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.,
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.,
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
An optional matrix conformable to
b, such as its product with
L %*% b
gives the linear combinations of the coefficients to be tested. Default is
A numeric vector giving the null hypothesis for the test. It must be as long as
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
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
An object of class
wald.test, printed with
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
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.
df is given, the \(\chi^2\) Wald statistic is divided by
m = the number of
linear combinations of coefficients to be tested (i.e.,
nrow(L)). Under the null
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.