rqpd {rqpd} R Documentation
Regression Quantiles for panel data (longitudinal data)
Description
Fit a panel data quantile regression model. The model is specified by using an extended formula syntax (implemented with the Formula package) and by easily configured model options (see Details).
Currently, the available models are (i) the penalized fixed-effects (FE) estimation method proposed by Koenker (2004) and (ii) the correlated-random-effects (CRE) method first proposed by Abrevaya and Dahl (2008) and elaborated on by Bache et al (2011).
The FE estimator is based on minimizing a weighted sum of K ordinary quantile regression objective functions corresponding to a selection of K values of tau, with user specified tau-specific weights. Slope coefficients of this objective function are tau dependent, whereas coefficients corresponding to the fixed effects are assumed to be independent of tau. The vector of fixed-effects coefficients are penalized by an l1 (lasso) penalty term with associated penalty parameter lambda, thereby shrinking these coefficients toward zero.
The CRE estimator do not estimate the fixed effects, but controls for time-invariant dependence between the fixed effects and a set of covariates by linearly including time-invariant CRE transformations of possibly endogenous time-varying variables. The conditional distribution of interest, is thus in some sense unconditional of the fixed effects.