[R] Help with SEM package: Error message

[John Fox]

Dear Lisa,

As I said, I don't have a whole lot of time today. At a quick glance, you simulation seems straightfoward except for 

> F_i ~ N(mu_i, Phi).
> 
> mu_i is fixed to Phi*z_i, where z_i is a 5x1 vector.

Why don't the factors have 0 means? I assumethat Phi is a correlation matrix.

John

On Tue, 8 Nov 2011 22:16:53 +0100
 Lisa Pham <lisamlpham at gmail.com> wrote:
> 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 at 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 at 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 at 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

------------------------------------------------
John Fox
Sen. William McMaster Prof. of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox/