Difference Testing using Chi-square PreviousNext
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 Sung Joon Jang posted on Thursday, October 20, 2011 - 12:01 pm
Please let me know whether I'm using the formulas correctly, found in "Difference Testing Using Chi-Square," http://www.statmodel.com/chidiff.shtml).

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
 Bengt O. Muthen posted on Friday, October 21, 2011 - 9:56 am
Yes, you are doing this correctly.
 Sung Joon Jang posted on Friday, October 21, 2011 - 11:13 am
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?
 Sung Joon Jang posted on Friday, October 21, 2011 - 11:26 am
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?
 Bengt O. Muthen posted on Friday, October 21, 2011 - 4:26 pm
1st post: Right.

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.
 Lisa M. Yarnell posted on Thursday, March 14, 2013 - 8:22 pm
Hi Linda and Bengt,

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
 Linda K. Muthen posted on Friday, March 15, 2013 - 9:04 am
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).

Thank you
 Linda K. Muthen posted on Tuesday, April 02, 2013 - 2:01 pm
The one for the H0 model -- what is posted above.
 ri ri  posted on Friday, August 29, 2014 - 3:21 am
I would like to compare two Mediation models:

model 1: x-m-y1-y2-y3
x-m-y1-y4
model 2: x-m-y1-y4
x-m-y2-y3

y3 and y4 are binary. Both models seem to work in Terms of Mediation. SO I Need to prove one model is better than the other.

Can I follow the instruction of doing the chi square test for WLSMV? I did not find any description regarding H0 and H1 models, scale correction info in Output.
 Bengt O. Muthen posted on Friday, August 29, 2014 - 4:40 pm
Looks like the only difference is that model 2 has a direct effect from m to y2.
 ri ri  posted on Saturday, August 30, 2014 - 4:08 pm
Yes, as far as I know one Needs to do a chi square difference test to compare the two models. In regular way, one just uses the chi square values. But since I have categorical data, I shall do it differently I suppose? I used the difftest command, but could not find the scale correction to calculate the difference with the formula provided at the Website.
 Bengt O. Muthen posted on Saturday, August 30, 2014 - 4:44 pm
With only one parameter difference you can just look at the z-test for that parameter in the model that is less restrictive.

In the general case you use DIFFTEST, first running the less restrictive model and then the more restrictive model. You don't need the scaling correction factors or the computations on the website. DIFFTEST does it for you.
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