

Likelihood ratio test between nested ... 

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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 chisquare 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 ChiSquare Value 15932.368 Degrees of Freedom 268435144 PValue 1.0000 Likelihood Ratio ChiSquare 3892.824 Degrees of Freedom 268435144 PValue 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 ChiSquar Value 16608.856 Degrees of Freedom 268435137 PValue 1.0000 Likelihood Ratio ChiSquare 3940.894 Degrees of Freedom 268435137 PValue 1.0000 


You use the H0 loglikelihood values and their scaling correction factors as described on the website under Chisquare difference test for MLM and MLR. 


“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)) / (1114) = 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 Chisquared significance table? 3. But in this case, the Chisquared is negative, so cannot be interpreted? 4. If so, is it sufficient to say that the GMM has a higher loglikelihood value without employing a Chisquared difference test? Do you have any alternative suggestions? 


The models are not nested and the likelihood ratio test is not applicable. We recommend using the BIC for comparing such nonnested models (smaller BIC is better). 

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