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Firth bias correction originally was applied to correct bias of the variance components estimator that obtained by the maximum likelihood method. Extensive research has shown that Firth bias correction is powerful to reduce bias for normal distributed response model. Questions have been raised about the use of Firth bias correction in binomial distributed response model which has under dispersion problem. The motivation of this study is giving contribution to exploring the Firth bias correction for binomial distributed response model. The binomial distributed response model which is estimated by the maximum likelihood method obtain an under-dispersion estimator. Therefore, the Penalized Quasi-Likelihood (PQL) is used as alternative numerical method to estimate the model. This paper aims to investigate whether the Firth method can reduce bias of the variance components using the PQL technique in longitudinal data.

Firth bias correction for estimating variance components of logistics linear mixed model using penalized quasi likelihood method