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, ...)
```

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
\(\chi^2\) 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`

.

An object of class `wald.test`

, printed with `print.wald.test`

.

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 \(\chi^2\) 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.

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.

```
# NOT RUN {
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)
# }
```

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