GEE Poisson model estimates with independent and exchangeable correlation structure

[Mohieddine Rahmouni]

Hi Statalisters,
I have a question regarding the difference between the "independent" and "exchangeable" estimates produced from a population-average GEE Poisson model. How can I explain the large difference between the estimates and the z-values?
Thank you.


. xtgee newCases totConfirmed_1 Lockdown_26 XLockdown_26, family(poisson) link(log) corr(ind) vce(robust) fo
> rce nolog

GEE population-averaged model Number of obs = 1,847
Group variable: ISO1 Number of groups = 15
Link: log Obs per group:
Family: Poisson min = 114
Correlation: independent avg = 123.1
max = 124
Wald chi2(3) = 41.17
Scale parameter: 1 Prob > chi2 = 0.0000

Pearson chi2(1847): 2697850.2 Deviance = 1668152.3
Dispersion (Pearson): 1460.666 Dispersion = 903.1685

(Std. Err. adjusted for clustering on ISO1)
--------------------------------------------------------------------------------
| Robust
newCases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
totConfirmed_1 | .0000208 3.66e-06 5.67 0.000 .0000136 .000028
Lockdown_26 | -.7625692 .1480221 -5.15 0.000 -1.052687 -.4724512
XLockdown_26 | -.0000146 3.40e-06 -4.30 0.000 -.0000213 -7.94e-06
_cons | 5.614772 .369222 15.21 0.000 4.89111 6.338434
--------------------------------------------------------------------------------

. xtgee newCases totConfirmed_1 Lockdown_26 XLockdown_26, family(poisson) link(log) corr(exchan) vce(robust)
> force nolog

GEE population-averaged model Number of obs = 1,847
Group variable: ISO1 Number of groups = 15
Link: log Obs per group:
Family: Poisson min = 114
Correlation: exchangeable avg = 123.1
max = 124
Wald chi2(3) = 18.41
Scale parameter: 1 Prob > chi2 = 0.0004

(Std. Err. adjusted for clustering on ISO1)
--------------------------------------------------------------------------------
| Robust
newCases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
totConfirmed_1 | 3.92e-06 1.28e-06 3.06 0.002 1.41e-06 6.43e-06
Lockdown_26 | .0003296 .0093974 0.04 0.972 -.018089 .0187482
XLockdown_26 | -6.00e-06 1.80e-06 -3.32 0.001 -9.53e-06 -2.46e-06
_cons | 8.714457 .5006671 17.41 0.000 7.733168 9.695747

[Joseph Coveney]

How can I explain the large difference between the estimates and the z-values?

Don't know, but maybe consider (i) you've got 15 ISO1 entities, (ii) Poisson isn't the best distribution family for getting the means right, (iii) one of the explanatory variables (totConfirmed) contains the outcome variable, (iv) the model contains an interaction term (XLockdown_26) but only one of the two main-effects contributors (just guessing on that one given the dearth of description).

[Mohieddine Rahmouni]

Thank you very much Joseph Coveney,
The explanatory variable totConfirmed_(t-1) does not contain the outcome variable newCases_(t). I think there the problem is the endogeneity of the variable totConfirmed_(t-1).

Thanks.
MR