How can I interpret interaction plot according to effect test tabel?

[#1]

While most of the sources are significant in the parameter estimates and the effect test table, why no intersections are seen in the interaction plot?

[#2]

You have not provided enough information like where did your data come from (e.g., observational, experimentation) to give a specific reason, so here are some things to consider.  Statistical significance in your table depends on 2 things: MS of the terms (source or model) AND MS error (F-test = MSfactors/MSerror).  If the estimate of the MSe is very small (and not representative), then everything can be "statistically significant".  This would be my first guess.  How was your MSe estimated?  Is it a function of randomized replicates (what statisticians like to call pure error) or lack of fit  (removing insignificant terms from the model)?  How does the MSe compare with actual variation in the process?  Have you considered practical significance?  

[#3]

Hi @Nimaxim . Hard to say for sure with the limited information you’ve provided. But, my guess is sample size. If your sample size (error df) is very large, even very small effects come out as “statistically significant”. So, while the interactions may be “statistically significant”, the differences (as shown by non-parallel lines in the plots) may be negligible. This phenomenon is sometimes called “overpowered”. 

[#4]

@statman , @MRB3855 Thank you for responses to my question. In fact, this RSM analysis uses a neural network for the responses. The factor values are based on real RFM Model data. I'm attaching some of the results.

[#5]

Hi @Nimaxim : All of the things mentioned in the other posts are at play here. First I need some further clarity:

1. The inputs are the several X's (what you are calling "factor values")

2. The response Y comes from a NN model that is/was built based on those same several X's (as in 1 above)?

3. Then you are using a multiple regression/response surface to model Y (which is output from a NN model as in 2 above) as a function of the same X's (as in 1 above)? i.e., you are trying to predict the output from a NN model with a multiple regression/ Response Surface model (6 linear effects, 6 quadratic effects, and 15 interactions to make up the 27 model degrees of freedom)?

Do I have that correct?   

If so, your results are not surprising. There is no pure error (i.e., replicates give identical results), so the only source of error is due to model misspecification (lack of fit). Before we get too far down this road...why are you doing this?

[#6]

Hello,

Thanks for posting a picture for context, that's super useful. 

The parameter estimates table is the one you will find more helpful. Based on your profiler picture, I suspect the interactions are significant, but also small. Also, it's likely you have a lot of observations behind your model? This will help make small effects significant. A large number of degrees of freedom can increase sensitivity, but also increase the chance of false positives. 

Cheers,

-B