Help with SEM package: Error message

library(MASS) # for mvrnorm()
set.seed(12345) # for replication

R <- matrix(1, 5, 5)
R[lower.tri(R)] <- R[upper.tri(R)] <- round(runif(10, min=0.2, max=0.8),

R

eigen(R)$values

F <- mvrnorm(1000, rep(0, 5), R)

Lambda <- matrix(0, 15, 5)
Lambda[c(1:3, 18+1:3, 36+1:3, 54+1:3, 72+1:3)] <- round(runif(15, min=0.5,

Lambda

Y <- (F %*% t(Lambda)) + matrix(rnorm(1000*15), 1000, 15)
colnames(Y) <- paste("y", 1:15, sep="")

library(sem)

mod.cfa <- specifyEquations(covs=c("F1, F2, F3, F4, F5"))

(sem.cfa <- sem(mod.cfa, data=data.frame(Y)))

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
project.org] On Behalf Of Lisa Pham
Sent: November-08-11 4:17 PM
To: John Fox
Cc: r-help at r-project.org
Subject: Re: [R] Help with SEM package: Error message

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

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--
**************************
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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