eba (version 1.10-0)

wald.test: Testing Linear Hypotheses in Elimination-by-Aspects (EBA) Models

Description

Tests linear hypotheses of the form \(Cp = 0\) in elimination-by-aspects (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 utility 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, uscale, cov.u.

Examples

# NOT RUN {
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 elimination-by-aspects model

## Test whether JU, CY, and AJF have equal utility scale values
C1 <- rbind(c(0,0,0,1,-1, 0,0,0,0),
            c(0,0,0,1, 0,-1,0,0,0))
wald.test(eba1, C1)

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