lr_lmr {tidySEM}

Lo-Mendell-Rubin Likelihood Ratio Test

Description

A likelihood ratio test for class enumeration in latent class analysis, proposed by Lo, Mendell, & Rubin (2001) based on work by Vuong (1989). See Details for important clarification.

Usage

lr_lmr(x, ...)

Arguments

x

An object for which a method exists.

...

Additional arguments.

Details

The likelihood ratio test for non-nested models, based on work by Vuong (1989), is often used for class enumeration in latent class analysis (see Lo, Mendell, & Rubin, 2001). Following work by Merkle, You, & Preacher (2016), the models to be compared must first be tested for distinguishability in the population, using the w2 test. The null hypothesis is that the models are indistinguishable. If this null hypothesis is not rejected, there is no point in statistical model comparison, either using the LMR LRT or other statistics. If the null hypothesis is rejected, the LMR LRT can be evaluated using a Z-test. This function wraps ⁠\link[nonnest2]{vuongtest}⁠ to perform that test.

Value

A data.frame containing the Z-value for the likelihood ratio test, its p-value, df (which indicates the difference in number of parameters, not true degrees of freedom, which may be zero), w2 (omega squared) statistic for the test of distinguishability, an its p-value.

References

Lo Y, Mendell NR, Rubin DB. Testing the number of components in a normal mixture. Biometrika. 2001;88(3):767–778. doi:10.1093/biomet/88.3.767

Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57, 307-333. doi:10.2307/1912557

Merkle, E. C., You, D., & Preacher, K. (2016). Testing non-nested structural equation models. Psychological Methods, 21, 151-163. doi:10.1037/met0000038

Examples

df <- iris[c(1:5, 100:105), 1:3]
names(df) <- letters[1:3]
res <- mx_profiles(df, classes = 1:2)
lr_lmr(res)