in the generalized linear mixed models to describe

"inter-location" population variation in variance components

for modeling complicated data obtained from applications such as

antenna manufacturing. Our distribution studies lead to

a complicated integrated extended quasi-likelihood (IEQL) for

parameter estimations and large sample inference derivations.

Laplace's expansion and several approximation methods

are employed to simplify the IEQL estimation procedures.

Asymptotic properties of the approximate IEQL estimates are

derived for general structures of the covariance matrix of random scales.

Focusing on a few special covariance structures in simpler forms,

the authors further simplify IEQL estimates such that the typically used software

tools such as weighted regression can perform the estimates easily.

Moreover, these special cases

allow us to derive interesting asymptotic results in much more

compact expressions. Finally, numerical simulation results show that IEQL estimates

perform very well in several special cases studied.]]>

Industrial and Systems Engineering

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