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st: Re: Estimating residuals following nbreg


From   Paul Seed <paul.seed@kcl.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Re: Estimating residuals following nbreg
Date   Fri, 31 Oct 2008 14:07:28 +0000

Dear Tom,
That seems to fix it. Many thanks.
The correct lines are:
gen n_pred_formula = exp(xb - ln(demog_exposure))*demog_exposure
* This equals n_pred.

* Re-arranging, gives xb = ln(n_pred/demog_exposure) + ln(demog_exposure)

* so, xb_formula should be the same as xb

gen xb_formula = ln(n_pred/demog_exposure) + ln(demog_exposure)

* and xb_obs should be the observed value of xb
gen xb_obs = log(n_copd /demog_exposure) + ln(demog_exposure)

Paul




Date: Wed, 29 Oct 2008 17:27:53 -0400

From: "Steichen, Thomas J." <SteichT@RJRT.com>

Subject: st: RE: Estimating residuals following nbreg



Paul,



I think the problem is that

 . predict xb, xb



Does not produce xb = x_j*beta, it produces x b = x_j*beta + ln(demog_exposure_j) when you specify the exposure(option).



Thus,

 . gen n_pred_formula = exp(xb)*demog_exposure

does not get what

 . predict n_pred

gives.



Instead, try

 . gen n_pred_formula = exp(xb - ln(demog_exposure))*demog_exposure



Tom





- -----------------------------------

Thomas J. Steichen

steicht@rjrt.com

- -----------------------------------



- -----Original Message-----

From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Paul Seed

Sent: Wednesday, October 29, 2008 4:15 PM

To: statalist@hsphsun2.harvard.edu

Subject: st: Estimating residuals following nbreg



Dear all,



I fitted a negative binomial regrression, and tried to check the model

residuals by

estimating the differences and the standard errors, without success.

Can anyone tell me what I am doing wrong?

I am using stata 9.2 (fully up to date) on Windows XP, Dell latitue

laptop, if it is relevant.



xi: nbreg n_copd i.sha i.imd_nat , nolog exposure(demog_exposure) irr

predict xb, xb

predict stdp , stdp

predict n_pred

* According to the manual, the predicted number of events = exp(xb)*exposure

gen n_pred_formula = exp(xb)*demog_exposure

* so, xb_formula should be the same as xb

gen xb_formula = log(n_pred/demog_exposure)

* and xb_obs should be the observed value of xb

gen xb_obs = log(n_copd /demog_exposure)



* and this should be a z-score for the residuals with mean 0, SD 1

gen z = (xb_obs - xb)/stdp



su z  n_pred* xb*



* This is what I get: for the regression and the summaries:

i.sha             _Isha_1-10          (naturally coded; _Isha_3 omitted)

i.imd_nationa~e   _Iimd_natio_0-5     (naturally coded; _Iimd_natio_5

omitted)



Negative binomial regression                      Number of obs

=       8192

                                                 LR chi2(14)     =

2217.96

Dispersion     = mean                             Prob > chi2     =

0.0000

Log likelihood = -39291.575                       Pseudo R2       =

0.0274



- ------------------------------------------------------------------------------

     n_copd |        IRR   Std. Err.      z    P>|z|     [95% Conf.

Interval]

- -------------+----------------------------------------------------------------

    _Isha_1 |   1.329169   .0266175    14.21   0.000      1.27801

1.382376

    _Isha_2 |   1.250265   .0236651    11.80   0.000     1.204732

1.297518

    _Isha_4 |   1.721701   .0407484    22.96   0.000     1.643659

1.803447

    _Isha_5 |   1.539672   .0247868    26.81   0.000     1.491849

1.589028

    _Isha_6 |   1.228066   .0271053     9.31   0.000     1.176073

1.282357

    _Isha_7 |   1.233594   .0249431    10.38   0.000     1.185663

1.283464

    _Isha_8 |   1.320831   .0251773    14.60   0.000     1.272395

1.371111

    _Isha_9 |   1.169725   .0204633     8.96   0.000     1.130298

1.210528

   _Isha_10 |   1.479601   .0271344    21.36   0.000     1.427363

1.533751

_Iimd_nati~0 |    1.32367   .0337734    10.99   0.000     1.259103

1.391547

_Iimd_nati~1 |   1.558233   .0252282    27.40   0.000     1.509562

1.608472

_Iimd_nati~2 |   1.360677   .0223115    18.78   0.000     1.317642

1.405117

_Iimd_nati~3 |   1.206407   .0201443    11.24   0.000     1.167564

1.246542

_Iimd_nati~4 |   1.110986   .0190818     6.13   0.000     1.074209

1.149023

demog_expo~e | (exposure)

- -------------+----------------------------------------------------------------

   /lnalpha |   -1.84722   .0176387                     -1.881791

- -1.812648

- -------------+----------------------------------------------------------------

      alpha |   .1576749   .0027812                      .1523171

.1632213

- ------------------------------------------------------------------------------

Likelihood-ratio test of alpha=0:  chibar2(01) = 7.2e+04 Prob>=chibar2 =

0.000





   Variable |       Obs        Mean    Std. Dev.       Min        Max

- -------------+--------------------------------------------------------

          z |      8181   -253.3219    59.07685  -523.0276   56.79291

     n_pred |      8192     94.1288    69.12208   1.554023   699.5399

n_pred_for~a |      8192    12220.43    18677.29    1.63849     381644

         xb |      8192    4.284738     .749684   .4408472   6.550423

 xb_formula |      8192    .0281945    .2300367  -.4633753   .5234895

- -------------+--------------------------------------------------------

     xb_obs |      8181   -.0675564    .5262027  -4.380957   2.350302





Paul T Seed MSc CStat, Lecturer in Medical Statistics,
tel  (+44) (0) 20 7188 3642, fax (+44) (0) 20 7620 1227
Wednesdays: (+4) (0) 20 7848 4148

paul.seed@kcl.ac.uk, paul.t.seed@gmail.com

King's College London, Division of Reproduction and Endocrinology
St Thomas' Hospital, Westminster Bridge Road, London SE1 7EH


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