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Hi! I am running a model and want to see if the paths are moderated by sex (boys vs. girls). I get nonsignificant chi square difference, suggesting that the paths are not moderated by sex. When I look at the paths coefficients in the unconstrained model, one of the paths in my mediation model going from the mediator to the outcome is significant for girls but not for boys. I can make theoretical sense of it. However, what I don't understand is why the chi square shows the moderation but when I look at the individual paths for boys and girls the path for girls is significant and for boys is not. Since there is no moderation based on the chi square diff. test, do I report this path that is significant for girls but not boys? What would be the name of this effect (obviously not interaction effect). Will simple main effect for that particular group (girls) be accurate? Thanks in advance. 


The test in each group of a coefficient is a test that the parameter is significantly different from zero. A difference test is a test of whether or not the two parameters are equal to each other. You can get a ztest to test if the parameters are equal to each other using MODEL CONSTRAINT. It should agree with the chisquare difference test. MODEL CONSTRAINT: NEW (diff); diff = p1  p2; whre p1 and p2 are labels in the MODEL command for the parameters to be tested. 


Hi Linda, I have a similar situation  the Chi square (difftest) shows a significant difference between two groups on one moderator w. When I look at the path size (and p) for each group however, the two paths have a p>.05. Additionally, when exploring a second moderator I obtain a significant Chi square but when I explore the paths for the two groups, I find that the path is significant for 1 group but not the other. Is there any point reporting these results? especially, if the path is not significant for the groups of interest? Or should I simply report and focus on the estimate of the path for each group and ignore the p value? Thanks! 


The tests you are comparing don't test the same thing. In one case, you test if the coefficients are equal to each other. In the other case, you test if they are equal to zero. 


Thanks Linda  I am now working with imputed data so I was thinking about using the 'diff' approach as difftest does not work on imputed data MODEL CONSTRAINT: NEW (diff); diff = p1  p2; Would that be OK? also can it be used when you have more than 3 groups to compare? Thanks 


This tests if p1 and p2 are equal. It can be used with more than two groups. 


Having 3 groups, would I need to incorporate 3 difference scores for the combinations? MODEL CONSTRAINT: NEW (diff1 diff2 diff3); diff1 = p1  p2; diff2 = p1  p3; diff3 = p2  p3; or can it be done in a more efficient way? 


That looks okay. 


can I build an overall test in the style of ANOVA analyses: MODEL CONSTRAINT: NEW (overall diff1 diff2 diff3 ); overall = (p1^2+p2^2+p3^2)(p1+p2+p3)^2; diff1 = p1  p2; diff2 = p1  p3; diff3 = p2  p3; 


Do this in MODEL TEST where you will get a Wald test for the set of tests: MODEL TEST; 0 = p1  p2; 0 = p1  p3 


Thanks Linda; Can I check with you that the command (implicitly) includes the third comparison (i.e, 0 = p2p3)? If this is the case, is this the equivalent to the difftest when comparing the free model with the model where all three groups are set to be equal? Is there any reference I should be citing/reading? Thanks again, Francesca 


one more thing. I found in previous threads that before multiple group testing, one needs to test for measurement invariance across groups when using latent variables. Is that a necessary prerequisite? 


Yes, it includes the third comparison. Yes, it is equivalent to DIFFTEST in that case. You must establish measurement invariance for comparisons of factors across groups to be valid. 


Thanks Linda! 

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