Exploring interactions: continous and categorical (4 levels)

[#1]

 Hi all!

I really need some help. How can I test a significant interaction between a continuous and categorical variable? I ran a linear mixed model with continuous dependent (e.g. engagement), fixed effects "compulsive buying-score", advertising category (4 categories) and their interaction, and random effects "Subject ID" and "StimuliName" . The interaction between "compulsive buying-score" and advertising category was significant. Now, I would like to test, in which advertising category (I have 4) the interaction was significant and what was the effect? How could I do that? Thanks so much in advance!

[#2]

Click the red triangle at the top and select Estimates. You will find Custom Tests and Joint Factor Tests available. You can then select Tools > Help and click on the report to go directly to the documentation about these tests for more information.

You can also select Factor Profiling > Profiler and visually explore the nature of the interactions. The latter is not a formal hypothesis test but it should help your understanding of this effect.

[#3]

Hi Mark, 

Thank you very much for your reply. I tried to do the estimates, and I am still a bit puzzled with this option. I tried to check the help section, which did not prove to be very helpful at the end. When I did the joint factor tests for my interaction, I have got one factor to be significant, which is advertising product category and another non-significant (Compulsive - buying score). What does that mean? In the initial analysis, where I included all the factors and their interaction, advertising product category and CB-score were both non-significant. But interaction significant. Does that mean that this interaction is driven by the differences between advertising category? 

Another question. When I am running the custom tests, I would like to know, if interaction between CB-score and Social Advertising category is significant and what is the effect, as well if  interaction between CB-score and FMCG ad category is significant and what is the effect, CB-score and Fashion AD category is significant and what is the effect, and CB-score and Food ad category. When I look at the custom tests, I have an option to choose what I want to test. If i only want to compare there 4 interactions, how do I code that? As well, the CB-score and Social advertising category variable is not exposed in there... Would be really grateful for your advice! I attach the regression results. 

[#4 · Accepted solution]

In this case, the most significant and important effect is the interaction. The main effects are not significant but they should remain in the model to maintain the model hierarchy.

The labeling CBS-32.4792 indicates that JMP centered the continuous CBS predictor for you.

I regret that the explanation of the joint factor test in the JMP Help was not useful. Here it is:

The Joint Factor Test option appears when interaction effects are present. For each main effect in the model, JMP produces a joint test of whether all the coefficients for terms involving that main effect are zero. This test is conditional on all other effects being in the model. Specifically, the joint test is a general linear hypothesis test of a restricted model. In that model, all parameters that correspond to the specified effect and the interactions that contain it are set to zero.

The Fixed Effect Tests report is used to determine if individual terms in the model are significant. The interaction introduces a hierarchy. The Joint Factor Test spans all of the parameters for all of the terms that include the predictor. That is the reason for the large number of degrees of freedom. So Ad Category is significant in your case when you jointly consider all of the terms, even if individual terms are not significant. It is an 'all or nothing' test. The null hypothesis is that all of the parameters for this predictor are zero. The alternative is that at least one of them is not zero.

[#5]

Dear Mark

I would like to rephrase the question a bit since I am still not sure, how can I do what I am aiming for. I add a figure in here of interaction that I would like to specify. In the figure, I show the interaction effect of Ad category and Compulsive buying score on total time fixation.  What I want to do is to statistically prove that the relationship between compulsive buying score and total fixation time is only significant at Social Cause Ad category. While the relationship between these two variables is not significant within other 3 categories. While it is seen from the figure, I need to provide the statistical argumentation. And I am not sure, if this is where I use Joint Tests or Custom tests analyses, since I think they aimed at different goal. 

Thanks so much!
Dalia

[#6 · Accepted solution]

I think that the Parameter Estimates provides the answer you seek. The Fixed Effect Tests are for the significance of the whole term in the model. The Parameter Estimates are tests for each estimate. The estimate for the Social Cause Ad is not shown, though, because it is dependent on the other levels. It must be equal to the negative of the sum of the other estimates: -( (-0.003415) + (-0.012818) + (-0.014721) ) = 0.030954. The significance is found by clicking the red triangle next to Response in the upper left and selecting Estimates > Expanded Estimates.

[#7]

Thank you so much, now it is much more clear. The only problem is that I am running the linear mixed model analysis with random factors, so this type of regression as I can see in the menu, doesn't have the option of Extended Estimates under the Estimates...