CFA with four factors: problem in covariance matrix (I think)

[Allison Ames]

Good evening,

I'm working on a 4-factor confirmatory item factor analysis with binary predictors. The model has simple structure, but all latent factors are correlated.  

Items 1-3 load onto factor 1; Items 4-6 load onto factor 2; Items 7-10 onto factor 3; Items 11-15 onto factor 4. 

The model compiles, but when I attempt to sample, Initialization between (-5,5) fails after 100 attempts. I changed the range of initial parameters to (-5,5) because it wasn't working in the default. 

My best guess is that the covariance matrix is misspecified, but I'm not quite sure. 

[593] "Rejecting initial value:"                                                                                                              

[594] "  Error evaluating the log probability at the initial value."                                                                          

[595] "Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:"                        

[596] "Exception thrown at line 69: bernoulli_logit_log: Logit transformed probability parameter is nan, but must not be nan!"                

[597] "If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,"

[598] "but if this warning occurs often then your model may be either severely ill-conditioned or misspecified."  

My model is attached, and the data file is also attached. Any insight into why this may be happening is much appreciated. Thank you, in advance. I apologize for my limited understanding. 

Best wishes,

Allison 

[Stephen Martin]

With this type of parameterization, you need multi_normal_cholesky to use a cholesky factor of a covariance matrix, but you're feeding it a cholesky factor of a correlation matrix.
I think you need to transform the cholesky correlation matrix (L) to a cholesky covariance matrix, and you need to estimate the sigmas for each of the factors.

See page 328 of the manual.

[Allison]

Dear Stephen,

Thank you very much for that information. I'm going to try to implement your suggestion today after some reading. 

Best wishes,

Allison 

[Mike Lawrence]

Not sure if it's pertinent, since your code is taking a different approach to achieving identifiability than mine, but I have a demo of doing CFA in Stan here:

https://gist.github.com/mike-lawrence/dd2435f290a567bd1fd03370ee669688

--
Mike Lawrence
Graduate Student
Department of Psychology & Neuroscience
Dalhousie University

~ Certainty is (possibly) folly ~

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