I proposed and tested a mediation model (X-M-Y; in this case M is a mediator). But it is possible that there are other arrangements of the variables (e.g., M-X-Y; Y-M-X) due to the cross-sectional design. So, can I use fit analyses to justify the proposed model? What is "fit analysis" (is this even a correct term)? How to perform this? Suggestions or references would be highly appreciated.
please note that mxy and ymx are the same 3-way interaction term because real numbers are commutative and thus one gives the same information as the other. All of this is a subset of factorial experimental designs, the study of interaction effects in experiments. google these terms and get a good regression and experimental design text and study it, this should help quite a bit. BTW there is a large literature on these topics in these questions. You can learn a lot by searching them. This link should be a good beginning: https://www.google.com/search?q=university+of+Virginia+research+moderation+and+mediation+R&rlz=1C1CHBF_enUS917US917&oq=university+of+Virginia+research+moderation+and+mediation+R&aqs=chrome..69i57j33l4.57616j0j1&sourceid=chrome&ie=UTF-8
Best wishes, David Booth
David Eugene Booth I am not sure that the question is about three-way interaction effects. I suspect that "X-M-Y" is intended to be a short hand for "variable M mediates the effect of variable X on variable Y).
Hello Qing,
"Fit" of model and data can be quantified in many ways so long as the model is not fully saturated. Here's a link to a very nice summary of many of the players in the fit family: http://davidakenny.net/cm/fit.htm
How to get these?
1. Use just about any SEM software package (e.g., CALIS, EQS, LISREL, AMOS, lavaan in R) and set up your hypothesized model as (what appears in your query to be a) path model.
2. As long as you have at least 1 df, you can elicit any of the fit indices offered by that package and make judgments about the adequacy of your model to account for the observed relationships in the data set.
Good luck with your work.
Some packages like mediation, processR, robmed can perform mediation analysis in R.
David Morse Dear David, thanks much for your comments, I find the suggestions very helpful!
A further related question: is it possible that a mediation model is well supported when using traditional regression analysis (e.g., PROCESS in SPSS), but the fit indices can be poor when using a structural equation model (e.g., in Amos)?
That is, the mediation effect can be significant with both methods (PROCESS & SEM), but the "fit" of the mediation model can be poor when using SEM.
If so, Why can it happen? What does this imply? Does this mean the hypothesized model is unreliable? (but we can see many empirical articles were using PROCESS which did not report fit indices). BTW, can we use both of the two methods in one study?
Thanks much!
Qing Yang I am going to suggest you look at the materials at this link from the University of Virginia especially. First this is all about variable interactions in Factorial experimental designs. These interactions are called in some social sciences Mediation and moderation The only differences are how many variables interact. That is why the model fit is unimportant we aren't trying to predict values of the DV where fit is important. here we only wish to know which IVs interact. If you look at the link material this should help. Notice that SPSS is a poor package to do these in because at the extra stuff takes yhou mind off of the important thing, which variables interact and what happens when they do. Best wishes, D. Booth Here is the link:
https://www.google.com/search?client=firefox-b-1-d&q=moderation+and+mediation+Research+University+of+Virginia
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