Abstract:
The presence of clusters within data is often encountered in medicine,
biology and social sciences. With such data, the observations in the data
cannot be regarded as independent since the observations within a cluster
might have similar patterns than observations across clusters. The method of
sandwich variance estimation (SVE) is commonly used with correlated data
to adjust the standard errors for correlation. This study evaluates the
usefulness of SVE in generalized linear mixed models (GLMMs) which are
specialized to model correlated data. The properties of the test for examining
a repeated measures scenario with three periods is evaluated using a
simulation study for the case of binary responses. A known method for
simulating correlated binary data was modified and the correlation of first
and second periods was set to 0.4 and 0.35, for first and third periods to 0.22
and 0.19 and for the second and third periods to 0.34 and 0.33 under the null
and alternative hypotheses respectively to approximately represent an
autoregressive pattern which is often observed in this type of repeated
measurements. As properties of comparison, Type I error and the power
were compared among the two GLMMs with and without SVE. The
simulation consisted of 1000 replicates of sample sizes 20, 50, 100, 250 and
500. While the Type I errors of the GLMMs without SVE were conventional,
the type I errors of the GLMMs with SVE were within the 95% probability
interval for a 5% error rate for all the sample sizes except 20. For sample size
20, the error rate given by SVE is inflated. This indicates that except for very
small sample size (20), the use of SVE in GLMMS gives superior results
than not using SVE. In par with the power of the test, both the GLMMs with
and without SVE reached 100% power in large sample sizes (n=250,500).
But, the GLMM with SVE had a higher power than that of the GLMM
without SVE for small sizes (n=20, 50, 100). Therefore, the results of this
research suggested that the performance of GLMMs for binary correlated
data can be enhanced further by using SVE.
