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Plot a classical circular regression fit

Source: R/plot-circ_lm.R
plot.circ_lm.Rd

The default plot method for circ_lm fits: the closed-form sibling of plot.circ_gam, drawing the same three regression geometries – circular–linear (cylinder), circular–circular (torus) and linear–circular (the upright can) – from the fit's type. A multi-covariate "cl" fit has no single covariate axis and defers with a message to coef / predict / summary.

Usage

# S3 method for class 'circ_lm'
plot(
  x,
  view = c("flat", "geometry", "both"),
  n = 200,
  se = TRUE,
  pages = 1,
  rug = TRUE,
  ...
)

Arguments

x

A fitted circ_lm model.

view

"flat" (default) draws one panel per modelled parameter on the response scale against the covariate. A circular location carries a band of \(\pm\) one circular standard deviation of the fitted law (the von Mises spread \(\sqrt{-2\log A_1(\kappa)}\) of the fitted concentration); the concentration panel keeps a delta-method 2-SE band. A circular location is broken at the \(\pm\pi\) branch jump and the observed responses are overlaid. type = "cl" draws the mean direction and the concentration \(\kappa\); type = "cc" / "lc" draw the single fitted location. "geometry" draws the fitted location curve on its natural surface – a cylinder for circular–linear ("cl": the response angle wraps the tube, the linear covariate runs along the axis), a torus for circular–circular ("cc": the covariate around the ring), or an upright can for linear–circular ("lc": the cyclic covariate wraps the ring, the linear response is the height). "both" places the geometry canvas beside the full set of flat panels ("cl": the mean direction and \(\kappa\); "cc"/"lc": the single location) – exactly the panels "flat" draws, so the two views never disagree.

n

Number of grid points along the covariate.

se

Draw the uncertainty band (filled shadow on the flat panels, translucent ribbon on the geometry surface): \(\pm\) the circular standard deviation for a circular location, a 2-SE interval for the concentration.

pages

If 1, lay the flat panels out on a single page.

rug

Add a covariate rug to the location panel.

...

Currently ignored.

Value

The fitted model, invisibly.

Details

The geometry canvas is base-graphics only (persp + trans3d) and shares the surface, panel and band helpers with plot.circ_gam, so a circ_lm leg renders in the same idiom as the matching circ_gam leg. A circular location is banded by \(\pm\) the circular standard deviation of the fitted law – the von Mises spread \(\sqrt{-2\log A_1(\kappa)}\) for the per-point concentration of "cl" and the residual concentration of "cc" – the predictive angular spread, not a confidence interval of the mean. The remaining bands are the usual intervals: the "cl" concentration on the log scale through \(Z\,V Z'\), the "lc" linear response the ordinary least-squares prediction band.

See also

circ_lm, plot.circ_gam

Examples

set.seed(1)
n <- 80
x <- rnorm(n)
theta <- (1 + 2 * atan(1.5 * x) + rnorm(n) / 4) %% (2 * pi)
dat <- data.frame(theta = theta, x = x)

## cl: the mean direction on the cylinder, with the kappa panel beside it
m <- circ_lm(theta ~ x, dat, type = "cl")
plot(m)                      # flat: mu (circular) and kappa
plot(m, view = "geometry")   # the fitted angle on the cylinder

## cc / lc: a single location on the torus / can
phi <- runif(n, 0, 2 * pi)
dcc <- data.frame(psi = (phi / 2 + rnorm(n) / 5) %% (2 * pi), phi = phi)
plot(circ_lm(psi ~ phi, dcc, type = "cc"), view = "both")

dlc <- data.frame(y = 5 + 2 * cos(phi) + rnorm(n) / 2, phi = phi)
plot(circ_lm(y ~ phi, dlc, type = "lc"), view = "geometry")