Modification indices, TECH2, and LM test PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Min Jung Kim posted on Thursday, February 09, 2006 - 11:31 am
I am running MGCFA to test measurement invariance with both categorical and continuous variables using WLSMV estimator because of missing data. First, I ran an unconstrained model (i.e., all factor loadings except reference indicators, thresholds, intercepts, and covariances among latent factors are freely estimated), and then ran a constrained model fixing factor loadings, thresholds, intercepts, and the covariances are to be equal across two groups. Because DIFFTEST showed significant differences between un- and constrained models, I like to revise the constrained model until I have non-significant chi-square difference using TECH2 or modification indices. Another thing I would like to know is what factor loadings are significantly different across two groups. In my model, I have two groups, 6 latent factors having 3-4 indicators (both categorical and continuous indicators), and 3 out of the 6 latent factors consist of one second order factor, and missing data.
Here are my questions:

1) I think I need to look at the TECH2 report instead of modification indices, but I am not sure whether I should look at TECH2 results only for categorical variables and use modification indices for continuous indicators. Because I have both modification indices and TECH2 reports, I am not sure how I should use both outputs to improve model fits.

2) Looking at TECH2 reports, there are different kinds of derivatives. If I used DELTA parameterization, should I look at only those derivatives presented with respect to DELTA? If not, what derivatives I need to look at?

3) Looking at modification indices and TECH2, values of the MI and derivatives are different across two groups. My thought was that I constrained factor loadings, etc. to be equal across two groups, so should obtain one value (MI or derivatives) on a path for both groups indicating if the path is freely estimated across two groups. In EQS, LM test to see group invariance shows only one part of results in the very end of the multiple population analysis section combining two groups. I donít know why MI and derivatives are different across two groups, how MI or derivatives and LM test are comparable, and how to interpret different results in MI and derivatives across two groups.

4) I like to see what constraints on factor loadings are different across two groups. How do I test group differences in factor loadings?
 bmuthen posted on Saturday, February 11, 2006 - 7:07 am
1. Mplus has modification indices also for categorical outcomes.

2. you don't have to use tech2 anymore

3. don't worrry about tech2. Also, Mplus version 4 has Wald testing.

4. it is hard to separately test loading and threshold invariance because with categorial outcomes, those 2 parameters interact to produce the item probability curve as a function of the factor. I would not try to separate them, but instead check if for a given item its thresholds *and* loadings are invariance or not. This is done by DIFFTEST and the parameter settings described in the User's Guide.
 Min Jung Kim posted on Monday, February 13, 2006 - 6:31 pm
Thank you very much for your answers. I would like to ask you following up questions.
(1) I am still vague why I have different values in modification indices (MI) for the same factor loadings across two groups. For example, my substance use factor has 4 categorical indicators (cigarettes, alcohol, marijuana, and others) that have the same number of thresholds across two groups. Looking at MIs, in the first group, MIs of cigarettes and alcohol are greater than 4.0, while those of alcohol and marijuana are greater than 4.0 in the second group. Also the values of the MI for the alcohol indicators are different between two groups. I constrained the 4 pairs of the factor loadings to be equal across two groups (i.e., cigar1=cigar2, alcohol2=alcohol2, etc, so I have 4 constraints across two groups) and what I wanted to see in the MIs is how chi-square decreases if those constraints are released. I don°Įt understand why I have two separate results of MIs for two groups and they are different across two groups rather than do I have one kind of MIs on the 4 loadings indicating whether they are invariant across two groups (i.e., only 4 MIs for the substance use factor).

(2) What I would like to do is to list factor loadings across two groups in a table and to show what factor loadings are significantly different between two groups with * marks. To do that, do I need to run DIFFTEST as many times as numbers of indicators I have in my model?

I appreciate you answers in advance.
 Linda K. Muthen posted on Tuesday, February 14, 2006 - 8:01 am
I think you are saying that when you hold a factor loading equal across two groups, you get different modification indices in each group. They should be approximately the same I believe. Please send your input, output, data, and license number to

Yes, you would have to run DIFFTEST several times.
 Reetu Kumra posted on Tuesday, February 20, 2007 - 8:38 am
What does it mean when there is a modification index of 999?
 Thuy Nguyen posted on Wednesday, February 21, 2007 - 11:01 am
999 indicates the modification index was not computable.
 Elayne Livote posted on Wednesday, May 12, 2010 - 11:32 am
I am running a 1-factor CFA (version 6) with 30 binary indicator variables and I am also getting MI = 999 and what's more confusing is that it's the latent variable (GEN) on 4 of the indicator variables, i.e.
GEN on SAD 999

Does it mean anything or should I ignore it?

Thank you very much.
 Linda K. Muthen posted on Wednesday, May 12, 2010 - 11:37 am
Please send the full output and your license number to
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