Clustered data are traditionally handled using models with covariate-independent random effects in the statistical community. Models with covariatedependent random effects have recently gained attention. In this thesis, we discuss the application of Tweedie models with covariate-dependent random effects proposed by Ma (1999). Tweedie models with covariate-dependent random effects are applied to analyses of count, continuous and semi-continuous data from transportation, education and health studies. Tweedie models with covariate-dependent random effects have flexible parametric interpretation for multilevel data since the cluster-specific covariates can be incorporated into random effects. Similar to Tweedie models with covariate-independent random effects, the parameter estimation and random effect prediction of Tweedie models with covariate-dependent random effects can also be done using the orthodox best linear unbiased predictor (BLUP) approach which does not require inverse calculation of large covariance matrices; therefore it is in general computationally efficient. On the basis of simulations and worked examples, we illustrated that Tweedie models with covariate-dependent random effects are useful for situations where the clustering effects are likely influenced by covariates at the relevant cluster levels.
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