india (version 0.1)

relative.condition: Relative change in the condition number

Description

Compute the relative condition index to identify collinearity-influential points in linear models.

Usage

relative.condition(x)

Value

To assess the influence of the ith row of \(\bold{X}\) on the condition index of \(\bold{X}\), Hadi (1988) proposed the relative change,

$$\delta_i = \frac{\kappa_{(i)} - \kappa}{\kappa},$$

for \(i=1,\dots,n\), where \(\kappa = \kappa(\bold{X})\) and \(\kappa_{(i)} = \kappa(\bold{X}_{(i)})\)

denote the (scaled) condition index for \(\bold{X}\) and \(\bold{X}_{(i)}\), respectively.

Arguments

x

the model matrix \(\bold{X}\).

References

Chatterjee, S., Hadi, A.S. (1988). Sensivity Analysis in Linear Regression. Wiley, New York.

Hadi, A.S. (1988). Diagnosing collinerity-influential observations. Computational Statistics & Data Analysis 7, 143-159. tools:::Rd_expr_doi("10.1016/0167-9473(88)90089-8").

Examples

data(portland)
fm <- ridge(y ~ ., data = portland, x = TRUE)
x <- fm$x
rel <- relative.condition(x)
plot(rel, ylab = "Relative condition number", ylim = c(-0.1,0.4))
abline(h = 0, lty = 2, lwd = 2, col = "red")
text(3, rel[3], label = as.character(3), pos = 3)