Across-time measurement invariance PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Tony Stoneriver posted on Wednesday, July 02, 2008 - 12:53 am
I am running a SEM-Modell with 5 categorical items at each timepoint, 2 timepoints of measurement and 3 latent variables (2 states and 1 trait).
I would like to account for measurement invariance. Therefore I set equal factor loadings between the timepoints (congeneric model, first loading fixed to 1) and the intercepts are per default fixed to zero (thus, equal).
Because I am regarding only the covariance structur (no means), it is not possible in MPlus to set the thresholds equal.
Is the threshold equality neccessary to have measurement invariance?
Or is the metric invariance (equal factor loadings) and scalar invariance (equal intercepts) sufficient?
Thanks a lot
 Linda K. Muthen posted on Wednesday, July 02, 2008 - 2:28 pm
With categorical outcomes, I would consider both thresholds and factor loadings while testing for measurement invariance. See Chapter 13 after the multiple group discussion for the models to be considered when testing for measurement invariance. Examples 5.16 and 5.17 show partial measurement invariance for categorical outcomes. These examples are for multiple groups but the same principles apply across time.
 Tony Stoneriver posted on Thursday, July 03, 2008 - 1:53 am
Many thanks for your quick reply.

I read Chapter 13 and tried to specify the equality of both, factor loadings and thresholds for 4-point-Likert items with this input:

MODEL: ETA1 BY var11@1
ETA2 BY var12@1

XI BY ETA1@1 ETA2@1;

[var11$1 var12$1](4);
[var11$2 var12$2](5);
[var11$3 var12$3](6);
... (the same for the other variables).

But I am not sure, if itīs the right way to do that?!

Or would you recommend theta parameterization? (I tried it, but I was not able to produce the right input file...).
 Tony Stoneriver posted on Thursday, July 03, 2008 - 4:00 am
I forgot about to ask, if it is really important to have equality of thresholds when I solely analyze the covariance structure of the variables (without the meanstructure)?

To my knowledge the thresholds are (more) important when regarding the mean structure of the variables?!

Thanks a lot, Tony
 Linda K. Muthen posted on Thursday, July 03, 2008 - 4:25 pm
I do not believe that measurement invariance with categorical outcomes should exclude the thresholds. The s-shaped item characteristic curves that are the essence of categorical data modeling depend on both the threshold and the factor loading. Measurement invariance for categorical outcomes should consider both of these in tandem.

Your input looks correct. But check TECH1 and the results to be sure that the proper equalities are there.
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