Directional (version 7.0)

Score test for many simple CIPC and SMPL regressions: Score test for many simple CIPC and SPML regressions

Description

Score test for many simple CIPC and SPML regressions.

Usage

score.cipc(y, X, rads = TRUE, tol = 1e-06)
score.spml(y, X, rads = TRUE, tol = 1e-06)

Value

A matrix with two columns, the test statistic and its associated p-value.

Arguments

y

The dependent variable, a numerical vector, it can be in radians or degrees.

X

A matrix with many numerical independent variables.

rads

If the dependent variable is expressed in rads, this should be TRUE and FALSE otherwise.

tol

The tolerance value to terminate the Newton-Raphson algorithm in the null model (CIPC without covariates).

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

Details

The score test uses the first derivative (score function) of the regression log-likelihood and it is asymptotically correct. So, this function requires sample sizes or at least 1,000 observations. The CIPC is basically the Wrapped Cauchy distribution (Tsagris and Alzeley, 2024) and SPML is the bivariate projected normal (Presnell et al., 1998).

References

Tsagris M. and Alzeley O. (2024). Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling. Australian & New Zealand Journal of Statistics (accepted for publication). https://arxiv.org/pdf/2302.02468.pdf

Presnell B., Morrison S. P. and Littell R. C. (1998). Projected multivariate linear models for directional data. Journal of the American Statistical Association, 93(443): 1068--1077.

See Also

cipc.reg, spml.reg, cipc.mle, spml.mle,

Examples

y <- rcipc(500, omega = 2, g = 5)
x <- matrix( rnorm(500 * 10), ncol = 10 )
a <- score.cipc(y, x)