wald.test {sommer} | R Documentation |
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 class 'wald.test'
print(x, digits = 2, ...)
Arguments
Sigma |
A var-cov matrix, usually extracted from one of the fitting functions (e.g., |
b |
A vector of coefficients with var-cov matrix |
Terms |
An optional integer vector specifying which coefficients should be jointly tested, using a Wald
|
L |
An optional matrix conformable to |
H0 |
A numeric vector giving the null hypothesis for the test. It must be as long as |
df |
A numeric vector giving the degrees of freedom to be used in an |
verbose |
A logical scalar controlling the amount of output information. The default is |
x |
Object of class “wald.test” |
digits |
Number of decimal places for displaying test results. Default to 2. |
... |
Additional arguments to |
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.
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(DT_yatesoats)
DT <- DT_yatesoats
m3 <- mmer(fixed=Y ~ V + N + V:N-1,
random = ~ B + B:MP,
rcov=~units,
data = DT)
wald.test(b = m3$Beta$Estimate, Sigma = m3$VarBeta, Terms = 2)
LL <- matrix(0,nrow=1, ncol=12)
LL[1,2] <- 1
LL[1,3] <- -1
LL
wald.test(b = m3$Beta$Estimate, Sigma = m3$VarBeta, L=LL)