > .
> > .
> > .
> > # Factor variances (I fixed all factor variances to 1)
> > F.i <-> F.i, NA, 1
> > .
> > .
> > .
> > # Factor covariances (I represent all factor covariances, i.e. the upper
> or
> > lower triangle of a covariance matrix)
> > F.i <-> F.k, FiFk, NA
> > .
> > .
> > .
> >
> > Did I do something wrong here?
> > Here are my uploaded files:
> > CFA script:  http://r.789695.n4.nabble.com/file/n4016569/CFA_script.txt
> > CFA_script.txt
> > Covariance matrix:
> > http://r.789695.n4.nabble.com/file/n4016569/covariance_matrix.RData
> > covariance_matrix.RData
> >
> >
> > Thank you so much for any and all of your help.
> > Lisa
> >
> > --
> > View this message in context:
> http://r.789695.n4.nabble.com/Help-with-SEM-package-Error-message-tp4016569p4016569.html
> > Sent from the R help mailing list archive at Nabble.com.
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
>
>
>


-- 
**************************
Lisa Pham
PhD Candidate
Department of Biomedical Engineering
Bioinformatics Program
Boston University

To raise new questions, new possibilities, to regard old problems from a
new angle, requires creative imagination and marks real advance in science.
- Albert Einstein

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