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Abstract:
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Penalized quasi-likelihood (PQL), an approximate method of inference, is a simple estimation procedure for hierarchical generalized linear models. However, it has been noticed that PQL tends to underestimate variance components, especially when the response variable is binary. A modified estimation procedure based on method of moments, that is computationally less intensive than the original PQL method, is proposed here. The modified estimation procedure is illustrated on the simple one way random effects model. Using a simple adjustment, approximately unbiased estimators are obtained. The estimator can be adjusted to incorporate sampling weights, that arise for example in modeling complex sample survey data. This is illustrated using data from the National Assessment of Educational Progress (NAEP).
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