Modification Indices for Categorical ...
Message/Author
 Linda K. Muthen posted on Thursday, November 18, 1999 - 2:50 pm
TECH2 in OUTPUT provides parameter derivatives. The derivatives for constrained parameters (fixed or equal) can be used as modification indices although they have not been scaled to a chi-square metric. The relative size of the derivatives rather than their absolute value should be considered. When all variables are categorical, the derivatives can be examined to determine which parameters are most likely to improve model fit.
 Michael Bohlig posted on Saturday, July 07, 2001 - 12:43 am
Hello. I would like to verify that I am using the derivatives correctly to determine which parameters may help improve model fit. I have been looking at the magnitude of the absolute value of the derivatives as an indicator of potential parameters to free. Is this correct? If the sign is important, how would I interpret negative versus positive derivatives?
Thanks for your assistance.
 Linda K. Muthen posted on Sunday, July 08, 2001 - 9:23 am
The sign of the derivatives is the opposite of the sign that the parameter will take when it is freed if it was fixed at zero. Derivatives are not scale free so they cannot be compared across variables of different scales.
 Anonymous posted on Wednesday, August 27, 2003 - 2:38 pm
I have four questions about the use of TECH2 in Mplus.

1. Is it the case that TECH2 derivatives can only be used when "forward fitting" a model -- in other words, in a strategy where one starts with a restricted model and then successively frees parameters to achieve a better fit ?

2. How should the TECH2 derivatives for parameters already included in the model be interpreted ? Do large parameters suggest free terms that one might want to consider restricting to zero ?

3. What do you suggest should be considered a large TECH2 derivative in Mplus ?

4. Mplus often gives derivatives that don't seem to have any readily discernable meaning -- such as the derivative of the coefficient between the indicator of a CFA indicator with respect to an outcome variable with respect to a lambda. Does this make sense ?
 Linda K. Muthen posted on Wednesday, August 27, 2003 - 7:10 pm
1. Yes.
2. If the parameters are free, the derivatives should be zero. For fixed parameters, the absolute value of the derivative are not meaningful.
3. This can only be determined by freeing a parameter and seeing how large the chi-square decrease is.
4. Derivatives are given for all fixed parameters. It is up to the researcher to decide which parameters are meaninigful.
 Anonymous posted on Tuesday, November 30, 2004 - 2:58 pm
Hello,
I'm doing a two group CFA. In my nested model, I have both factor laodings and respective thresholds constrained to be equal across the two groups. I would like to use derivatives to see which factor loading/threshold should be freed to improve the chi square diff test. Could you please let me know what derivatives (Theta, Tau, etc) would give me the proper information? In freeng parameters, should I first look at factor loadings to be freed or the threshold?
 Linda K. Muthen posted on Tuesday, November 30, 2004 - 5:28 pm
In Version 3, modification indices are available for models with categorical outcomes. You don't need to look at derivatives. If you wanted to look at derivatives, factor loadings are found in lambda and thresholds in tau.
 Laura A. Szalacha posted on Friday, March 03, 2006 - 8:19 am
Sorry if this is too elementary - but, when I have my intervention parameter fixed it is positive and the model fits, when I free the parameter, it is negative. The rest of the model remains much the same.
Any help would be appreciated.
Thank you,
 Linda K. Muthen posted on Friday, March 03, 2006 - 9:34 am
It is unclear what you mean when you say that you have your intervention parameter fixed and it is positive. Have you fixed it at a positive value? The parameter estimates says that you have a negative intervention effect.
 Lois Downey posted on Friday, January 05, 2007 - 11:53 am
I notice that for CFAs with categorical outcomes, modification indices do not consider the addition of correlated residuals until one has actually specified at least one correlated residual in the model. Is there a way to see the Lagrange Multiplier test results associated with adding "WITH" relationships when the current model includes none?
 Linda K. Muthen posted on Sunday, January 07, 2007 - 9:01 am
No, you need to include them set at zero to open that matrix. For example,

u1 WITH u2@0;
 Kathy posted on Wednesday, April 16, 2008 - 8:18 am
I have a two group (categorical data) mgfa and I have a MI between two questionnaire items for one group which is : sd3 with sd19 = 157.13. Is this MI indicating that the error terms are correlated between these two questionnaire items? Is it appropriate to allow this correlation for one group and not the other? How would I do this in Mplus?
Would I:
model zz:
sd3 with sd19@0
 Linda K. Muthen posted on Wednesday, April 16, 2008 - 9:17 am
The modification index says that if you free the residual covariance between the two items in that group, chi-square will drop approximately 157.13. I wonder why this residual covariance is important for model fit in only one group. A residual covariance is a measurement parameter and this could be an indication of measurement non-invariance. It could represent a minor factor. I wonder if you did an EFA in each group separately as a first step in your analysis to determine if a model with the same number of factors fits best in each group.

To free the parameter you would specify:

model zz:
sd3 with sd19;

The @0 specification means fixed at zero.
 Li Lin posted on Wednesday, April 21, 2010 - 11:13 am
When I ran "model: f1 by y1 - y10; f2 by y11 - y18" where all y's were categorical with 5 categories, I got modification index of "F1 ON F1 / F1 BY F1 999.000". What does this mean? Thanks.
 Linda K. Muthen posted on Wednesday, April 21, 2010 - 1:22 pm
The value 999 indicates the value could not be computed. You should ignore this.
 Alyssa Thomas posted on Wednesday, July 30, 2014 - 7:27 pm
Hi there,
I have a question on obtaining modificiation indices for a categorical outcome. I am using WLSMV as the estimator and so am unable to select the 'modification indices with minimum..." option.
Should I use the TECH2 option to obtain this?
My independent variables are all Likert Scale and only my (one) outcome variable is categorical.
My supervisor has never worked with categorical outcomes so is unable to help.
Thank you in advance for your help
 Linda K. Muthen posted on Thursday, July 31, 2014 - 5:37 am
You should be able to do this unless you are using an older version that does not have this option. Try asking only for MODINDICES.
 Maria posted on Monday, December 07, 2015 - 6:48 pm
Hello Dr. Muthen, I conducted multi-group analyses in my two groups, with WLMVS estimator for categorical variables with the TECH2 option, but I do not get chi-square information to compare my models in the output. I also tried MODINDICES but no still no model fit information is provided. I am also not sure how to interpret derivatives on Lambda, Psi, Nu in the output between models.
 Linda K. Muthen posted on Tuesday, December 08, 2015 - 9:48 am
It sounds like the model did not converge. Please send the output and your license number to support@statmodel.com.
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