Description Usage Arguments Details Value Author(s) Examples

This function explore the fitting process of nonlinear quantile regression

1 | ```
frame_nlrq(formula, data, tau, start)
``` |

`formula` |
non-linear quantile regression model |

`data` |
data frame |

`tau` |
quantiles |

`start` |
the initial value of all parameters to estimate, must be a list |

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|*

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

Wenjing Wang [email protected]

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.

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