lavaan (version 0.5-21)

lavTestScore: Score test

Description

Score test (or Lagrange Multiplier test) for releasing one or more fixed or constrained parameters in model.

Usage

lavTestScore(object, add = NULL, release = NULL, univariate = TRUE, cumulative = FALSE, epc = FALSE, verbose = FALSE, warn = TRUE)

Arguments

object

An object of class lavaan.

add

Either a character string (typically between single quotes) or a parameter table containing additional (currently fixed-to-zero) parameters for which the score test must be computed.

release

Vector of Integers. The indices of the constraints that should be released. The indices correspond to the order of the equality constraints as they appear in the parameter table.

univariate

Logical. If TRUE, compute the univariate score statistics, one for each constraints.

cumulative

Logical. If TRUE, order the univariate score statistics from large to small, and compute a series of multivariate score statistics, each time adding an additional constraint.

epc

Logical. If TRUE, and we are releasing existing constraints, compute the expected parameter changes for the existing (free) parameters, for each released constraint.

verbose

Logical. Not used for now.

warn

Logical. If TRUE, print out warnings if they occur.

Value

A list containing at least three elements: the Score test statistic (stat), the degrees of freedom (df), and a p-value under the chi-square distribution (p.value). If univariate tests were requested, an additional element (TS.univariate) containing a numeric vector of univariate score statistics. If cumulative tests were requested, an additional element (TS.order) showing the order of the univariate test statistics, and an element (TS.cumulative) containing a numeric vector of cumulative multivariate score statistics.

Details

This function can be used to compute both multivariate and univariate score tests. There are two modes: 1) releasing fixed-to-zero parameters (using the add argument), and 2) releasing existing equality constraints (using the release argument). The two modes can not be used simultaneously.

When adding new parameters, they should not already be part of the model (i.e. not listed in the parameter table). If you want to test for a parameter that was explicitly fixed to a constant (say to zero), it is better to label the parameter, and use an explicit equality constraint.

References

Bentler, P. M., & Chou, C. P. (1993). Some new covariance structure model improvement statistics. Sage Focus Editions, 154, 235-255.

Examples

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

    b1 == b2
    b2 == b3
'
fit <- cfa(HS.model, data=HolzingerSwineford1939)

# test 1: release both two equality constraints
lavTestScore(fit, cumulative = TRUE)

# test 2: the score test for adding two (currently fixed
# to zero) cross-loadings
newpar = '
    visual =~ x9
    textual =~ x3
'
lavTestScore(fit, add = newpar)