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Abstract:
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Despite its popularity in diverse disciplines, quantile regression is originally designed for the continuous response and cannot be directly applied when the response variable is discrete. A common feature with count responses is the presence of excess zero counts, formally known as zero-inflation. Recently, a model-aware approach was proposed to model the conditional quantiles for a Poisson distribution. To tackle the aforementioned challenges, we propose a comprehensive modelling strategy that extends the approach to more complicated situations. In particular, our model combines quantile regression with zero-inflation. Various competing computational routines are examined, while residual analysis and model selection procedures are included to validate our method. The performance of these methods is characterized through extensive Monte Carlo simulations. An application to the Oregon Health Insurance Experiment will also be discussed.
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