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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)
Orion
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1 Answers1

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$G^2$ 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.

As for conditional independence, as the authors of the package point out:

The latent class model seeks to stratify the cross-classification table of observed (or, “manifest”) variables by an unobserved (“latent”) unordered categorical variable that eliminates all confounding between the manifest variables. Conditional upon values of this latent variable, responses to all of the manifest variables are assumed to be statistically independent; an assumption typically referred to as “conditional” or “local” independence

If you would like to demonstrate conditional independence after you have settled on a latent class solution you can consider the Cochran-Mantel-Haenszel test.

Matt Barstead
  • 2,154