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.
lr_lmr(x, ...)An object for which a method exists.
Additional arguments.
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.
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.
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
df <- iris[c(1:5, 100:105), 1:3]
names(df) <- letters[1:3]
res <- mx_profiles(df, classes = 1:2)
#> Running mix1 with 6 parameters
#> Running mix2 with 10 parameters
#> Running mix2 with 10 parameters
lr_lmr(res)
#> Lo-Mendell-Rubin adjusted Likelihood Ratio Test:
#>
#> null alt lr df p w2 p_w2
#> mix1 mix2 3.77 4 8.31e-05 2.44 0.258