# Re: st: Questions about xtnbreg ... , fe

 From Partha Deb To statalist@hsphsun2.harvard.edu Subject Re: st: Questions about xtnbreg ... , fe Date Thu, 18 Aug 2005 13:23:29 -0400

John,

1. It's not uncommon in nonlinear models for predicted means not to coincide with their sample counterparts. Cauchy-Schwarz type-inequalities at work.

2. The fact that constant-within-group variables don't drop out in the FE-NB model bothers many people, but is correct. The FE-NB (like the linear-FE model) conditions on a sufficient statistic for the Fixed effect. In the linear (and a class of nonlinear cases), this eliminates all constant-within-group variables, but this is not a general statement. And it does not apply in the NB case.

Hope this helps.

Partha

************************************************************************
Partha Deb ph: (212) 772-5435
Department of Economics fax: (212) 772-5398
Hunter College http://urban.hunter.cuny.edu/~deb/

Emancipate yourselves from mental slavery
None but ourselves can free our minds.
- Bob Marley
************************************************************************

--On Thursday, August 18, 2005 9:53 AM +0900 John Plummer <john.plummer@flinders.edu.au> wrote:

```I have a data set in which counts were collected at 2 time points under 2
conditions for each subject.  There are no missing data.  Data for one
subject look like this:

id   time   condit~n   diagno~s   count
5      0          0          2       0
5      0          1          2       8
5      1          0          2       5
5      1          1          2       7

Question 1.

I fitted a fixed effects negative binomial model including time,
condition, and their interaction:

. xi: xtnbreg  count i.time*condition, i(id) fe irr nolog
i.time            _Itime_0-1          (naturally coded; _Itime_0 omitted)
i.time*condit~n   _ItimXcondi_#       (coded as above)

Conditional FE negative binomial regression     Number of obs      =
544 Group variable (i): id                          Number of groups   =
136

Obs per group: min =
4                                                                avg =
4.0                                                                max =
4

Wald chi2(3)       =
154.25 Log likelihood  = -646.33027                    Prob > chi2
=    0.0000

-------------------------------------------------------------------------
-----        count |        IRR   Std. Err.      z    P>|z|     [95%
Conf. Interval]
-------------+-----------------------------------------------------------
-----     _Itime_1 |   2.069823   .1629906     9.24   0.000     1.773798
2.415249    condition |   1.201935   .1071924     2.06   0.039
1.009179    1.431508 _ItimXcond~1 |   .3432684   .0418947    -8.76
0.000     .2702388    .4360336
-------------------------------------------------------------------------
-----

From the IRRs I calculated a table of predicted relative cell counts, with
time = 0 and condition = 0 as the reference category.  They are:

------------------------
|  condition
time |     0      1
----------+-------------
0 |     1  1.202
1 |  2.07   .854
------------------------

The means of observed cell counts are below:

----------------------------
|    condition
time |       0        1
----------+-----------------
0 | 2.09559  2.64706
1 | 4.36765  1.91176
----------------------------

These are in the ratios below, which differ from the predicted ratios:

------------------------
|  condition
time |     0      1
----------+-------------
0 |     1  1.263
1 | 2.084   .912
------------------------

I had expected that the observed and predicted relative cell frequencies
would be the same for the fitted model.  Can anyone explain why they are
not?

Question 2.

I believed that variables which are constant within ID could not be used
in a fixed effects model. Am I wrong?  It seems that I am, as illustrated
by the inclusion of diagnosis (which is constant within a subject).

. xi: xtnbreg  count   diagnosis i.time*condition, i(id) fe irr nolog
i.time            _Itime_0-1          (naturally coded; _Itime_0 omitted)
i.time*condit~n   _ItimXcondi_#       (coded as above)

Conditional FE negative binomial regression     Number of obs      =
544 Group variable (i): id                          Number of groups   =
136

Obs per group: min =
4                                                                avg =
4.0                                                                max =
4

Wald chi2(4)       =
172.78 Log likelihood  = -643.28819                    Prob > chi2
=    0.0000

-------------------------------------------------------------------------
-----        count |        IRR   Std. Err.      z    P>|z|     [95%
Conf. Interval]
-------------+-----------------------------------------------------------
-----    diagnosis |   7.784788   5.952364     2.68   0.007     1.739424
34.8408     _Itime_1 |   2.072968   .1601387     9.44   0.000
1.781708    2.411841    condition |   1.180407   .1038162     1.89
0.059     .9935027    1.402473 _ItimXcond~1 |   .3444533   .0414192
-8.86   0.000     .2721301    .4359976
-------------------------------------------------------------------------
-----

Question 3

Can anyone offer advice as to how to assess goodness of fit for xtnbreg
... , fe? (some models I want to fit are rather more complex than the
above examples).

Thanks

John Plummer

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/

```
```

************************************************************************
Partha Deb				ph:  (212) 772-5435
Department of Economics		fax: (212) 772-5398
Hunter College			http://urban.hunter.cuny.edu/~deb/

Emancipate yourselves from mental slavery
None but ourselves can free our minds.
- Bob Marley
************************************************************************

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```