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Abstract:
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The semiparametric proportional likelihood ratio model proposed by Luo and Tsai (2012) extends the generalized linear model by leaving the probability distribution unspecified. We propose to extend this model into longitudinal analysis by incorporating random effects besides fixed effects. By using this model as the conditional density of the response variable given random effects, we present a maximum likelihood approach for model estimation and inference. A numerical estimation procedure was developed for outcomes with finite support based on the generalized expectation maximization algorithm where the Gauss-Hermite quadrature is employed to approximate the integrals. Upon convergence, the observed information matrix is estimated through the second-order numerical differentiation of the log likelihood. Asymptotic properties of the maximum likelihood estimator are established under certain regularity conditions and simulation studies are conducted to assess its finite-sample properties and compare the proposed model to the generalized linear mixed model. The proposed method is illustrated in an analysis of data from a multi-site observational study of prodromal Huntington disease.
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