In mbojan/lspline: Linear Splines with Convenient Parametrisations

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)

`lspline`: Linear Splines with Convenient Parameterizations

Linear splines with convenient parameterizations such that:

coefficients are slopes of consecutive segments
coefficients capture slope change at consecutive knots

Knot locations can be specified

manually (lspline())
at breaks dividing the range of x into q equal-frequency intervals (qlspline())
at breaks dividing the range of x into n equal-width intervals (elspline())

Inspired by Stata command mkspline and function lspline() from package ares [@r-ares]. As such, the implementation follows @greene2003econometric, chapter 7.5.2.

Installation

From CRAN or development version using remotes:

remotes::install_github("mbojan/lspline", build_vignettes = TRUE)

Examples

See package homepage and the vignette.

library(hexSticker)
library(tidyverse)
library(ggforce)

# 1 ----------------------------------------------------------------------------
d1 <- tibble::tribble(
  ~x, ~y,
  0, 0,
  4, 1, # b = 1/4
  8, -1, # b = 1/2
  10, 2 # b = 3
) 
d2 <- tibble::tribble(
  ~x, ~y,
  4, 1,
  6, 1.5
)
d3 <- tibble::tribble(
  ~x, ~y,
  8, -1,
  10, -2,
)

arcs <- tibble::tribble(
  ~x0, ~y0, ~r, ~start, ~end,
  4, 1, 0.5, pi/2 - atan(1/4), pi/2 + atan(1/2),
  8, -1, 0.5, pi/2 - atan(3/2), pi/2 + atan(1/2)
)

d1 |>
  ggplot() +
  geom_line(aes(x=x, y=y), data = d1, linetype = "solid") +
  geom_line(aes(x=x, y=y), data = d2, linetype = "dotted") +
  geom_line(aes(x=x, y=y), data = d3, linetype = "dotted") +
  geom_arc(aes(x0 = x0, y0 = y0, r = r, start = start, end = end),
           data = arcs) +
  coord_fixed()


# 2 ----------------------------------------------------------------------------

d <- tibble(
  y = c(0, 2, 1, 1.5),
  x = seq(along = y)
)

ggplot() +
  geom_line(aes(x=x, y=y), data = d, linetype = "solid") +
  coord_fixed()


# 3 ----------------------------------------------------------------------------

d <- tibble::tribble(
  ~x, ~y,
  0, 0,
  2, 2,
  3, 3,
  5, 1,
  6, 0
) |>
  map(embed, 2) |>
  imap(~ structure(.x, dimnames=list(NULL, paste0(.y, c('end', ''))))) |>
  map(as_tibble) |>
  bind_cols() |>
  mutate(
    lt = rep(c("s", "d"), length = 4)
  )

d |>
  ggplot(aes(x=x, y=y, xend=xend, yend=yend)) +
  geom_segment(data = filter(d, lt == "s")) +
  scale_linetype_manual(
    breaks = c("s", "d"),
    values = c("solid", "dotted"),
    guide = "none"
  )


# 4 ----------------------------------------------------------------------------

# Generate data for the spline based on the sequence of values for 'y'.

y <- c(0, 3, 1, 2)

# Solid line
d_solid <- tibble(x = seq(along=y), y = y)

# Extends
d_dashed <- tibble::tribble(
  ~x, ~y, ~xend, ~yend,
  2, 3, 2.5, 4.5,
  3, 1, 3.5, 0
)

d_arcs <- tibble::tribble(
  ~x0, ~y0, ~r, ~start, ~end,
  2, 3, 0.5, pi/2 - atan(3), pi/2 + atan(2),
  3, 1, 0.5, pi/2 - atan(1), pi/2 + atan(2)
)

d_labels <- tibble::tribble(
  ~x, ~y, ~label,
  2, 3, "beta[1]",
  3, 1, "beta[2]"
)

p <- ggplot() +
  geom_line(aes(x=x, y=y), data = d_solid) +
  geom_segment(aes(x=x, y=y, xend=xend, yend=yend), data = d_dashed, 
               linetype = "dotted"
  ) +
  geom_arc(aes(x0=x0, y0=y0, r=r, start=start, end=end), data = d_arcs) +
  geom_label(aes(x=x, y=y, label=label), data = d_labels, parse = TRUE,
             nudge_x = 0.25, nudge_y = 0) +
  coord_fixed() +
  theme_void()

sticker(
  p,
  s_x = 1,
  s_y = 1,
  s_width = 2,
  s_height = 2,
  package = "lspline",
) |> plot()