Abstract:
There is no literature on outlier-robust parametric
mixed-effects quantile regression models for continuous
proportion data as an alternative to systematically
identifying and eliminating outliers. To fill this gap, we
formulate a robust method by extending the recently
proposed fixed-effects quantile regression model based
on the heavy-tailed Johnson-t distribution for continuous
proportion data to the mixed-effects modeling context,
using a Bayesian approach. Our proposed method
is motivated by and used to model the extreme quantiles
of the vitality of cushion plants to provide insights into
the ecology of the system in which the plants are dominant.
We conducted a simulation study to assess the
new method’s performance and robustness to outliers.
We show that the new model has good accuracy and confidence
interval coverage properties and is remarkably
robust to outliers. In contrast, our study demonstrates
that the current approach in the literature for modeling
hierarchically structured bounded data’s quantiles
is susceptible to outliers, especially when modeling
the extreme quantiles. We conclude that the proposed model is an appropriate robust alternative to the cur-rent approach for modeling the quantiles of correlated
continuous proportions when outliers are present in the
data.
