wald.test {aods3} | R Documentation |
Wald Test for Model Coefficients
Description
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.
Usage
wald.test(b, varb, Terms = NULL, L = NULL, H0 = NULL, df = NULL, verbose = FALSE, ...)
## S3 method for class 'wald.test'
print(x, ..., digits = max(3, getOption("digits") - 3))
Arguments
b |
A vector of coefficients with their var-cov matrix |
varb |
A var-cov matrix of coefficients |
Terms |
An optional integer vector specifying which coefficients should be jointly tested, using a Wald chi-squared test or a |
L |
An optional matrix conformable to |
H0 |
A numeric vector giving the null hypothesis |
df |
A numeric vector giving the degrees of freedom to be used in an |
verbose |
A logical scalar controlling the amount of output information. The default is |
x |
An object of class “wald.test” |
digits |
A numeric scalar indicating the number of digits to be kept after the decimal place. |
... |
Additional arguments to |
Details
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.
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.
Examples
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)