# wald.test: Wald Test for Model Coefficients In aod: Analysis of Overdispersed Data

 wald.test R Documentation

## Wald Test for Model Coefficients

### Description

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.

`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)
```

aod documentation built on April 2, 2022, 9:05 a.m.