Quantile regression represents a well established technique for modelling data when
the interest is on the effect of predictors on the conditional response quantiles. When
responses are repeatedly collected over time, or when they are hierarchically nested,
dependence needs to be properly considered.
A standard way of proceeding is based on including higher level unit-specific random
coefficients in the model. The distribution of such coefficients may be either specified
parametrically or left unspecified. In the last case, it can be estimated non
parametrically by using a discrete distribution defined on G locations. This may
approximate the distribution of time-constant and/or time-varying random
coefficients, leading to a static, dynamic, or mixed-type mixture of linear quantile
regression equations.
An EM algorithm and a block-bootstrap procedure are employed to derive parameter
estimates and corresponding standard errors. Standard penalized likelihood criteria are
used to identify the optimal number of mixture components.
This class of models is described by using a benchmark dataset and employing the
functions in the newly develop lqmix R package.
11 Novembre 2022
Marco Alfò
Sapienza University of Rome