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I established scalar measurement invariance for a two-group CFA. The output from my final model showed that the latent mean in group 1 is lower than the latent mean in group 2. Can this difference in latent means also be explained by different response styles (e.g., disacquiescence response style)? Why (not)?

I know this is similar to this question, but somehow fail to connect the dots: In measurement invariance testing, how can one differentiate between differences in response styles and differences in latent means?

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If all of the items are coded in the same direction, then you cannot distinguish between a positive (yea-saying) or negative (nay-saying) response style and a difference in means.

If the responses are heavily skewed in one direction you cannot distinguish between a more extreme response style and latent mean differences.

This is essentially an identification problem - you can add a latent response style variable, but that model will not be identified with the data that you have. When you have items coded in opposite directions you can add a response style factor (a class of multiple-trait multiple methods model; also called a method factor) and the response style latent variable will be identified.

You can never know (for example) women have fewer symptoms than men, or women report fewer symptoms than men - my spouse says I complain more than they do; I say I suffer more than they do. There is no way to obtain a unique (identified) solution to demonstrate who is right.

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  • $\begingroup$ Thank you! As a follow-up: (1) I often read that scalar invariance is a prerequisite for comparing latent means. Does your answer imply that scalar invariance is a necessary yet insufficient condition for meaningful group comparisons of latent means, as the groups could differ also in terms of another factor (let's say, the latent response style factor)? (2) Although I like the example in the final paragraph, I'm a bit confused by the words 'you can never know'. Does this also entail the MTMM scenario where you include the extra factor? I assume there you would? $\endgroup$
    – user321797
    Commented Dec 17, 2023 at 19:57
  • $\begingroup$ You compare the latent means, and they are different. Why? Is that because of a real difference, or because of a response bias? You don't know. Correlation isn't causation. $\endgroup$
    – Jeremy Miles
    Commented Dec 17, 2023 at 20:53
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    $\begingroup$ I largely agree with @JeremyMiles. However, there are ways to isolate "latent" response styles in surveys by using mixture distribution (latent class) models. See: $\endgroup$
    – Christian Geiser
    Commented Dec 18, 2023 at 12:03
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    $\begingroup$ Eid, M., & Rauber, M. (2000). Detecting measurement invariance in organizational surveys. European Journal of Psychological Assessment, 16(1), 20–30. doi.org/10.1027/1015-5759.16.1.20 $\endgroup$
    – Christian Geiser
    Commented Dec 18, 2023 at 12:03
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    $\begingroup$ if you expect the same response style to manifest across many factors, then you could potentially partial that out with a factor for all such items. Try searching for papers about modeling acquiescence bias with CFA. $\endgroup$
    – Terrence
    Commented Dec 18, 2023 at 14:33

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