In R, performing a chi-square difference test—often referred to in structural equation modeling (SEM) as a Likelihood Ratio Test (LRT)—is used to compare the fit of two nested models to determine if a more complex model provides a statistically significant improvement over a simpler model.
While users often search for terms like ChiSquareDiff or chiSqDiff, the actual implementation in modern R workflows relies on native functions within the popular lavaan package or helper functions in extension packages. What are Nested Models?
Two models are nested if the simpler model (the constrained model) can be derived from the more complex model (the unconstrained model) by fixing or removing certain parameters.
The Null Hypothesis (H₀): The constraints placed on the simpler model are valid, and it fits the data just as well as the complex model.
The Alternative Hypothesis (H₁): The complex model fits the data significantly better; removing those parameters hurts the model fit. Core Implementation in R using lavaan
The standard way to run this test is using the anova() function or the explicit lavTestLRT() function on two fitted lavaan objects. 1. Standard Likelihood Ratio Test (ML Estimator)
When using regular Maximum Likelihood estimation, the difference between the two chi-square statistics is itself distributed as a chi-square:
Lavaan (CFA, SEM): Are Your Models Nested? – regorz statistik
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