PAPER ON ZERO-INFLATED NEGATIVE bINOM [SAS]

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From: Dale McLerran on 13 Apr 2007 12:44

From: Dale McLerran on 13 Apr 2007 13:19

--- Jeff Miller <jeffmiller(a)ALPHAPOINT05.NET> wrote:

> I don't really have time to get too much into this either right
> now...and
> have only been skimming these posts. But, I am interested.
>
> I can say that I had problems with the quasi-Newton in SAS and wound
> up
> switching to R for that reason. I was able to converge successfully
> quite
> frequently in a Monte Carlo using the BFGS and Nelder-Mead (in place
> of
> SAS's quasi-Newton). Yes, it was a bit slower but it was worth it.
> They
> worked fine for the ZIP, NB-ZIP, Hurdle, and NB-Hurdle. (Of course,
> NB-ZIP,
> as usual, had the most convergence problems but not anything
> ridiculous
> (except in one condition but that's a different story)).
>
> I'm far from being an optimization-expert. Any comments on this that
> might
> persuade me to try SAS again without having to spend hours
> programming stuff
> would that ideally be built in the the proc?
>
> Thanks,
> Jeff
>

Jeff,

That is an awfully broad topic to try to address. Let me respond
with reference to an example I encountered just this week where
someone was having problems fitting a ZIP model employing the
NLMIXED procedure. The data had zero values for about 45% of the
response. The remaining response values had mean of about 24.
The person who requested my help did not initially code the ZIP
model correctly. But that can be only part of the problem.
The other part of the problem can be parameter initilization
which and values of the predictor variables. These data had two
predictor variables and each had values which were as high as 90
to 100.

Now, if you do not specify initial starting values for the
parameters of the model, then the NLMIXED procedure will use
starting values of 1 for every parameter. If you have a log link
function for the Poisson response, then you present NLMIXED with
an initial model as follows:

eta = 1 + X1 + X2;
lambda = exp(eta);

If eta is close to 200, then we have exp(eta) being outrageously
large. NLMIXED just could not iterate on the Poisson component
from the default initial parameters. Any starting values which
produce very large lambda would cause problems.

Actually, the same is true for the excess zero probability part
of the model. There you have

eta_zip = 1 + X1 + X2;
p_zip = exp(eta_zip) / (1 + exp(eta_zip));

so that if you start with very large values for eta_zip, you
estimate the probability of the excess zero component as being 1.
If all observations have large p_zip, you may not be able to
iterate away from your initial starting values.

So, what is the solution? A good solution would be to have a
ZIP package where the parameters for the covariates are all
initialized to zero. You might also separate the zero values
from the non-zero values, compute a mean for the non-zero values
and the probability of zero values, and then initialize the
intercept for the poisson component as log(mean(Y>0)) and the
intercept for the zero probability component as log(P(0)/(1-P(0))).
Also, with a packaged solution, the user would not misspecify
the model construction.

When you have a packaged program for estimating ZIP models, all
this work may be done for you under the hood. The folks who have
put together the program have probably thought about these issues
ahead of time. But these issues are often specific to the type of
model which is being fit. So, I don't know that there is any
good generalization that I - or anyone else - can write about
model parameterization. You have to have some idea how the model
behaves in order to do a good job coding a general solution
package.

In SAS, a general solution package for something like a ZIP model
would involve, then, writing a macro which would do some
preprocessing of the data. For the ZIP model, we would initialize
all slope coefficient parameters to be zero. Intercept parameters
would be initialized based on your data preprocessing. Only then
would you start the ZIP estimation employing the NLMIXED procedure.
The ZIP model would be constructed after the response and predictor
variables are named. If someone wrote such a macro, I think you
would find that it would work every bit as well as routines written
for other statistical packages.

Does this address your question?

Dale

p.s. Sorry about the early post which occurred when my fingers
slipped and hit the wrong keystroke. That is the second time in
the past week that has happened to me!

---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra(a)NO_SPAMfhcrc.org
Ph: (206) 667-2926
Fax: (206) 667-5977
---------------------------------------

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From: Hans Skaug on 13 Apr 2007 15:17

Jeff and SAS-list,

Two years ago I made a post to the list (attached at the end) stating
that I intended to compare NLMIXED and AD Model Builder. The work has not
been completed, mainly due to the fact that I am not a skilled
SAS programmer. The comparison is an interesting one because
we are not talking about plain numerical optimization.
A quadrature rule is applied to the user specified likelihood,
and this opens for plenty of numerical difficulties.

I will be grateful to receive NLMIXED code for problems considered
to be difficult by people.

Regards,

hans

>I don't really have time to get too much into this either right now...and
>have only been skimming these posts. But, I am interested.
>
>I can say that I had problems with the quasi-Newton in SAS and wound up
>switching to R for that reason. I was able to converge successfully quite
>frequently in a Monte Carlo using the BFGS and Nelder-Mead (in place of
>SAS's quasi-Newton). Yes, it was a bit slower but it was worth it. They
>worked fine for the ZIP, NB-ZIP, Hurdle, and NB-Hurdle. (Of course, NB-
ZIP,
>as usual, had the most convergence problems but not anything ridiculous
>(except in one condition but that's a different story)).
>
>I'm far from being an optimization-expert. Any comments on this that might
>persuade me to try SAS again without having to spend hours programming
stuff
>would that ideally be built in the the proc?
>
>Thanks,
>Jeff

2005 post:

Dear SAS-list,

I am planning to conduct a comparison of SAS proc NLMIXED and
the software ADMB-RE:

http://otter-rsch.com/admbre/admbre.html

To my knowledge these two software packages are the only ones that
allow flexibility in model formulation for nonlinear mixed models.

Both packages use adaptive quadrature to calculate the marginal likelihood,
so they should be directly comparable. My goal is to make comparison
wrt 1) computational speed and 2) numerical accuracy.

The plan is to publish the results in some form. I will do the
ADMB-RE part, while I am searching for somebody to do the NLMIXED part.
We will need to decide on which datasets to use (real and simulated).
There should be no overlap with:
http://multilevel.ioe.ac.uk/softrev/index.html

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