R: Nesting and Equivalence Testing

net {semTools} | R Documentation

## 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 = 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 χ^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 does not apply to models that estimate thresholds for categorical data, so an error message will be issued if such a model is provided.

### 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; TJorgensen314@gmail.com)

### References

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

### 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)

[Package semTools version 0.5-1 Index]