Plotting quantile regression estimates as function of their quantiles in R

The following code is a reproducible example based on the Swiss dataset (datasets::swiss).

My question is that I would like to plot the betas, which are the quantile regression estimates provided by the smrq() function on the y-axis, according to the tau values (the quantiles) ranging from [0:1]; but unfortunately I am not succeeding. Many thanks for the precious help, of course I can edit my post if I have forgotten anything.

Code:

library(quantreg)
library(limma)

#Generalized Functions

minimize.logcosh <- function(par, X, y, tau) {
  diff <- y-(X %*% par)
  check <- (tau-0.5)*diff+(0.5/0.7)*logcosh(0.7*diff)+0.4
  return(sum(check))
  }

smrq <- function(X, y, tau){
  p <- ncol(X)
  op.result <- optim(
    rep(0, p),
    fn = minimize.logcosh,
    method = 'BFGS',
    X = X,
    y = y,
    tau = tau
  )
  beta <- op.result$par
  return(beta)
  }

run_smrq <- function(data, fml, response) {
  x <- model.matrix(fml, data)[,-1]
  y <- data[[response]]
  X <- cbind(x, rep(1,nrow(x)))
  
  n <- 99
  betas <- sapply(1:n, function(i) smrq(X, y, tau=i/(n+1)))
  return(betas) 
}

#Callers

swiss <- datasets::swiss
smrq_models <- run_smrq(data=swiss, fml=Fertility~., response="Fertility")

@langtang’s solution gives this graphical output:

>Solution :

Without making any comment on the "correctness" of the output of run_smrq(), you can try this:

library(dplyr)
library(tidyr)
library(ggplot2)

as.data.frame(t(smrq_models)) %>% 
  mutate(q=row_number()) %>% 
  pivot_longer(!q,names_to="beta",values_to = "coef") %>% 
  ggplot(aes(q,coef,color=beta)) + 
  geom_point()

Also, if the betas are on largely different scales, this your visualization approach may not be the most appropriate. As as starting point, you might add + facet_wrap(~beta, scales="free_y")