Likelihood ratio test between nested ... PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
Message/Author
 Jinseok Kim posted on Sunday, November 28, 2010 - 12:38 am
Hi, I am conducting an LCA using a set of categorical(ordinal) indicators. I am trying to impose a few constraints in the original model (M0) and to test whether the model with the constraints (M1) should be selected. In the following, I presented the outputs from M0 & M1 and wonder if you could direct me regarding which numbers should I use to determine likelihood ratio chi-square value for the test. Also, do I have to consider scaling correction factor in the test? Thanks.

Jinseok

M0 (no constraints):

TESTS OF MODEL FIT
Loglikelihood
H0 Value -11384.819
H0 Scaling Correction Factor 1.291

Information Criteria
Number of Free Parameters 62
** omitted ***

Pearson Chi-Square Value 15932.368
Degrees of Freedom 268435144
P-Value 1.0000

Likelihood Ratio Chi-Square 3892.824
Degrees of Freedom 268435144
P-Value 1.0000


M1 (with constraints):

TESTS OF MODEL FIT
Loglikelihood
H0 Value -11464.515
H0 Scaling Correction Factor 1.320

Information Criteria
Number of Free Parameters 59

** omitted **

Pearson Chi-Squar Value 16608.856
Degrees of Freedom 268435137
P-Value 1.0000

Likelihood Ratio Chi-Square 3940.894
Degrees of Freedom 268435137
P-Value 1.0000
 Linda K. Muthen posted on Monday, November 29, 2010 - 9:31 am
You use the H0 loglikelihood values and their scaling correction factors as described on the website under Chi-square difference test for MLM and MLR.
 Alice Wickersham posted on Thursday, February 13, 2020 - 7:12 am
“If the GMM model gives a considerably better log likelihood value for fewer ... parameters than the LCGA, GMM should clearly be chosen over LCGA” (Muthén 2006). I am using http://www.statmodel.com/chidiff.shtml to look into this. Please can I check my understanding of the following:

1. Using the formulas in the link, the following output can be compared by:

GMM (2 classes)
Number of Free Parameters 11
Loglikelihood
H0 Value -537782.542
H0 Scaling Correction Factor 1.3080
for MLR


LCGA (4 classes)
Number of Free Parameters 14
Loglikelihood
H0 Value -544635.032
H0 Scaling Correction Factor 1.5112
for MLR

cd = ((11*1.3080) - (14*1.5112)) / (11-14) = 2.256
df = 14 - 11 = 3
TRd = -2*(-537782.542 + 544635.032) / 2.256 = -6074.184

2. The resulting TRd and df can then be compared to a Chi-squared significance table?
3. But in this case, the Chi-squared is negative, so cannot be interpreted?
4. If so, is it sufficient to say that the GMM has a higher log-likelihood value without employing a Chi-squared difference test? Do you have any alternative suggestions?
 Tihomir Asparouhov posted on Thursday, February 13, 2020 - 2:44 pm
The models are not nested and the likelihood ratio test is not applicable. We recommend using the BIC for comparing such non-nested models (smaller BIC is better).
Back to top
Add Your Message Here
Post:
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Password:
Options: Enable HTML code in message
Automatically activate URLs in message
Action: