Measurement invariance PreviousNext
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 Marie Eisenkolb posted on Friday, February 03, 2012 - 1:07 am
I established a structural equation model for testing measurement invariance over two conditions in four groups and I tested by using the command grouping.
That leads me to bad model fits, but if I leave out this command, it fits better. Can you help me to explain these results?
Another question: I established these nested models by starting with configural invariance. To make mplus to test the configural model, I have to restrict the first factor loading to 1 and so I have to fix the first factor loadings in the weak, strong and strict invariance models, too,right? By keeping this restrictions, I achieve bad model fits.
Is there any chance to avoid the restiction of the first factor loadings? Here are my commands:
usevar = P_NEO_1 P_NEO_6 P_NEO_11 P_NEO_16 P_NEO_21 P_NEO_26
P_NEO_31 P_NEO_36 P_NEO_41 P_NEO_46 P_NEO_51 P_NEO_56 C_NEO_1 C_NEO_6 C_NEO_11 C_NEO_16 C_NEO_21 C_NEO_26
C_NEO_31 C_NEO_36 C_NEO_41 C_NEO_46 C_NEO_51 C_NEO_56 Reihe;
missing = all(99);
GROUPING IS Reihe (0=g1 1=g2 2=g3 3=g4);
MODEL: N_P BY P_NEO_1 P_NEO_6 P_NEO_11 P_NEO_16 P_NEO_21 P_NEO_26 P_NEO_31 P_NEO_36 P_NEO_41 P_NEO_46 P_NEO_51 P_NEO_56;
N_C BY C_NEO_1 C_NEO_6 C_NEO_11 C_NEO_16 C_NEO_21 C_NEO_26 C_NEO_31 C_NEO_36 C_NEO_41 C_NEO_46 C_NEO_51 C_NEO_56;
 Linda K. Muthen posted on Friday, February 03, 2012 - 8:57 am
When you use the GROUPING option, intercepts and factor loadings are held equal as the default. When you don't, the full sample is used and there are no equalities imposed.

You can set the metric by fixing the factor variance to one instead of the first factor loading to one:

f BY y1* y2 y3;

See the Topic 1 course handout on the website under the topic Multiple Group Analysis. The inputs for measurement invariance are given there.
 Marie Eisenkolb posted on Friday, February 03, 2012 - 1:55 pm
Thank you very much for your answer. That helped me a lot.

So I have to test my groups against each other. Can you tell me, how to use only a part of the data within one variable? So that I can test within one variable the group of person 1 till 73 against the group of person 143 till 202?

I'd be happe for any advise.
 Linda K. Muthen posted on Friday, February 03, 2012 - 2:07 pm
Use the USEVARIABLES option to use part of the data.
 Marie Eisenkolb posted on Saturday, February 04, 2012 - 1:23 am
I did use the USEVARIABLES option, but all of my groups are in one variable and I need to test the model fit for example within only one group.
If I consider four variables (one for each group) instead of one, mplus says "FATAL ERROR", because the data matrix is too big (more variables than 350 variables).
 Linda K. Muthen posted on Saturday, February 04, 2012 - 6:59 am
Please send the outputs and your license number to
 Marie Eisenkolb posted on Monday, February 13, 2012 - 11:12 am
For the FATAL ERROR I made a programming fault, but I found and corrected it. Thank you very much for your offering.

Now, to test the sequence effects, I need to override the default, that fixes the factor loadings and intercepts to be equal over the groups. How can I test a configural or weak Modell of measurement invariance?

The command * does only work for different conditions and having different variables loading on different factors, doesn't it?

Here are my commands:
GROUPING IS Reihe (1=t1 2=t2);
IF (Reihe==0 OR Reihe==1) THEN Reihe=1;
IF (Reihe==2 OR Reihe==3) THEN Reihe=2;
N_P BY P_NEO_1* (a)
P_NEO_6 (b)
P_NEO_11 (c)
P_NEO_16 (d)
P_NEO_21 (e)
P_NEO_26 (f)
P_NEO_31 (g)
P_NEO_36 (h)
P_NEO_41 (i)
P_NEO_46 (j)
P_NEO_51 (k)
 Linda K. Muthen posted on Tuesday, February 14, 2012 - 5:26 pm
See the Topic 1 course handout under multiple group analysis.
 Geneviève Taylor posted on Wednesday, March 28, 2012 - 1:04 pm
Dear Mplus team,

I am trying to test gender invariance in a path analysis model with continuous variables. I have looked at your Topics 1 handout but I am confused as to what I should specifiy exactly in my input file.
The only thing I changed to test whether the models are different for each gender in the GROUPING command. Here is the input I have so far:
USEVAR ARE Sexe azagg azpop bzpop czpop dzpop aengcpt7 bengcpt7 cengcpt7 dengcpt7
eengcpt7 azaggami bzaggami czaggami dzaggami;

GROUPING IS Sexe (0 = filles 1 = garçons);
dzaggami ON cengcpt7 czaggami czpop;
czaggami ON bengcpt7 bzaggami bzpop;
bzaggami ON aengcpt7 azaggami azpop;
dzpop ON czpop czaggami cengcpt7;
czpop ON bzpop bzaggami bengcpt7;
bzpop ON azpop azaggami aengcpt7;
eengcpt7 ON dengcpt7 dzaggami dzpop;
dengcpt7 ON cengcpt7 czaggami czpop;
cengcpt7 ON bengcpt7 bzaggami bzpop;
bengcpt7 ON aengcpt7 azaggami azpop;
azpop ON azagg;
azaggami ON azagg;
aengcpt7 ON azagg;

Is there anything else I should be adding to test this correctly?
Many thanks in advance for your help!
Genevieve Taylor
 Linda K. Muthen posted on Wednesday, March 28, 2012 - 1:32 pm
The GROUPING option should be used in all but the first step of testing for measurement invariance. The first step is to run the model separately for each group. The correct inputs are shown in the Topic 1 course handout under Multiple Group Analysis. Please refer to these inputs.
 Geneviève Taylor posted on Thursday, March 29, 2012 - 8:30 am
Hi Dr Muthen,

Thanks for your response. I understand the handout now. I will follow these steps for my analysis.
Many thanks,
 Yoonjeong Kang posted on Wednesday, August 28, 2013 - 2:31 pm
Dear Mplus team,

I am trying to understand a new approach to measurement invariance (approximate measurement invariance)implemented in Version of Mplus 7.11.

Q1. I ran a two-group CFA model for testing measurement invariance based on example 5.33. Under the DIFFERENCE OUT, I got average of estimate, standard deviation, deviations from the mean for each parameter and each group. I specified difference between two options like, N(0,0.01).

For example, I got
Average: 1.422
SD: 0.031
Deviation from the mean: -0.03 (Lamda1), 0.03(Lamda2)
--> How do I know whether the deviations from the mean in Lamda1 and 2 are significant or not?

Q2. Based on Muthen (2013) paper, it says that
" With only two groups/timepoints, the difference relative to the average can be augmented by the difference across the two groups/timepoints which can be expressed in MODEL CONSTRAINT.
If I want to test approximate measurement invariance between two group, what kinds of model constraint I need?

 Bengt O. Muthen posted on Wednesday, August 28, 2013 - 6:24 pm
q1. There is an asterisk if the value is significant.

q2. Use parameter labels a and b in the MODEL command, where those parameters are the 2 parameters in question. Then use Model Constraint to do

diff = a-b;
 Yoonjeong Kang posted on Thursday, August 29, 2013 - 9:26 am
Dear Dr. Muthen,

Thanks a lot for your answer.

I have one more question. Can I test approximate measurement invariance in multilevel context? For example, can I conduct approximate measurement invariance test for between-level factor loadings? I have tried to do it by extending ex5.33 code but I couldn't. Please let me know.

Thanks a lot in advance.
 Bengt O. Muthen posted on Friday, August 30, 2013 - 2:41 pm
It is in principle possible but is quite complex given that the DO-DIFF options haven't been tailored to multilevel applications. I would not recommend trying.
 Elina Dale posted on Friday, February 07, 2014 - 12:15 pm
Dear Dr. Muthen,

I would like to test measurement invariance where my loadings are constant across groups, but thresholds are allowed to vary.

As per Ex. 5.16, since I am allowing thresholds to vary across groups, I fixed the scale factors to 1. I don't understand what is wrong with my input:

GROUPING IS g (1 = male 2 = female) ;
CLUSTER = clust;
MISSING = ALL (-9999) ;
Analysis: TYPE = COMPLEX ;
f1 BY i1 i2 i3 ;
f2 BY i4 i5 i6;
f3 BY i7 i8 i9 ;
Model female:
[i1$1 i2$1 i3$1 i4$1 i5$1 i6$1 i7$1 i8$1 i9$1 i1$2 i2$2 i3$2 i4$2 i5$2 i6$2 i7$2 i8$2 i9$2 i1$3 i2$3 i3$3 i4$3 i5$3 i6$3 i7$3 i8$3 i9$3];
{i1@1 i2@1 i3@1 i4@1 i5@1 i6@1 i7@1 i8@1 i9@1};

I keep getting an error message:

I have checked this parameter and it is Alpha for F1, which is an intercept I guess.

Thank you!!!
 Linda K. Muthen posted on Friday, February 07, 2014 - 12:25 pm
If you free the thresholds, you must fix the factor variances to zero.
 deana desa posted on Tuesday, March 18, 2014 - 6:56 am
I would like to know if factor scores computed from the alignment method and the convenient features (i.e., configural, metric or scalar) are (directly) comparable or related?

How much these scores are expected to be correlated?

Is there any literature out there that I can refer to for the scores computed from these different techniques?
 Linda K. Muthen posted on Tuesday, March 18, 2014 - 1:35 pm
No, the factor scores from alignment are not the same as those from configural, metric, or scalar. They start from a configural model and maximize measurement invariance. The correlation between the different factor scores would depend on the amount of measurement invariance.

I doubt there is any literature on this yet.
 Bilge Sanli posted on Friday, August 08, 2014 - 11:25 am
Drs. Muthen and Muthen,

Using the National Identity Module of the ISSP, I am adopting a two-level EFA approach in my exploratory research on different dimensions of nationhood, and their contextual and individual predictors. My cluster variable is countries, and my variables
are all at the ordinal level of measurement. In a subsequent two-level SEM analysis, (upon your suggestion in an earlier inquiry) I will use the factor scores I obtained from the initial two-level EFA analysis as dependent variables and regress them onto independent variables at both individual and contextual levels.
My question is the following: since I am engaging in a cross-national analysis, should I be establishing measurement invariance first? If I am to do this, is multiple group CFA the only option? In this scenario, how shall one take into account the multi-levelness of the data? Once I establish measurement invariance, shall I proceed with the two-level SEM?
Apologies for the deluge of questions. I'd greatly appreciate your help. Thank you very much in advance.
 Bengt O. Muthen posted on Friday, August 08, 2014 - 3:54 pm
These are good questions. I think you will be interested in reading the paper on our website (see Recent papers):

Muthén, B. & Asparouhov, T. (2013). New methods for the study of measurement invariance with many groups. Mplus scripts are available here.

This paper compares the fixed-effect multiple-group approach with the random-effect multilevel approach. It turns out that 2-level FA can be seen as a random intercept model, that is, measurement non-invariance that still makes factor comparisons possible.
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