Test a General Linear Hypothesis for a Regression Model
Test, print, or summarize a general linear hypothesis for a regression model
glh.test(reg, cm, d=rep(0, nrow(cm)) ) ## S3 method for class 'glh.test' print(x, digits=4,...) ## S3 method for class 'glh.test' summary(object, digits=4,...)
reg |
Regression model |
cm |
matrix . Each row specifies a linear combination of the coefficients |
d |
vector specifying the null hypothis values for each linear combination |
x, object |
glh.test object |
digits |
number of digits |
... |
optional parameters (ignored) |
Test the general linear hypothesis
C %*% \hat{beta} == d
for the regression model reg.
The test statistic is obtained from the formula:
F = (C Beta-hat - d)' ( C (X'X)^-1 C' ) (C Beta-hat - d) / r / ( SSE / (n-p) )
Under the null hypothesis, f will follow a F-distribution with r and n-p degrees of freedom.
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 |
null.value |
d |
method |
description of the method |
data.name |
name of the model given for |
matrix |
matrix specifying the general linear hypotheis
( |
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.
Gregory R. Warnes greg@warnes.net
R.H. Myers, Classical and Modern Regression with Applications, 2nd Ed, 1990, p. 105
# 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 )
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