Circular-linear regression of a heading on linear covariates

Fits the Fisher-Lee circular-linear regression \(\theta_i \sim \mathrm{vM}(\mu_0 + 2\arctan(x_i'\beta), \kappa)\) via lm.circular (type = "c-l"), behind a formula interface. The response is a heading in radians (unit-circle convention); the right-hand side supplies one or more linear covariates (factors and interactions are expanded by model.matrix).

Usage

circ_regression(data, formula, init = NULL)

# S3 method for class 'circ_regression'
summary(object, conf.level = 0.95, ...)

# S3 method for class 'circ_regression'
predict(object, newdata = NULL, ...)

# S3 method for class 'circ_regression'
fitted(object, ...)

# S3 method for class 'circ_regression'
print(x, ...)

Arguments

data

A data frame containing the response and predictor columns.

formula

A formula `heading ~ x1 + x2`; the LHS is the angle column.

init

Optional numeric starting values for the slope coefficients (length = number of predictor columns). Default a vector of zeros.

object

A circ_regression object.

conf.level

Confidence level for the coefficient interval. Default 0.95.

...

Unused.

newdata

Optional data frame of new covariate values. Default uses the training data.

x

A circ_regression object.

Value

An S3 object of class "circ_regression". Use summary() for a tidy coefficient data frame, predict() / fitted() for fitted mean angles, and print() for a compact report. On non-convergence or too few rows, converged is FALSE and the coefficients are NA.

References

Fisher, N. I. & Lee, A. J. (1992). Regression models for an angular response. Biometrics 48, 665-677. Mardia, K. V. & Jupp, P. E. (2000). Directional Statistics. Wiley.

See also

circ_cor, vonmises_fit, simulate_tracks

Examples

# Headings whose mean turns with x: mu0 = 1, slope 1.5
set.seed(1)
x <- runif(60, -1, 1)
noise <- as.numeric(circular::rvonmises(60, circular::circular(0), kappa = 8))
hd <- data.frame(x = x, heading = (1 + 2 * atan(1.5 * x) + noise) %% (2 * pi))
fit <- circ_regression(hd, heading ~ x)
fit
#> Circular-linear regression (Fisher-Lee)
#>   mu0 = 0.9204, kappa = 10.03, n = 60, converged = TRUE
#>   term estimate         se statistic p_value conf.low conf.high
#> 1    x 1.513717 0.07762576  19.50019       0 1.361573  1.665861
summary(fit)
#>   term estimate         se statistic p_value conf.low conf.high
#> 1    x 1.513717 0.07762576  19.50019       0 1.361573  1.665861
predict(fit, newdata = data.frame(x = c(-1, 0, 1)))
#> [1] 5.229655 0.920445 2.894420