# How to assess the assumption of conditional independence in latent class analysis (poLCA)?

I'm performing latent class modelling using poLCA package in R. Below is an example from the documentation.

How to interpret G^2?

And how to assess whether the assumption of conditional independence holds between each two of the manifest variables A, B, C and D?

> library(poLCA)
> data(values)
> f <- cbind(A,B,C,D)~1

poLCA(f,values,nclass=3,maxiter=8000)

Conditional item response (column) probabilities,
by outcome variable, for each class (row)

$A Pr(1) Pr(2) class 1: 0.5188 0.4812 class 2: 0.0022 0.9978 class 3: 0.1557 0.8443$B
Pr(1)  Pr(2)
class 1:  0.9053 0.0947
class 2:  0.0204 0.9796
class 3:  0.5013 0.4987

$C Pr(1) Pr(2) class 1: 0.7310 0.2690 class 2: 0.0000 1.0000 class 3: 0.5522 0.4478$D
Pr(1)  Pr(2)
class 1:  0.9251 0.0749
class 2:  0.0874 0.9126
class 3:  0.7983 0.2017

Estimated class population shares
0.2266 0.193 0.5804

Predicted class memberships (by modal posterior prob.)
0.1435 0.1944 0.662

=========================================================
Fit for 3 latent classes:
=========================================================
number of observations: 216
number of estimated parameters: 14
residual degrees of freedom: 1
maximum log-likelihood: -503.3011

AIC(3): 1034.602
BIC(3): 1081.856
G^2(3): 0.3868563 (Likelihood ratio/deviance statistic)
X^2(3): 0.4225484 (Chi-square goodness of fit)


$G^2$ is the likelihood ratio. The package authors provide additional detail including its formula here. It is akin to $\chi^2$ (formula also provided in the same link) with large values indicating greater model-data misfit.