aods3: wald.test – R documentation

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

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 aF 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.

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)

aods3

Analysis of Overdispersed Data using S3 Methods

v0.4-1.1

GPL (>= 2)

Authors

Matthieu Lesnoff <matthieu.lesnoff@cirad.fr> and Renaud Lancelot <renaud.lancelot@cirad.fr>

Initial release