Wald test

Wald test for testing a linear hypothesis about the parameters of fitted lavaan object.

lavTestWald(object, constraints = NULL, verbose = FALSE)

Arguments

object

An object of class lavaan.

constraints

A character string (typically between single quotes) containing one or more equality constraints. See examples for more details.

verbose

Logical. If TRUE, print out the restriction matrix and the estimated restricted values.

Details

The constraints are specified using the "==" operator. Both the left-hand side and the right-hand side of the equality can contain a linear combination of model parameters, or a constant (like zero). The model parameters must be specified by their user-specified labels. Names of defined parameters (using the ":=" operator) can be included too.

Value

A list containing three elements: the Wald test statistic (stat), the degrees of freedom (df), and a p-value under the chi-square distribution (p.value).

Examples

HS.model <- '
    visual  =~ x1 + b1*x2 + x3
    textual =~ x4 + b2*x5 + x6
    speed   =~ x7 + b3*x8 + x9
'

fit <- cfa(HS.model, data=HolzingerSwineford1939)
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.747972e-02) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.

# test 1: test about a single parameter
# this is the 'chi-square' version of the 
# z-test from the summary() output
lavTestWald(fit, constraints = "b1 == 0")
#> $stat
#> [1] 34.52594
#> 
#> $df
#> [1] 1
#> 
#> $p.value
#> [1] 4.206083e-09
#> 
#> $se
#> [1] "standard"
#> 

# test 2: several constraints
con = '
   2*b1 == b3
   b2 - b3 == 0
'
lavTestWald(fit, constraints = con)
#> $stat
#> [1] 7.064159
#> 
#> $df
#> [1] 2
#> 
#> $p.value
#> [1] 0.02924404
#> 
#> $se
#> [1] "standard"
#>