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." <[email protected]>
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
[email protected]
- -----------------------------------
- -----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Paul Seed
Sent: Wednesday, October 29, 2008 4:15 PM
To: [email protected]
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
[email protected], [email protected]
King's College London, Division of Reproduction and Endocrinology
St Thomas' Hospital, Westminster Bridge Road, London SE1 7EH
*
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