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Given $F$ is a latent construct (cause), and $Y_1$, $Y_2$, and $Y_3$ are the manifest (indicator) variables (effects) which are measured. Then, there are two groups of people (A and B). According to the measurement result, people in Group A averagely have higher scores in all effects: Y1, Y2, and Y3. Namely:

  • Group A's average score of Y1 is higher than Group B's average score of Y1
  • Group A's average score of Y2 is higher than Group B's average score of Y2
  • Group A's average score of Y3 is higher than Group B's average score of Y3.

Then, how can I conclude or interpret the result:

  1. All people in Group A have higher X than do all people in Group B.
  2. The people in Group A averagely have higher X than do the people in Group B.
  3. The people in Group A may averagely have higher X than may the people in Group B.
  4. The people in Group A are more likely to have higher X than are the people in Group B.

Which interpretation(s) are correct or none of the above? I guess (3) and (4) are correct, but not sure. (2) also looks not bad.

Could anyone please teach me how to interpret the result of reflective models?

Thank you!!

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In your sample, only 2) is a valid interpretation. In your population, only 3) is a valid interpretation. The interpretation is no different than that of a t-test with observed variables. But this should be based on a measurement model and an appropriate statistical technique; making inferences just based on the distributions of the indicators is not enough. For example, do the items measure the construct in the same way in groups A and B? If not, you can't make inferences just by looking at the items. You need a latent variable model and to test measurement invariance before you can make any conclusion. It's not clear that you have done this.

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