In latent class analysis (LCA) it is desirable to compare the fit of a model with k classes to that of a model with k-1 classes. Mplus performs this test and gives for example (from here: https://stats.oarc.ucla.edu/mplus/dae/latent-class-analysis/ ) the following output
TECHNICAL 11 OUTPUT
VUONG-LO-MENDELL-RUBIN LIKELIHOOD RATIO TEST FOR 2 (H0) VERSUS 3 CLASSES
H0 Loglikelihood Value -4251.208
2 Times the Loglikelihood Difference 39.025
Difference in the Number of Parameters 10
Mean 20.255
Standard Deviation 22.224
P-Value 0.1457
The sited paper is Vuong, Q.H. (1989), and we are looking at nested models in the LCA case I believe. I understand how the H0 Loglikelihood, 2 times the likelihood difference, and the difference in the number of parameters are obtained but I do not understand where the mean and standard deviation listed come from. Further their inclusion makes me think we should compare to a Z distribution as an approximation of the complex to calculate gamma but when compare it my pvalues do not match. In short I want to understand how the mean and standard deviation are calculated and what they represent in this calculation. Thank you!!
pnorm(39.025,mean = 20.255,sd = 22.224, lower.tail = FALSE)#should be .1457 according to above
0.199172
