R: Wald Test for Model Coefficients

wald.test {aod} | 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.

### See Also

`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)

[Package aod version 1.3 Index]