# st: RE: Re: predict after Poisson

 From "German Rodriguez" To Subject st: RE: Re: predict after Poisson Date Fri, 7 Oct 2005 12:45:13 -0400

```Joe,

I believe everything depends on whether your Poisson model includes an
offset. This is explained in the help system if you type

help poisson postestimation, marker(predict)

If the model doesn't have an offset, then |predict ir, ir| gives the fitted
count. This is the same as |predict mu| (with no options), and the same as
|gen mu = exp(xb)| after |predict xb, xb|.

If the model has an offset, then |predict ir, ir| gives the predicted rate,
which is the number of events divided by exposure. This is not the same as
|predict mu|, which gives the expected count taking exposure into account.
Note also that |predict xb, xb| gives the linear predictor *including* the
offset. Another way to obtain the incidence rate is |gen rate =
events/exposure| after |predict events|, assuming your exposure variable is
called exposure.

In either case it is possible for the rate to exceed one; you could expect
more than one event (no offset) or more than one event per unit of exposure
(with offset). For example the number of children ever born per woman can be
more than one.

Cheers,
German

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jhilbe@aol.com
Sent: Friday, October 07, 2005 12:10 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Re: predict after Poisson

A couple of days ago Rich Goldstein posted a note  concerning values greater

than 1 when using the -predict x, ir- command  following a Poisson
regression.
He wondered if values over 1 were correct. I  checked the output of several
of the poisson postestimation predict options and  discovered that there may
be
a problem with Stata's output. I used a user  written program that I wrote
to
double check results, but the findings could be  obtained without the check.

Rich responded that the output he obtains  after the use of -predict, ir-
following -poisson- is different than I get when  using -poisson-. This is
more
disturbing. Not only does there appear to be a  possible inconsistency in
predict's output following the poisson command, it  seems that predict
output
differs between Rich's and my programs. I am using  version 9.1, I do not
know
which version Rich is using. But it should not make a  difference.

Perhaps someone else has a solution to our findings, showing  that there
really is no inconsistency. With Rich's OK, our correspondence is  listed
below.

Joe Hilbe
=======

Rich:

I looked at the  problem you identified. First I checked the predict
help file for poisson  postestimations. It shows the options for predict
as below. I used the cancer  data set, modeled it, and employed the
predict command with the n, ir, and  xb options.  I also simply used the
command -predict mu-. Thereafter I  list the predictions for the first 5
observations. Note that n, ir, and mu  are all the same, which is incorrect.
n and ir should differ. I next modeled  the same with the poisson program
I wrote to use with my short courses. I  like to at least have the AIC
statistic
displayed so that I can more easily  compare models. Anyhow, the stats come
out
correctly. The base predict  command should give the linear predictor, with
the
inverse link providing  the fitted value. This is the case of all ML
programs. Of course,
the  predict command after poisson has been given different, and more
extensive,
options.

The fitted value, mu, with my program, matched the values  of n, ir, and mu
for
the use of predict following Stata's -poisson- command.  Both -xb-'s were
the same   - as they should be.

My  original thought about the -ir- option yielding the fitted value was
correct.
That's why you obtained values in excess of 1.0, which was to be expected.
Perhaps Stata's tech support needs to look at the Poisson postestimation
commands.
It would be helpful if someone reading this try out the model  and the
predict commands to
see if their results are the same.

My output is below: Rich's final remark of this morning is below that.

Joe  Hilbe

000000000000000000000000000000000000000000000000000000000000000000000000
help  poisson postestimation
..

Syntax for  predict

predict [type] newvar  [if] [in] [, statistic nooffset]

statistic    description
----------------------------------------------------------------------
Main
n          predicted number of  events; the default
ir         incidence rate  exp(xb)
xb         linear  prediction
stdp       standard error of the linear  prediction
score       first derivative of the log likelihood with respect to xb
----------------------------------------------------------------------

STATA'S  POISSON MODEL AND  POSTESTIMATION
========================================

. use  cancer

. poisson time died age d2 d3, nolog irr

Poisson  regression                                 Number of obs   =

48
LR chi2(4)      =      160.82
Prob > chi2     =     0.0000
Log  likelihood =  -188.28729                        Pseudo R2       =
0.2993

----------------------------------------------------------------------------
--
time |        IRR   Std.  Err.      z     P>|z|     [95% Conf.  Interval]
-------------+--------------------------------------------------------------
--
died |   .9237044    .081715     -0.90   0.370     .7766618     1.098586
age |    .9700189   .0071361    -4.14    0.000     .9561329     .9841067
d2  |   1.618461    .184698      4.22   0.000     1.294087     2.024142
d3  |   2.586837   .2674132      9.19   0.000     2.112402     3.167829
----------------------------------------------------------------------------
--

.  predict cnt, n
. predict ircnt, ir
. predict mu
(option n assumed;  predicted number of events)
. predict xb, xb
. l cnt ircnt mu xb in  1/5

+-------------------------------------------+
|      cnt       ircnt          mu         xb  |
|-------------------------------------------|
1. |  7.609622   7.609622   7.609622   2.029413  |
2. | 6.737269   6.737269   6.737269    1.907655 |
3. | 8.087283   8.087283    8.087283   2.090293 |
4. | 10.00786    10.00786   10.00786    2.30337 |
5. |  8.860577   8.860577   8.860577   2.181612  |
+-------------------------------------------+

USER WRITTEN POISSON  PROGRAM,  VERSION  9.1
======================================================

. drop cnt  ircnt mu xb

. jhpoisson time died age d2 d3, nolog irr

Poisson  Regression                                 Number of obs   =

48
Wald chi2(4)    =     154.82
Log  likelihood =  -188.28729                        Prob > chi2     =
0.0000

----------------------------------------------------------------------------
--
time |        IRR   Std.  Err.      z     P>|z|     [95% Conf.  Interval]
-------------+--------------------------------------------------------------
--
died |   .9237044    .081715     -0.90   0.370     .7766618     1.098586
age |    .9700189   .0071361    -4.14    0.000     .9561329     .9841067
d2  |   1.618461    .184698      4.22   0.000     1.294087     2.024142
d3  |   2.586837   .2674132      9.19   0.000     2.112402     3.167829
----------------------------------------------------------------------------
--
AIC  Statistic =         8.054                         BIC Statistic =

3.186
Deviance      =       169.648                         Dispersion    =
3.945
LM  Value      =      6348.667                         LM Chi2(1)    =
0.000
Score test  OD =       123.055                         Score Chi(1)  =
0.000

. predict xb,  xb
. gen mu=exp(xb)
. l xb mu in 1/5

+---------------------+
|        xb         mu  |
|---------------------|
1. |  2.029413   7.609622 |
2. | 1.907655     6.73727 |
3. | 2.090293   8.087282 |
4. |   2.30337   10.00786 |
5. | 2.181612   8.860576  |
+---------------------+

NOTE: Our xb and mu  results are identical. The question remains about the
values following
-predict xn, n- and -predict xir, ir-, which are the same as -mu- when I
model it with -poisson-.

000000000000000000000000000000000000000000000000000000

Joe,

Note  that in my case I did NOT get the same predictions using:

predict  newvar

and

predict newvar, ir.

When using no option, the  max predicted value was just over 9.  When using
the
ir option, the max  predicted value was about 1.13.

Rich

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```