eba (version 1.5-2)

wald.test: Testing Linear Hypotheses

Description

Tests linear hypotheses of the form $Cp = 0$ in EBA models using the Wald test.

Usage

wald.test(object, C, u.scale = TRUE)

Arguments

object

an object of class eba, typically the result of a call to eba

C

a matrix of contrasts, specifying the linear hypotheses

u.scale

logical, if TRUE the test is performed on the u-scale, if FALSE the test is performed on the EBA parameters directly

Value

• C
  the matrix of contrasts, specifying the linear hypotheses
• W
  the Wald test statistic
• df
  the degrees of freedom ($rk(C)$)
• pval
  the p-value of the test

Details

The Wald test statistic, $$W = (Cp)' [C cov(p) C']^{-1} (Cp),$$ is approximately chi-square distributed with $rk(C)$ degrees of freedom.

C is usually of full rank and must have as many columns as there are parameters in p.

See Also

eba, group.test, cov.u.

Examples

data(celebrities)  # absolute choice frequencies
A <- list(c(1,10), c(2,10), c(3,10), c(4,11), c(5,11), c(6,11),
          c(7,12), c(8,12), c(9,12))  # the structure of aspects
eba1 <- eba(celebrities, A)  # fit a preference tree

## Test whether JU, CY, and AJF have equal preference scale values
C1 <- matrix(c(0,0,0,1,-1,0,0,0,0,
               0,0,0,1,0,-1,0,0,0), 2, 9, TRUE)
wald.test(eba1, C1)

## Test whether the three branch parameters are different
C2 <- matrix(c(0,0,0,0,0,0,0,0,0,1,-1,0,
               0,0,0,0,0,0,0,0,0,1,0,-1), 2, 12, TRUE)
wald.test(eba1, C2, u.scale = FALSE)