semTools (version 0.4-12)

net: Nesting and Equivalence Testing

Description

This test examines whether models are nested or equivalent based on Bentler and Satorra's (2010) procedure.

Usage

net(..., crit = .0001)

Arguments

...

The lavaan objects used for test of nesting and equivalence

crit

The upper-bound criterion for testing the equivalence of models. Models are considered nested (or equivalent) if the difference between their chi-squared fit statistics is less than this criterion.

Value

The Net object representing the outputs for nesting and equivalent testing, including a logical matrix of test results and a vector of degrees of freedom for each model.

Details

The concept of nesting/equivalence should be the same regardless of estimation method. However, the particular method of testing nesting/equivalence (as described in Bentler & Satorra, 2010) employed by the net function is based on a limited-information estimator (analyzing model-implied means and covariance matrices, not raw data). In the case of robust methods like MLR, the raw data is only utilized for the robust adjustment to SE and chi-sq, and the net function only checks the unadjusted chi-sq for the purposes of testing nesting/equivalence. This method does not apply to models that estimate thresholds for categorical data, so an error message will be issued if such a model is provided.

References

Bentler, P. M., & Satorra, A. (2010). Testing model nesting and equivalence. Psychological Methods, 15, 111-123. doi:10.1037/a0019625

Examples

m1 <- ' visual  =~ x1 + x2 + x3
	textual =~ x4 + x5 + x6
	speed   =~ x7 + x8 + x9 '

	
m2 <- ' f1  =~ x1 + x2 + x3 + x4
	f2 =~ x5 + x6 + x7 + x8 + x9 '

m3 <- ' visual  =~ x1 + x2 + x3
	textual =~ eq*x4 + eq*x5 + eq*x6
	speed   =~ x7 + x8 + x9 '
	
fit1 <- cfa(m1, data = HolzingerSwineford1939)
fit1a <- cfa(m1, data = HolzingerSwineford1939, std.lv = TRUE) # Equivalent to fit1
fit2 <- cfa(m2, data = HolzingerSwineford1939) # Not equivalent to or nested in fit1
fit3 <- cfa(m3, data = HolzingerSwineford1939) # Nested in fit1 and fit1a

tests <- net(fit1, fit1a, fit2, fit3)
tests
summary(tests)