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We propose a consistent and locally efficient estimator to estimate the model parameters of the logistic mixed effect model with random slopes. Our approach relaxes two typical assumptions made for computational simplicity: the random effects being normally distributed, and that the covariates and random effects are independent.
Our method generalizes framework presented in \cite{tanya2016} which also deals with a mixed effect model but only considers a random intercept. A simulation study reveals that our proposed estimator remains unbiased unlike the maximum likelihood estimator even when the independence and normality assumptions are violated. Application of this work to a Huntington disease study reveals that disease diagnosis can be further improved using cognitive measures based on how many color words that were printed in colored ink (eg. BLUE printed in green ink or BLUE printed in blue ink) and correctly verbally read by a subject in a certain amount of time.
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