aods3 (version 0.4-1.2)

wald.test: 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 wald.test
print(x, ..., digits = max(3, getOption("digits") - 3))

Value

An object of class wald.test, printed with print.wald.test.

Arguments

b

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.

varb

A var-cov matrix of coefficients b (see above).

Terms

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.

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 \(H_0\) 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.

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 varb 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

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 print.

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.

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)