Analysis of clustered data using Tweedie models with covariate-dependent random effects
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Date
2013
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University of New Brunswick
Abstract
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.