semTools (version 0.4-14)

wald: Calculate multivariate Wald statistics

Description

Calculate multivariate Wald statistics based on linear combinations of model parameters

Usage

wald(object, syntax)

Arguments

object

An output from lavaan

syntax

Syntax that each line represents one linear constraint. A plus or minus sign is used to separate between each coefficient. An asterisk is used to separate between coefficients and parameters. The coefficient can have a forward slash to represent a division. The parameter names must be matched with the names of lavaan parameters investigated by running the coef function on a lavaan output. Lines can be separated by semi-colon. A pound sign is allowed for comments. Note that the defined parameters (created by ":=") do not work with this function.

Value

Chi-square value with p value.

Details

The formula for multivariate Wald test is

$$ \chi^2 = \left(C\hat{b}\right)^\prime\left[C\hat{V}C^\prime\right]^{-1}\left(C\hat{b}\right),$$

where \(C\) is the contrast matrix, \(\hat{b}\) is the estimated fixed effect, \(\hat{V}\) is the asymptotic covariance matrix among fixed effects.

Examples

# NOT RUN {
# Test the difference in factor loadings
library(lavaan)
HS.model <- ' visual  =~ x1 + con1*x2 + con1*x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + con2*x8 + con2*x9 '

fit <- cfa(HS.model, data=HolzingerSwineford1939)
wald(fit, "con2 - con1")

# Simultaneously test the difference in the influences 
# of x1 and x2 on intercept and slope
model.syntax <- '
    i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4
    s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4
    i ~ x1 + x2
    s ~ x1 + x2
    t1 ~ c1
    t2 ~ c2
    t3 ~ c3
    t4 ~ c4
'

fit2 <- growth(model.syntax, data=Demo.growth)
wald.syntax <- '
	i~x1 - i~x2
	1/2*s~x1 - 1/2*s~x2
'
wald(fit2, wald.syntax)

# Mplus example of MODEL TEST
model3 <- ' f1  =~ x1 + p2*x2 + p3*x3 + p4*x4 + p5*x5 + p6*x6
			p4 == 2*p2'

fit3 <- cfa(model3, data=HolzingerSwineford1939)
wald(fit3, "p3; p6 - 0.5*p5")
# }