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I want to evaluate if I there are structural group differences (two groups) in my path analysis model. I compared the models with and without allowing group differences (lavaan:: sem(..., group =)):

enter image description here

Does the worse fit mean, that there are no group differences or that in one group the structure of the model is wrong?

Here is the summary ouptut of the model with group differences: enter image description here

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When you add constraints, you remove parameters from a model, and increase degrees of freedom. This will always increase chi-square - the question is whether the increase is greater than would be expected by chance.

In your group_diff model, you've removed four parameters, and you therefore have four additional degrees of freedom.

The chi-square associated with this increase is (almost) 40, and is therefore highly significant, indicating that the parameters you have constrained across groups are not equal.

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  • $\begingroup$ Thx for your answer. I did not yet constrain parameters: For the no_group_diff model, lavaan calculates one model using the data of both groups; In the group_diff model lavaan calculates two models (with different parameters) one for each group. $\endgroup$ – Rizzi Sep 25 '18 at 9:43
  • $\begingroup$ The parameters are constrained to be equal across groups. That's the constraint. $\endgroup$ – Jeremy Miles Sep 25 '18 at 21:31

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