An implementation of circular-linear locally-weighted regression (LOESS)

Provides an locally-weighted average when the independent variable is circular and depended variable is linear. Mainly to use with ggplot2.

circ_loess(
  formula = NULL,
  data = NULL,
  angle = NULL,
  y = NULL,
  xseq = NULL,
  weights = NULL,
  circ_space = NULL,
  span = 0.75,
  ...
)

Arguments

formula

the formula, e.g., y ~ x

data

data to use

angle

a vector of angles (not used if a formula is provided)

y

dependent variable vector (not used if a formula is provided)

xseq

a grid to compute predictions on (optional, the default is to use 500 points spanning the circle)

circ_space

circular space to use (90, 180, 360, or 2*pi)

span

a span to adjust the degree of smoothing

...

other arguments (ignored)

Value

an object of circ_loess class with the following parameters:

• angle the angles in the data

• y the dependent variable vales in the data

• xseq the grid on which the loess values are estimated

• y_est the estimated loess values

• y_se standard errors

• w weights

• circ_space circular space used

• span span used

Details

Weights for the regression are computed as \[w = (1-(d/d_{max})^3)^3\] where d is the angular difference between the point at which the estimate is computed and the angles in the data, and \(d_{max}\) is the maximum possible distance. If span is above 1, all points are included and \(d_{max} = {circ\_space}/(4*span)\). Otherwise, a proportion \(\alpha\) of the points included based on their distance to the point at which the estimate is computed and \(d_{max}\) is the corresponding maximal distance.

See also

stats::loess()

Examples

p <- ggplot(Pascucci_et_al_2019_data, aes(x = orientation, y = err))+geom_point(alpha = 0.05)+labs(x = 'Orientation, deg.', y = 'Error, deg.')
p1 <- p + geom_smooth(method = 'loess') + ggtitle('Standard LOESS')
p2 <- p + geom_smooth(method = 'circ_loess', method.args = list(circ_space = 180, span = 0.5)) + ggtitle('Circular LOESS, span = 0.5')
p3 <- p + geom_smooth(method = 'circ_loess', method.args = list(circ_space = 180, span = 0.2)) + ggtitle('Circular LOESS, span = 0.2')
(p1+p2+p3)
#> `geom_smooth()` using formula = 'y ~ x'
#> `geom_smooth()` using formula = 'y ~ x'
#> `geom_smooth()` using formula = 'y ~ x'