Computes a Wald chi-squared test for 1 or more coefficients, given their variance-covariance matrix.
Usage
wald.test(Sigma, b, Terms = NULL, L = NULL, H0 = NULL,
df = NULL, verbose = FALSE)
## S3 method for class 'wald.test'
print(x, digits = 2, ...)
Arguments
Sigma
A var-cov matrix, usually extracted from one of the fitting functions (e.g., lm, glm, ...).
b
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,...).
Terms
An optional integer vector specifying which coefficients should be jointly tested, using a Wald
chi-squared or F test. Its elements correspond to the columns or rows of the var-cov
matrix given in Sigma. Default is NULL.
L
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.
H0
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.
df
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.
verbose
A logical scalar controlling the amount of output information. The default is FALSE, providing minimum output.
x
Object of class “wald.test”
digits
Number of decimal places for displaying test results. Default to 2.
...
Additional arguments to print.
Details
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-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 H0, this new statistic follows an F(m, df) distribution.
Value
An object of class wald.test, printed with print.wald.test.
References
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.
See Also
vcov
Examples
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)