Re: st: problem with GLLAMM and a bernoulli mixed model

[David Pacheco <pacheco.david@gmail.com>]

Stas,

I've tried to fit another version of the model but without neither
factor loading nor constraints to the variance of normal latent
factor, case that I understand is the same who I've describe
previously (factor loading = std of latent factor). In these case
happen a similar thing, the variance of the latent factor is
reasonable but depend a lot of the integration points used. Idem when
I've changed the link function from probit to logit.

In other hand, the same model and data have been fitted, with success
by a friend, but he used the traditional Stata's Maximum Likelihood
Method and the solutions doesn’t have the problem of high sensitivity
to the cuadrature method and always with much less variance of the
latent factor than the solution by GLLAMM.

My model is a longitudinal model where the only one latent factor or
random effect change over the time and  impute the variability, so the
time "fecha_n" is the "id", while the cross-section is collapsed
because all the items are infinitely homogeneous with the same success
probability, so the variable "n_cuotas" and "df_cuotas" contains the
number of items and the number of success over the time, respectively.
The model is in the spirit of Vasicek's Model of Credit Risk, where:
all the loans of an portfolio have the same probability of default;
the number of loans is very large and all of them are homogeneous
(assumptions close to my data); and a systematic latent factor over
the time produces the variability in the portfolio’s probability of
default.

Why have I been working with GLLAMM?, because I think is more easy,
than traditional ML on Stata, subsequently generalize the basic model
including: latent coefficients on covariates;  other links functions;
and multivariate latent factors approach. But I don't know what is
wrong in my code or with GLLAMM?, especially with these simple
binomial mixed models, or what is the source of this positive skewness
in the variance of latent factor and its sensitivity to the
integration points?

Any suggestions would be very much appreciated!

2011/3/9 Stas Kolenikov <skolenik@gmail.com>:
> David Pacheco reported some difficulties in getting convergent
> solutions in -gllamm- with binary dependent variable factor analysis
> (no covariates) model.
>
> I suspect you might have (empirical) identification problems with this
> model. If you don't really have variability at the second level, then
> setting the variance parameter to 1 will send your loadings to
> infinity. Are your likelihoods the same for different models? You
> would want to try a likelihood ratio against the simple -probit-
> model, and you would probably want to run -xtprobit, re- with your
> data, just to see what comes out (it additionally imposes constraint
> of equal loadings of different items, but if that is at least
> approximately true, then you will get an estimate of the factor
> variance from it to gauge how far it is from zero).
>
> You would probably want to put in different intercepts for both
> -gllamm- and -xtmixed- models using
>
> tabulate items, gen( item_dummy )
> gllamm response item_dummy*, nocons ...
>
> if you have varying probabilities of success in different items. Thus
> far, you have imposed an implicit constraint of equal probabilities,
> and -gllamm- might be trying to accommodate that with wildly varying
> factor loadings, the only thing you allowed to vary in the model.
>
> On Wed, Mar 9, 2011 at 10:40 AM, David Pacheco <pacheco.david@gmail.com> wrote:
>> Hello,
>>
>> I'm seeking suggestions about a problem with GLLAMM. I've been working
>> with a specific and simple Bernoulli mixed model: link probit;
>> binomial family; 2 levels;  I don’t have covariate in any level; and
>> in the second level I have only one latent factor with normal
>> distribution and std=1 plus its factor loading. In general the model
>> is very simple, with 3 parameters. I've used this code:
>>
>> **************!
>> gen cons=1
>> eq fech1: cons   ***this allow me to create the equation for the
>> latent variable that only have a factor loading
>> constraint def 1 [fec1_1]cons = 1   *** this constraint the std=1 for
>> the normal factor
>> gllamm df_cuotas, i(fecha_n) link(probit) family(binom)
>> denom(n_cuotas) eqs(fech1) constr(1) frload(1)   **** where df_cuotas
>> is the response and I don't have covariate
>> **************
>>
>> The model looks very simple, but when I've tried with different number
>> of integration points (like nip(8), ... nip(20), nip(40), etc ) plus
>> the traditional or adaptative cuadrature, the solution for the factor
>> loading change a lot, so is very sensitive to the cuadrature setting.
>>
>> After that, I've tried to add start values to, maybe, neutralize this
>> sensitivity to the cuadrature setting. I've used like start values a
>> skew solution that I know for this model, in this way:
>>
>> **************!
>> matrix list e(b)   *** for see the structure of the parameter matrix
>>
>> Stata show me this:
>>
>> e(b)[1,3]
>>     df_cuotas:    fec1_1l:     fec1_1:
>>         _cons        cons        cons
>> y1           0         1.1          .5
>>
>> copy a=e(b)      *** to copy the structure of the parameter matrix
>> matrix a[1,1]= -1.1 *** replace the values on matrix "a" with my initial values
>> matrix a[1,2]= 0.016
>> matrix a[1,3]= 1
>> **************
>>
>> Thus, I've run the following code:
>>
>> **************
>> gllamm df_cuotas , i(fecha_n) link(probit) family(binom)
>> denom(n_cuotas) eqs(fech1) constr(1) frload(1) from(a)
>> **************
>>
>> but Stata send me the error:
>>
>> ******
>> initial vector: extra parameter df_cuotas:_cons found
>> specify skip option if necessary
>> (error occurred in ML computation)
>> (use trace option and check correctness of initial model)
>> ******
>>
>> However, the parameter "df_cuotas:_cons" exist in the model and in the
>> matrix e(b). I thought that I had to delete the parameter "
>> fec1_1:cons" from the matrix "a" of initial values, because this is
>> the std. of the latent variable that I've constrained to 1.
>> Nevertheless, Stata send me the same error.
>>
>> My questions:
>>
>> 1) Is something wrong on my code or is a common problem in GLLAMM, and
>> in this kind of models, the sensitivity of loading factor to the
>> cuadrature setting?...because with every number of integration point
>> that I've tried the solution of the factor loading has changed a lot
>>
>> 2)  What’s  wrong in my code or in my matrix of initial values, when I
>> try to use "from"?
>>
>> Any suggestions would be very much appreciated!
>>
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>>
>
>
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/