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I am testing a model using SEM. I have three independent measures (seemingly covarying) impacting a DV. This is the easy part I think. Now the hard part.. I believe that the relationship is modified by two measures that are to the most part correlated.I need to test if one of the IVs has a direct path impact on the DV due to high score on both continuous moderating variables, and all other conditions of the moderators suggest a route based upon the other two IVs. Am I crazy????? 


Sounds like a 3way interaction  you can create a product variable for the 2 continuous moderators and then multiply that with the one IV. Or, create a dummy variable for when both the 2 mediators are high and then do a 2group analysis to see how the paths vary across the 2 groups. 


Bengt: Thanks for your quick response. Let me clatify the situation in more detail so I'm sure that I get what you are suggesting. It sounds like I need to do three 3way interactions. There are actually 3 IVs – independent measures of a somewhat theoretically distinct although interrelated construct. At this point, I am not addressing the correlation between the IVs but instead exploring the independent contributions to the DV. My hypotheses argue that the two moderators (continuous measurements also somewhat correlated) impact the path chosen from the IVs to the DV. High/High score conditions of the IVs will choose 1 path while Low/Low will choose the other two. I need to support/negate the hypotheses of different paths for the different moderator levels (HH/LL). 


Sounds like we are on the same wave length. 


Good evening to all the community, I would elaborate a SEM model with also one moderation. Searching in literature, I have found that Cortina, Chen & Dunlap (2001) report all the syntax for elaborate this technique with LISREL. Unfortunately I was no able to find the syntax for Mplus nowhere. To clarify, I report the model that I want elaborate: ANALYSIS: TYPE = RANDOM; ALGORITHM = INTEGRATION; MODEL: A by a1 a2 a3; B by b1 b2 b3; C by c1 c2 c3; D by d1 d2 d3; E by e1 e2 e3; D on B C; BxC  B XWITH C; D on BxC; E on A D; Output: sampstat tech1 tech8; What you suggest to compute this model? Thanks in advance for your attention and availability 


You show an Mplus input with a latent variable interaction. I'm not sure I understand your question. This model looks at moderation. 


Good morning cordial Muthen and thanks for the answer. Considering always Cortina, Chen & Dunlap (2001), how I can compute "Moderated structural equation modeling (MSEM)" with Mplus? Are there some files in which is reported the syntax? Thanks in advance for your attention and availability 


It looks like you are on the right path in your specification. Also, look at the UG ex 5.13 which is on our website. The data and input can be downloaded. The 2001 reference you mention is now a bit outdated. Instead, check the 2011 Kelava et al article in the SEM journal's Teacher's Corner. 


Good evening cordial Muthen and thanks for the answer. I have understood your suggestion but I know that using TYPE = RANDOM, Mplus doesn't return R square and the indices fit of the model (as TLI, CFI...). How I can obtain these indices including a moderation in the model? Thanks again for your attention and availability 


That is a bit more complex with latent variable interactions. See our FAQs Latent variable interactions Latent variable interaction LOOP plot 


Good evening cordial Muthen, thank you so much for your help and for the suggested readings. Kind regards 

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