This test examines whether pairs of SEMs are nested or equivalent.
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.
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
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
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.
Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)
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
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## 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)
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