net {semTools}

Nesting and Equivalence Testing

Description

This test examines whether pairs of SEMs are nested or equivalent.

Usage

net(..., crit = 1e-04)

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^2 fit statistics is less than this criterion.

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 analyzes summary statistics (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 also applies to models for categorical data, following the procedure described by Asparouhov & Muthen (2019).

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.

Author(s)

Terrence D. Jorgensen (University of Amsterdam; [e-mail])

References

Bentler, P. M., & Satorra, A. (2010). Testing model nesting and equivalence. Psychological Methods, 15(2), 111–123. doi:10.1037/a0019625

Asparouhov, T., & Muthen, B. (2019). Nesting and equivalence testing for structural equation models. Structural Equation Modeling, 26(2), 302–309. doi:10.1080/10705511.2018.1513795

Examples

## Not run: 
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)

## End(Not run)