Computes a Wald \(\chi^2\) test for 1 or more coefficients, given their variance-covariance matrix.
wald.test(Sigma, b, Terms = NULL, L = NULL, H0 = NULL,
df = NULL, verbose = FALSE)
# S3 method for wald.test
print(x, digits = 2, ...)
A var-cov matrix, usually extracted from one of the fitting functions (e.g., lm
, glm
, ...).
A vector of coefficients with var-cov matrix Sigma
. These coefficients are usually extracted from
one of the fitting functions available in R (e.g., lm
, glm
,...).
An optional integer vector specifying which coefficients should be jointly tested, using a Wald
\(\chi^2\) or \(F\) test. Its elements correspond to the columns or rows of the var-cov
matrix given in Sigma
. Default is NULL
.
An optional matrix conformable to b
, such as its product with b
i.e., L %*% b
gives the linear combinations of the coefficients to be tested. Default is NULL
.
A numeric vector giving the null hypothesis for the test. It must be as long as Terms
or
must have the same number of columns as L
. Default to 0 for all the coefficients to be tested.
A numeric vector giving the degrees of freedom to be used in an \(F\) test, i.e. the degrees of freedom
of the residuals of the model from which b
and Sigma
were fitted. Default to NULL, for no
\(F\) test. See the section Details for more information.
A logical scalar controlling the amount of output information. The default is FALSE
, providing minimum output.
Object of class “wald.test”
Number of decimal places for displaying test results. Default to 2.
Additional arguments to print
.
An object of class wald.test
, printed with print.wald.test
.
The key assumption is that the coefficients asymptotically follow a (multivariate) normal distribution with mean =
model coefficients and variance = their var-cov matrix.
One (and only one) of Terms
or L
must be given. When L
is given, it must have the same number of
columns as the length of b
, and the same number of rows as the number of linear combinations of coefficients.
When df
is given, the \(\chi^2\) Wald statistic is divided by m
= the number of
linear combinations of coefficients to be tested (i.e., length(Terms)
or nrow(L)
). Under the null
hypothesis H0
, this new statistic follows an \(F(m, df)\) distribution.
Diggle, P.J., Liang, K.-Y., Zeger, S.L., 1994. Analysis of longitudinal data. Oxford, Clarendon Press, 253 p. Draper, N.R., Smith, H., 1998. Applied Regression Analysis. New York, John Wiley & Sons, Inc., 706 p.
# NOT RUN {
data(orob2)
fm <- quasibin(cbind(y, n - y) ~ seed * root, data = orob2)
# Wald test for the effect of root
wald.test(b = coef(fm), Sigma = vcov(fm), Terms = 3:4)
# }
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