Hi!

You want to check for measurement invariance across groups?

I would suggest the following:

factor_1 BY x1*(1)

x2*(2)

x3*(3);

etc....

factor_1@1;

Same with factor two.

However, I am not sure if this approach is working for binary coded indicators.

Hi!

You want to check for measurement invariance across groups?

I would suggest the following:

factor_1 BY x1*(1)

x2*(2)

x3*(3);

etc....

factor_1@1;

Same with factor two.

However, I am not sure if this approach is working for binary coded indicators.

Hi Jamil!

You can assess different levels of invariance with a straightforward procedure of comparing measurement models in a fixed order, from the least to the most restrictive model. However, in contrast to continuous variables, the invariance testing for categorical data requires varying factor loadings and thresholds in tandem. Therefore, metric invariance testing is dropped. Why and how to do this, is described in one of my papers (pp. 859-861) that you can download via RG: https://www.researchgate.net/publication/225091995_Equivalence_of_reading_and_listening_comprehension_across_test_media

Hope, this may help you, kind regards,

Ulrich

Article Equivalence of Reading and Listening Comprehension Across Test Media

Hi Jamil,

The commands que Michael gave are very usefull, indeed.

I would add that, as you want to teste gender invariance, you need to split the dataset in two (one for men and other for women). As long as you have two dataset, you need to pereform the same comands for the same factors in both datasets and to test the difference using the DIFFTEST comand combined with SAVEDATA comand.

Please, see the manual (chapter 13), for more details. Good luck.

Oh, don't forget (I guess you know) to tell the your variables are categorical, then Mplus will run tetrachoric correlations automatically.

Dear all thanks for the guidance:

Dear Ulrich, Michael, and Roger, thanks for all of your help.

With the help of article by Ulrich and code suggested by Michael, I successfully conducted invariance testing of item loadings and the DIFFTEST.

The DIFFTEST suggested a non-significant chi sqr value (happy with that).

Just for my satisfaction plz read the following syntax and confirm if I am using the right approach.

In first step I used following syntax

Categorical are cbq1-cbq44;

GROUPING IS gen (1=male 2=females);

ANALYSIS:

ESTIMATOR IS WLSMV;

TYPE = MEANSTRUCTURE;

PARAMETERIZATION=THETA;

MODEL:

AOP by cbq17-cbq44;

AOD by cbq1-cbq16;

OUTPUT: SAMPSTAT MODINDICES(10.00) STAND RESIDUAL TECH2;

SAVEDATA: DIFFTEST IS deriv.dat;

In second step I used following syntax

Categorical are cbq1-cbq44;

GROUPING IS gen (1=male 2=females);

ANALYSIS:

ESTIMATOR IS WLSMV;

TYPE = MEANSTRUCTURE;

PARAMETERIZATION=THETA;

DIFFTEST IS deriv.dat;

MODEL:

AOP by cbq17-cbq44 * (17-44);

AOD by cbq1-cbq16 * (1-16);

AOP@1;

AOD@2;

OUTPUT: SAMPSTAT MODINDICES(10.00) STAND RESIDUAL TECH2;

Looking for further guidance from you guise.

Personally i prefer specifying the Model Syntax for earch group seperately to have a better overview of which model parameters i did and did not constrain to be equal across groups.

For Example:

MODEL:

AOP by cbq17-cbq44 * (17-44);

MODEL female: *differences from the default model for the female group

AOP by cbq17-cbq44 * (17-44); (these would be equal factor loadings)

MODEL female:

AOP by cbq17-cbq44*; (these would be freely estimated factor loadings)

However your syntax should work as well. I would use the Tech 1 Output and have a look at the degrees of freedom to check if the parameters you meant to constrain were really constrained. If a parameter was constrained to be equal across 2 groups it should have the same parameter number in the Tech 1 Output for both groups. In general the Tech 1 Output is very useful for checking whether a model is correctly specified (misspecification can occur easily in Mplus because there are so many defaults).

PS: Why are you fixing the variacne of AOD to 2? I would fix it to 1 for identification purposes (just as AOP) or just exclude the command (it will be fixed for the standardized output by default).

Dear Malte, thanks for the guide line. I used separate model for group 2, it give me similar results. But that was good to have two groups cause model has to be different in both groups to check for strong invariance as suggested in the article by Ulrich. I now added following model

MODEL:

AOP by cbq17-cbq44 * (17-44);

AOD by cbq1-cbq16 * (1-16);

Model Females:

AOP by cbq17-cbq44 * (17-44);

AOD by cbq1-cbq16 * (1-16);

cbq1-cbq44@1;

AOP@1;

AOD@1;

[AOP] (0);

[AOD] (0);

The last two commands are to fix factor means of group 2 into zero.

Dear Ulrich, plz confirm if this model is fine to test strong invariance. I will be very thankful for any further guidance.

Regards, Jamil

Dear Jamil,

first, you have to decide on the parametrization (Theta vs. Delta, see the above mentioned paper or Mplus user's Guide for further details). Let's say you go with Theta parametrization. Then you need to have the following constraints for strong MI with categorical data:

a) factor loadings have to be equal across groups,

b) the same for thresholds,

c) residual variances have to be fixed at one in one group and freed in the other(s) and

d) factor means have to be constrained to zero in one goup and free in other(s).

a) looks OK, b) is missing, something like [cbq44$1] ( 50) for each item and each threshold, c) still missing, something like cbq44@1; and d) factor means are constrained with [AOP@0] ;

Good luck,

Ulrich

How are equality constraints placed on thresholds when testing for scalar invariance over two time-points?

Item1Threshold1Time1 (1)

Item1Threshold2Time1 (2)

Item1Threshold3Time1 (3)

Item2Threshold1Time1 (1)

Item2Threshold2Time1 (2)

Item2Threshold3Time2 (3)

Item1Threshold1Time2 (1)

Item1Threshold2Time2 (2)

Item1Threshold3Time2 (3)

Item2Threshold1Time2 (1)

Item2Threshold2Time2 (2)

Item2Threshold3Time2 (3)

OR

Item1Threshold1Time1 (1)

Item1Threshold2Time1 (1)

Item1Threshold3Time1 (1)

Item2Threshold1Time1 (2)

Item2Threshold2Time1 (2)

Item2Threshold3Time1 (2)

Item1Threshold1Time2 (1)

Item1Threshold2Time2 (1)

Item1Threshold3Time2 (1)

Item2Threshold1Time2 (2)

Item2Threshold2Time2 (2)

Item2Threshold3Time2 (2)

And if a scale has sub-scales, are the equality constraints held equal depending on which factor it loads to?