glh.test {gmodels}

Test a General Linear Hypothesis for a Regression Model

Description

Test, print, or summarize a general linear hypothesis for a regression model

Usage

glh.test(reg, cm, d = rep(0, nrow(cm)))

Arguments

reg

Regression model

cm

contrast matrix C . Each row specifies a linear combination of the coefficients

d

vector d specifying the null hypothesis values for each linear combination

Details

Test the general linear hypothesis C \hat{\beta} = d for the regression model reg.

The test statistic is obtained from the formula:

f = \frac{(C \hat{\beta} - d)' ( C (X'X)^{-1} C' ) (C \hat{\beta} - d) / r }{ SSE / (n-p) }

where

• r is the number of contrasts contained in C, and

• n-p is the model degrees of freedom.

Under the null hypothesis, f will follow a F-distribution with r and n-p degrees of freedom

Value

Object of class c("glh.test","htest") with elements:

call

Function call that created the object

statistic

F statistic

parameter

vector containing the numerator (r) and denominator (n-p) degrees of freedom

p.value

p-value

estimate

computed estimate for each row of cm

null.value

d

method

description of the method

data.name

name of the model given for reg

matrix

matrix specifying the general linear hypotheis (cm)

Note

When using treatment contrasts (the default) the first level of the factors are subsumed into the intercept term. The estimated model coefficients are then contrasts versus the first level. This should be taken into account when forming contrast matrixes, particularly when computing contrasts that include 'baseline' level of factors.

See the comparison with fit.contrast in the examples below.

Author(s)

Gregory R. Warnes [e-mail]

References

R.H. Myers, Classical and Modern Regression with Applications, 2nd Ed, 1990, p. 105

See Also

fit.contrast(), estimable(), stats::contrasts()

Examples

# fit a simple model
y <- rnorm(100)
x <-  cut(rnorm(100, mean=y, sd=0.25),c(-4,-1.5,0,1.5,4))
reg <- lm(y ~ x)
summary(reg)

# test both group 1 = group 2  and group 3 = group 4
# *Note the 0 in the column for the intercept term*

C <- rbind( c(0,-1,0,0), c(0,0,-1,1) )
ret <- glh.test(reg, C)
ret  # same as 'print(ret) '
summary(ret)

# To compute a contrast between the first and second level of the factor
# 'x' using 'fit.contrast' gives:

fit.contrast( reg, x,c(1,-1,0,0) )
	
# To test this same contrast using 'glh.test', use a contrast matrix
# with a zero coefficient for the intercept term.  See the Note section,
# above, for an explanation.

C <- rbind( c(0,-1,0,0) )
glh.test( reg, C )