The function returns a Wald chi-squared test or a \(F\) test for a vector of model coefficients (possibly of length one), given its variance-covariance matrix.
wald.test(b, varb, Terms = NULL, L = NULL, H0 = NULL, df = NULL, verbose = FALSE, ...)
# S3 method for wald.test
print(x, ..., digits = max(3, getOption("digits") - 3))
An object of class wald.test
, printed with print.wald.test
.
A vector of coefficients with their var-cov matrix varb
. Coefficients b
and var-cov matrix are usually extracted using appropriate coef
and vcov
functions.
A var-cov matrix of coefficients b
(see above).
An optional integer vector specifying which coefficients should be jointly tested, using a Wald chi-squared test or a\(F\) test. The elements of varb
correspond to the columns or rows of the var-cov matrix given in varb
. 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 \(H_0\) 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 varb
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.
An object of class “wald.test”
A numeric scalar indicating the number of digits to be kept after the decimal place.
Additional arguments to print
.
The assumption is that the coefficients follow asymptotically a multivariate normal distribution with mean equal to the model coefficients b
and variance equal to their var-cov matrix varb
.
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-squared 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 \(H_0\), 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.
data(orob2)
fm <- aodql(cbind(m, n - m) ~ seed * root, data = orob2, family = "qbin")
# Wald chi2 test for the effect of root
wald.test(b = coef(fm), varb = vcov(fm), Terms = 3:4)
L <- matrix(c(0, 0, 1, 0, 0, 0, 0, 1), nrow = 2, byrow = TRUE)
wald.test(b = coef(fm), varb = vcov(fm), L = L)
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