frame_nlrq: Visualization of fitting process of non-linear quantile... In quokar: Quantile Regression Outlier Diagnostics with K Left Out Analysis

Description

This function explore the fitting process of nonlinear quantile regression

Usage

 1 frame_nlrq(formula, data, tau, start) 

Arguments

 formula non-linear quantile regression model data data frame tau quantiles start the initial value of all parameters to estimate, must be a list

Details

To extentd the linear programming method to the case of non-linear response functions, Koenker & Park(1996) considered the nonlinear l_{1} problem

min_{t\in R^{p}} ∑{|f_{i}(t)|}

where, for example,

f_{i}(t)=y_i-f_{0}(x_i, t)

As noted by El Attar et al(1979) a necessary condition for t* to solve min_{t\in R^{p}} ∑{|f_{i}(t)|} is that there exists a vector d \in [-1, 1]^n such that

J(t*)^{'}d = 0

f(t*)^{'}d = ∑{|f_i(t*)|}

where f(t)=(f_i(t)) and J(t)=(\partial f_i(t)/\partial t_j). Thus, as proposed by Osborne and Watson(1971), one approach to solving min_{t\in R^{p}} ∑{|f_{i}(t)|} is to solve a succession of linearized l_1 problems minimizing

∑ |f_{i}(t)-J_{i}(t)^{'}δ|

Value

Weighted observations in non-linear quantile regression model fitting using interior algorithm

Author(s)

Wenjing Wang [email protected]

Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 library(tidyr) library(ggplot2) library(purrr) x <- rep(1:25, 20) y <- SSlogis(x, 10, 12, 2) * rnorm(500, 1, 0.1) Dat <- data.frame(x = x, y = y) formula <- y ~ SSlogis(x, Aysm, mid, scal) nlrq_m <- frame_nlrq(formula, data = Dat, tau = c(0.1, 0.5, 0.9)) weights <- nlrq_m\$weights m <- data.frame(Dat, weights) m_f <- m %>% gather(tau_flag, value, -x, -y) ggplot(m_f, aes(x = x, y = y)) + geom_point(aes(size = value, colour = tau_flag)) + facet_wrap(~tau_flag) 

quokar documentation built on Nov. 17, 2017, 6:20 a.m.