Implements the ad-hoc adjusted likelihood ratio test (LRT) described in Formula 15 of Lo, Mendell,
& Rubin (2001), also known as VLMR LRT (Vuong-Lo-Mendell-Rubin Adjusted LRT). This method is typically
used to compare models with L-1 and L classes. If the difference in the number of
classes exceeds 1, conclusions should be interpreted with extreme caution.
LRT.test.VLMR(object1, object2)An object of class "htest" containing:
statistic: VLMR adjusted test statistic
parameter: Degrees of freedom (\(df = npar_2 - npar_1\))
p.value: P-value from \(\chi^2_df\) distribution
method: Name of the test
data.name: Model comparison description
Fitted model object with fewer parameters (i.e., fewer npar, small model).
Fitted model object with more parameters (i.e., more npar, large model).
Note that since the small model may be nested within the large model, the result
of LRT.test.VLMR may not be accurate and is provided for reference only.
More reliable conclusions should be based on a combination of fit indices (i.e., get.fit.index),
classification accuracy measures (i.e., get.entropy, get.AvePP), and a bootstrapped
likelihood-ratio test (i.e., BLRT, LRT.test.Bootstrap, which is very time-consuming).
Above all and the most important criterion, is that the better model is the one that aligns with theoretical
expectations and offers clear interpretability.
The LRT.test.VLMR statistic is defined as:
$$VLMR = \frac{LRT}{c} \quad \text{where} \quad c = 1 + \frac{1}{df \cdot \log(N)}$$
where:
\(LRT\) is the standard likelihood ratio statistic. see LRT.test
\(df = npar_2 - npar_1\) is the difference in number of free parameters between models.
\(N\) is the sample size.
Under the null hypothesis (H_0: small model is true), VLMR asymptotically follows
a chi-square distribution with \(df\) degrees of freedom.
Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767-778. https://doi.org/10.1093/biomet/88.3.767
Nylund-Gibson, K., & Choi, A. Y. (2018). Ten frequently asked questions about latent class analysis. Translational Issues in Psychological Science, 4(4), 440-461. https://doi.org/10.1037/tps0000176