Jeff,

When one looks at the correlation matrix of the parameters, you'll see that phd is highly correlated with the intercept (ABS(corr(Intercept,PHD) > .8). When you remove phD from the model, all the other parameter estimates are virtually the same, with or without the '2nd' intercept:

remove phd from both the logit and poisson portions and add the n_p term:

Standard Parameter Estimate Error

bp_0 -0.576 0.3300 bp_fem 0.108 0.2802 bp_mar -0.354 0.3175 bp_kid5 0.219 0.1959 bp_ment -0.134 0.04231 bll_0 -0.689 0.03515 bll_fem -0.209 0.06341 bll_mar 0.105 0.07082 bll_kid5 -0.143 0.04735 bll_ment 0.018 0.002216 n_P 1.311 0.03515

now run it without phD and without the n_P term

Standard Parameter Estimate Error

bp_0 -0.576 0.3300 bp_fem 0.109 0.2802 bp_mar -0.354 0.3175 bp_kid5 0.219 0.1959 bp_ment -0.134 0.04231 bll_0 0.621 0.07029 bll_fem -0.209 0.06341 bll_mar 0.105 0.07082 bll_kid5 -0.143 0.04735 bll_ment 0.018 0.002216

The moral is, to always be aware of possible correlations of the parameter estimates in the X data when running NLMIXED, or in this case, a variable that does not "vary" much (in relation to the intercept and other terms)

Robin High UNMC

"Jeff Allard" <jeffrey.m.allard@gmail.com> 07/25/2008 10:06 AM

To "Robin R High" <rhigh@unmc.edu> cc SAS-L@listserv.uga.edu Subject Re: Long Book - Zip Model

Hi Robin-

Thanks (I think :-) ). Anyone have insight into why this works?

And Robin - what did you mean in regards to computing the log-likelihood directly?

Thanks for the help! Jeff

2008/7/25 Robin R High <rhigh@unmc.edu>:

Jeff,

I can't explain why the following modification "works", yet the results match the output: add "2" intercept terms to the Poisson part, the remaining coefficients produce the results found in Long's table for the Poisson example, that is, add n_P to the intercept:

etap = (b0 +n_P) + b1 * fem + b2 * mar + b3 * kid5 + b4 * phd + b5 * ment;

You can then produce the estimate the value of the Poisson intercept with:

ESTIMATE 'B0' b0 + n_P;

The parameter and additional estimates (in my linear predictor coding) are then:

Standard Parameter Estimate Error

bp_0 -0.577 0.5094 bp_fem 0.110 0.2801 bp_mar -0.354 0.3176 bp_kid5 0.217 0.1965 bp_phd 0.001 0.1453 bp_ment -0.134 0.04525

bll_0 -0.680 0.06065 bll_fem -0.209 0.06340 bll_mar 0.104 0.07111 bll_kid5 -0.143 0.04743 bll_phd -0.006 0.03101 bll_ment 0.018 0.002295 n_P 1.320 0.06065

Additional Estimates

Standard Label Estimate Error

INT: B0 0.6408 0.1213 A similar trick also gets the coefficients for the neg bin example in the next columns, though they aren't as close.

And I would compute the log-likelihood directly, whenever possible, as Kevin suggested.

Robin High UNMC

Jeff <jeffrey.m.allard@GMAIL.COM> Sent by: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU> 07/25/2008 09:30 AM

Please respond to Jeff <jeffrey.m.allard@GMAIL.COM>

To SAS-L@LISTSERV.UGA.EDU cc

Subject Re: Long Book - Zip Model

On Jul 25, 9:54 am, citam.s...@GMAIL.COM (Kevin Viel) wrote: > On Fri, 25 Jul 2008 05:01:14 -0700, Jeff <jeffrey.m.all...@GMAIL.COM> wrote: > >I am trying to match the output in j scott longs book Regression > >Models for Categorical and Limited Dependent Variables page 246. > >Specifically trying to model using a ZIP model using NLMIXED. I get > >very different coefficient estimates. Can anyone help with why - am I > >specifying a ZIP incorrectly? > > >Here is the code I am running: > > >/*zip*/ > >proc nlmixed data = data; > >parms a0 = 0 a1 = 0 a2 = 0 a3 = 0 a4 = 0 a5 = 0 > >b0 = 0 b1 = 0 b2 = 0 b3 = 0 b4 = 0 b5 = 0 ; > >eta0 = a0 + a1 * fem + a2 * mar + a3 * kid5 + a4 * phd + a5 * ment; > > >exp_eta0 = exp(eta0); > >p0 = exp_eta0 / (1 + exp_eta0); > > >etap =b0 + b1 * fem + b2 * mar + b3 * kid5 + b4 * phd + b5 * ment; > >exp_etap = exp(etap); > > >if art = 0 then ll = log(p0 + (1 - p0) * exp(-exp_etap)); > >else ll = log((1-p0)*(exp(-exp_etap)*exp_etap**art)/fact(art)); > > >model art ~ general(ll); > > >predict exp_etap out = zip_out1 ; > >predict p0 out = zip_out2 ; > >run; > > <snipped> > > >Any insight is appreciated - I cant figure out what I'm doing wrong. > >thanks! > > A link to the data would be helpful, if it exists. Your code looks > correct, so my next thought would be how the covariates are coded. Are > they yes/no (0/1)? I assume that the issue is not a simple matter of > replicating the referent groups. The next thought would be to be sure that > you are consistent with the meaning of p0. That is, does it Long model it > as the probability (odds) of the datum coming from the point mass at zero > (logit part) or from the Poisson distribution? I would think that this > would result in reciprocals for the estimates of the a's, but *suspect* it > would alter the estimates of the b's. Hmmm, interesting thing to test. > > Sorry I could not be of more help, but Long does not seem to have the data > on his website and I do not have a copy of the book. > > Kevin- Hide quoted text - >