This function calculates the Wald test for either fixed effects or variance parameters.

Usage,

`waldTest(fittedModel, type = c("beta", "Lambda"), coefs = NA, hypothesis = NA)`

- fittedModel
a model of class

`WeMixResults`

that is the result of a call to`mix`

- type
a string, one of "beta" (to test the fixed effects) or "Lambda" (to test the variance-covariance parameters for the random effects)

- coefs
a vector containing the names of the coefficients to test. For

`type="beta"`

these must be the variable names exactly as they appear in the fixed effects table of the summary. For`type="Lambda"`

these must be the names exactly as they appear in the theta element of the fitted model.- hypothesis
the hypothesized values of beta or Lambda. If

`NA`

(the default) 0 will be used.

Object of class `WeMixWaldTest`

.
This is a list with the following elements:

- wald
the value of the test statistic.

- p
the p-value for the test statistic. Based on the probabilty of the test statistic under the chi-squared distribution.

- df
degrees of freedom used to calculate p-value.

- H0
The vector (for a test of beta) or matrix (for tests of Lambda) containing the null hypothesis for the test.

- HA
The vector (for a test of beta) or matrix (for tests of Lambda) containing the alternative hypothesis for the test (i.e. the values calculated by the fitted model being tested.)

By default this function tests against the null hypothesis that all coefficients are zero. To identify which coefficients to test use the name exactly as it appears in the summary of the object.

```
if (FALSE) {
library(lme4) #to use the example data
sleepstudyU <- sleepstudy
sleepstudyU$weight1L1 <- 1
sleepstudyU$weight1L2 <- 1
wm0 <- mix(Reaction ~ Days + (1|Subject), data=sleepstudyU,
weights=c("weight1L1", "weight1L2"))
wm1 <- mix(Reaction ~ Days + (1 +Days|Subject), data=sleepstudyU,
weights=c("weight1L1", "weight1L2"))
waldTest(wm0, type="beta") #test all betas
#test only beta for days
waldTest(wm0, type="beta", coefs="Days")
#test only beta for intercept against hypothesis that it is 1
waldTest(wm0, type="beta", coefs="(Intercept)", hypothesis=c(1))
waldTest(wm1,type="Lambda") #test all values of Lambda
#test only some Lambdas.The names are the same as names(wm1$theta)
waldTest(wm1,type="Lambda", coefs="Subject.(Intercept)")
#specify test values
waldTest(wm1,type="Lambda", coefs="Subject.(Intercept)", hypothesis=c(1))
}
```