Answers to
Practice
Exercises
- The stationary 4-dependent working correlation struc-
ture uses four correlation parameters (a 1 ,a 2 ,a 3 , and
a 4 ). The correlation between responses from the same
infant 1 month apart isa 1. The correlation between
responses from the same infant 2, 3, or 4 months apart
isa 2 ,a 3 , anda 4 , respectively. The correlation between
responses from the same infant more than 4 months
apart is assumed to be 0. - Estimated OR¼exp(0.1636)¼1.18. 95% CI (with
empirical SE): exp[0.1636 1.96(0.8722)]¼(0.21,
6.51); 95% CI (with model-based SE): exp[0.1636
1.96(0.2841)]¼(0.67, 2.06). - The model-based variance estimator would be a con-
sistent estimator if the true correlation structure was
stationary 4-dependent. In general, model-based vari-
ance estimators are more efficient {i.e., smaller
var½dvarðb^Þ}if the correlation structure is correctly
specified. - The 95% confidence interval with the empirical stan-
dard errors is preferred since we cannot be confident
that the true correlation structure is stationary
4-dependent. - The stationary 8-dependent correlation structure uses
eight correlation parameters. With nine monthly
responses per infant, each correlation parameter
represents the correlation for a specific time interval
between responses. The unstructured correlation
structure, on the other hand, uses a different correla-
tion parameter for each possible correlation for a
given infant, yielding 36 correlation parameters.
With the stationary 8-dependent correlation struc-
ture, the correlation between an infant’s month 1
response and month 7 response is assumed to equal
the correlation between an infant’s month 2 response
and month 8 response since the time interval between
responses is the same (i.e., 6 months). The unstruc-
tured correlation structure does not make this
assumption, using a different correlation parameter
even if the time interval is the same. - There areð^9 Þð 28 Þ¼ 36 correlation parameters using the
unstructured correlation structure on the infant care
data and 8 parameters using the stationary 8-depen-
dent correlation structure. The difference is 28 corre-
lation parameters. - By examining the correlation estimates in the unstruc-
tured working correlation matrix, we can evaluate
which alternate, but more constrained, correlation
structures seem reasonable. For example, if the
564 15. GEE Examples