sommer (version 4.4.1)

wald.test: Wald Test for Model Coefficients

Description

Computes a Wald \(\chi^2\) 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 wald.test
print(x, digits = 2, ...)

Value

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

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 \(\chi^2\) 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.

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 \(\chi^2\) 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.

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(DT_yatesoats)
DT <- DT_yatesoats

m3 <- mmes(fixed=Y ~ V + N + V:N-1,
           random = ~ B + B:MP,
           rcov=~units,
           data = DT)

wald.test(b = m3$b, Sigma = m3$Ci[1:nrow(m3$b),1:nrow(m3$b)], Terms = 2)

LL <- matrix(0,nrow=1, ncol=12)
LL[1,2] <- 1
LL[1,3] <- -1
LL

wald.test(b = m3$b, Sigma = m3$Ci[1:nrow(m3$b),1:nrow(m3$b)], L=LL)