
Title | Handling singletons in GEE with exchangeable correlation | |
Author | James Hardin, StataCorp |
In 1997, there was a report that the estimation of the exchangeable working correlation parameter was incorrect whenever the dataset included singletons (panels of size 1). The original report cited several statistical software packages including Stata version 5.
This bug does not affect Stata version 6.
For Stata version 5, Stata responded to this report by updating the Stata executable and the xtgee.ado files in order to fix the bug.
To determine if this bug is present in any particular GEE solver, you can use the data below for id, y, and x
1 22.5324 0 2 22.1011 0 3 21.693 0 4 21.3061 0 6 20.2493 0 6 20.3324 230 6 19.6399 406 6 18.6703 593 6 20.9972 770 7 23.2159 0 8 23.4819 0 8 23.1031 242 8 23.6713 382 8 23.2609 551 8 23.7659 718 9 20.4287 0 9 18.9259 234 10 24.1646 0 10 23.5287 273 10 24.5693 416 10 24.0201 616 10 24.6849 806 12 21.1412 0 12 21.8088 225 12 22.8473 400 12 22.1797 595 12 21.7346 771
Flawed GEE solvers will report that the exchangeable correlation parameter is 0.748; the correct value is 0.953.
Here is the output of this test using Stata version 6:
. xtgee y x, i(id) Iteration 1: tolerance = .00309187 Iteration 2: tolerance = .00003388 Iteration 3: tolerance = 3.738e-08 GEE population-averaged model Number of obs = 27 Group variable: id Number of groups = 10 Link: identity Obs per group: min = 1 Family: Gaussian avg = 2.7 Correlation: exchangeable max = 5 Wald chi2(1) = 1.15 Scale parameter: 2.952649 Prob > chi2 = 0.2838 ------------------------------------------------------------------------------ y | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- x | .0003297 .0003076 1.072 0.284 -.0002732 .0009327 _cons | 21.95229 .5412312 40.560 0.000 20.89149 23.01308 ------------------------------------------------------------------------------ . xtcorr Estimated within-id correlation matrix R: c1 c2 c3 c4 c5 r1 1.0000 r2 0.9530 1.0000 r3 0.9530 0.9530 1.0000 r4 0.9530 0.9530 0.9530 1.0000 r5 0.9530 0.9530 0.9530 0.9530 1.0000