When testing factorial invariance between groups, in multigroup analysis, we first test the (1) unconstrained model. Then we test the second model (2) constraining factor loadings. Third, (3) we constrain items intercepts. Forth we (4) constrain the latent variables variances and the co-variances. Finally, the (5) items' error's variance.
When testing the longitudinal factorial invariance of a measure, the first step is to (1) run the unconstrained model. Then, we test the (2) metric invariance by constraining factor loadings. Finally, (3) we constrain item thresholds.
In Strutural Equation modeling (SEM) using AMOS, what parameters represent the item thresholds?
What is an item threshold?
Dear Alexandra,
I'm not familar with AMOS, but I got the impression that the strategies you decribe for testing invariance are different, because they refer to different estimation methods.
If you treat your observed indicators as continous and use ML or MLR for paramteter estimation, you fix the intercepts for testing strong invariance.
But if you treat your indicators as ordered categorical indicators and use WLSMV estimator, you fix the thresholds for testing strong invariance.
Using WLSMV as implemented in Mplus you assume a latent continous variable behind the obvsered ordered categorical variable. Brown (2015) decribes it nicely using a binary indicator (0=not depressed, 1=depressed). The threshold marks a certain point on the latent variable you assume behind this observed binary indicator. If you have a score on this latent that is smaller than the threshold, you take 0, if the value is bigger you take 1. If there are more categories you need additional thresholds (always one less than the number of categoriesm check how polychoric/tetrachoric correlations are determined to gain a better understanding of what thresholds are).
Therefore, the threshold is something you need to link the observed indicator to the assumed continous, normal-distributed behind that variable.
So if you use ML or MLR, you fix the intercepts when testing invariance, but fix the thresholds when using WLSMV (or comparable estimators).
Hope that helps.
Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford Publications.
Hello Alexandra,
If you have access to Mplus it is easy to run measurement in one go. In version 7.11 and any more recent you just prepare the output and then you can compare configural model (free model) with metric model (standardized factor loadings are restricted) and scalar model (both factor loadings and intercepts - item mean scores) are restricted.
Best wishes
Dear Alexandra,
You can refer to this article of mine wherein i have used AMOS (for multi-group analysis) with regard to gender as a moderating variable. Also, in the article, details related to threshold values and the citations have been mentioned. Hope it helps
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