cd = (d0 * c0 - d1*c1)/(d0 - d1) = (951 x 5.750 - 950 x 5.722)/(951 - 950) TRd = (T0*c0 - T1*c1)/cd = (2728.083 x 5.750 - 2717.094 x 5.722)/cd
COMPARISON MODEL Loglikelihood H0 Value -154318.940 H0 Scaling Correction Factor 5.722 for MLR H1 Value -151645.790 H1 Scaling Correction Factor 2.887 for MLR ... Chi-Square Test of Model Fit Value 2717.094* Degrees of Freedom 950 P-Value 0.0000 Scaling Correction Factor 1.968 for MLR NESTED MODEL: Loglikelihood H0 Value -154323.099 H0 Scaling Correction Factor 5.750 for MLR H1 Value -151645.790 H1 Scaling Correction Factor 2.887 for MLR ... Chi-Square Test of Model Fit Value 2728.083* Degrees of Freedom 951 P-Value 0.0000 Scaling Correction Factor 1.963 for MLR
Thanks for your confirmation. Let me ask a follow-up question. TRd was found to be 4.304958... Since the material says, "For MLM and MLR the products T0*c0 and T1*c1 are the same as the corresponding ML chi-square values," am I supposed to use 3.841 as critical value to determine whether the calculated S-B scaled chi-square difference is significant at the level of .05 or not? That is, is the difference (4.304958...) significant since TRd > 3.841?
I forgot asking another question. The equality constraint was imposed on a single parameter (which measures the effect of child maltreatment on violent offenses) for two ethnic groups, whites and Asian Americans. In the comparison model, the coefficient was found to be .031 (SE = .027) for whites, whereas it was .654 (SE = 1.430). As you can see, both coefficients are not significant, although the S-B scaled chi-square difference is larger than 3.841. As I supposed to say the coefficient is significantly different between whites and Asian Americans even though the coefficient was found to be not significant in each ethnic group?
2nd post: Each coefficient being significantly different from zero or not is not the same as testing that they are the same. Typically, if you use the independent-sample z test of equality using your SEs, you get the same thing as the chi2.
Step 1 on the Mplus website (http://www.statmodel.com/chidiff.shtml) for Difference Testing Using the Loglikelihood is: 1. Estimate the nested and comparison models using MLR. The printout gives loglikelihood values L0 and L1 for the H0 and H1 models, respectively, as well as scaling correction factors c0 and c1 for the H0 and H1 models, respectively.
Does this refer to H0 and H1 values given for the SAME model (i.e., in the same output file); or for DIFFERENT models (estimated in separate runs, with separate output files)?
I ask because while I have seen BOTH H0 and H1 values in some output files, I only see H0 for in a model I estimated using a NBI dependent variable, as seen below. There is no H1 value offered. Can I still utilize the steps on the website to compare the fit of this model with that of another nested model, using the H0 values only (the ones provided for each distinct model--because I did not get H0 and H1 values together in one output file). Thanks.
MODEL FIT INFORMATION Number of Free Parameters 14 Loglikelihood H0 Value -1189.806 H0 Scaling Correction Factor for MLR 1.1902
To do difference testing you need to run two analyses. The first is the least restrictive model. It is referred to as H1 in the writeup. The nested model is referred to as H0 in the write up. In both cases, the H0 values are taken from the output to use in the computations.
EFried posted on Tuesday, April 02, 2013 - 1:55 pm
When comparing 2 models using the MLR estimator, each model provides 3 scaling correction factors and 2 loglikelihoods. I don't find it specified which one to use for model comparison (http://www.statmodel.com/chidiff.shtml).