Re: [R] sem R: singular and Could not compute QR decomposition of Hessian

From: John Fox <jfox_at_mcmaster.ca>
Date: Sun, 06 Jun 2010 16:38:24 -0400

Dear Ana,

I copy here the response that I sent to you directly, for the other people reading this thread on r-help:

"I've now had a chance to look at your model. Because of its unusual structure, it's hard for me to know its identification status. For example, you specify that almost all of the exogenous latent variables are uncorrelated with each other. Similarly, you've specified that the exogenous observed variables, y1, y2, y3, y8, y9, and y10, are uncorrelated. Not only do these restrictions make it hard to figure out identification, but they also make it very unlikely that the model will fit the data reasonably; in fact, I'd be very surprised -- identified or not -- whether the model can be estimated. Although I haven't demonstrated that it is underidentified, the model has a very large number of latent variables, 11, relative to the number of observed variables, 22, and two of the latent variables, N4 and E6, are tied to only one indicator each."

In addition, as explained in ?sem, C is the reproduced rather than directly observed covariance matrix covariance matrix of the observed variables. From your remarks, the observed covariance matrix S is close to singular, but not exactly so. That sem computes a singular C (after how many iterations?) may reflect an underidentified model, as would aliased parameters. It is odd that you seem to get different results with the same input, but I suspect that you mean that you get different results for slightly different models, though all of them possible symptoms of underidentification.

Regards,
 John



John Fox
Senator William McMaster
  Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox

> -----Original Message-----
> From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org]
On
> Behalf Of sanchez ana
> Sent: June-04-10 3:31 PM
> To: r-help@r-project.org
> Subject: [R] sem R: singular and Could not compute QR decomposition of
> Hessian
>
> Can somebody help me with the following issue (SEM in R), please:
>
> When I run the model (includes second order models) in R, it gives me the
> following:
>
> 1) 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.
>
> 2) I have aliased parameters and NaNS
>
> or sometimes when I run it again I have the following message:
>
> 1) Error in solve.default(C) :
> The system is computationally singular: condition number = 4.28182e-19
(it
> says so in Spanish)
>
> Since the items are measured in likert scales I was using polychoric
> correlations, however, I saw that it can cause troubles, so I decided not
to
> use it anymore. I also check the following:
>
> 1) Variables with variance 0 (I do not have)
> 2) Linear combinations of variables (I do not have high correlations)
> 3) I already used initial values for the aliased parameters
> 4) I do not have missing data
> 5) The eigenvalues of the S matrix are all positive (no zeros)
> 6) I calculate the determinant of the correlation matrix, adding one
variable
> at a time, in order to look for multivariate dependencies, but the
> determinants are not cero, the lowest one is:0.0004054475
>
>
> Since the model has constructs that are measured with only one item, I
> decided to connect directly the variable (item) to the other constructs.
>
> Thanks
>
> Ana
>
>
>
> [[alternative HTML version deleted]]



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