Dear Muhammad,

First this:

A three way interaction. That means that there are at least three predictors.

You must also include the two way interactions; there are three of them.

And the three way interaction itself. And an intercept.

That is:8 parameters. This means at least (really at least!) 80 cases.

The analysis:

you should standardize the interval level predictors and the dependent variable. Do not standardize categorical or dichotomous predictors.

The standardisation makes interpretation easier; very low score is -2, mean score=0 and very high score is 2.

Then you compute all the interactions.

Next all 7 variables go in the regression, together. And than you check the (unstandardized, the B's) coefficients, for size and significance.

(Why would you do a hierarchic regression when your researchquestion postulates this moderation model? All the incomplete models will have a bias.)

To interpret the effects of the regression you write down the regression equation (with (all!) the found coefficients) and you fill in values for the variables.

And there are tests to see where (for which values of moderators)  the combined effects are significantly different.

Take care,

Pierre

Hello Muhammad

Please follow the attached link

Best wishes

https://www.youtube.com/watch?v=4k8JFvJRw_w

I may be misunderstanding your question, Muhammad, but I interpret a three factor interaction as a measure on the two way interactions not being equal in their effects. Why exactly do you need to consider a three way interaction in your project?

Dear Muhammad,

First this:

A three way interaction. That means that there are at least three predictors.

You must also include the two way interactions; there are three of them.

And the three way interaction itself. And an intercept.

That is:8 parameters. This means at least (really at least!) 80 cases.

The analysis:

you should standardize the interval level predictors and the dependent variable. Do not standardize categorical or dichotomous predictors.

The standardisation makes interpretation easier; very low score is -2, mean score=0 and very high score is 2.

Then you compute all the interactions.

Next all 7 variables go in the regression, together. And than you check the (unstandardized, the B's) coefficients, for size and significance.

(Why would you do a hierarchic regression when your researchquestion postulates this moderation model? All the incomplete models will have a bias.)

To interpret the effects of the regression you write down the regression equation (with (all!) the found coefficients) and you fill in values for the variables.

And there are tests to see where (for which values of moderators)  the combined effects are significantly different.

Take care,

Pierre

A lot depends on whether the variables in your interaction effects are nominal or interval. If they are dummy variables, then you are looking at a fairly straight forward set of products between those variables to test your three-way interaction.

You would also use products if you have a set of interval variables, but those products can to be difficult to interpret in two-way interactions, let alone three-way.

if you are asking simply how to code it, in R the syntax is model

Hi Muhammad,

I wrote an article on an alternative approach that you may find useful for interpreting a three-way interaction.  It is: Francoeur, R. B. (2011). Interpreting interactions of ordinal or continuous variables in moderated regression using the zero slope comparison: tutorial, new extensions, and cancer symptom applications. Special issue on "Assessment Methods in Social Systems Science," International Journal of Society Systems Science, 3 (1/2), 137-158. You can download this article at  https://www.researchgate.net/publication/230686383_Interpreting_interactions_of_ordinal_or_continuous_variables_in_moderated_regression_using_the_zero_slope_comparison_Tutorial_new_extensions_and_cancer_symptom_applications

In the article, I extended an algorithm for interpreting a two-way interaction (the Zero Slope Comparison, ZSC) into a algorithm for interpreting a three-way interaction (the Extended Zero Slope Comparison, EZSC). Both ZSC and EZSC overcome the need to re-estimate multiple regressions and construct related graphs to reveal the nature of moderator effects (magnifier and/or buffering). These graphs are not exhaustive; they are limited in displaying "snapshots" of moderator effects at pre-selected values of the predictor variables comprising the interaction. In contrast, both algorithms yield fewer interpretations of aggregate moderator effects across predictor ranges, and not at pre-selected values.

Good luck in your work.

Richard Francoeur

Article Interpreting interactions of ordinal or continuous variables...

Usually, when se do the regression analyses, we need follows the hierarchical principle, if a model three way interaction is significant, and it is used in the model, all two ways interactions and all main effects should be included.

Reading the attachment,

In step 3, it shows that sex_age_neg is significant, since sex is binary, the three way interaction could be explained, the two way interaction age_neg is different between males and females, the neg_age=0.001, p=0.6 it means for male, there is no interaction between age and neg, i.e the age effect among males is not change when you change neg value., however, the age_neg for female would be .001+0.007=0.008, which should be significant according the results in attachment.  It means the age effect among female varies by neg value, or the neg effect is different for different age among females. This means the three way interaction examine the homogeneity of two way interaction

Because, excepf for neg, age and sex, there is no other factors on your data, you can get the same results for run y=age, neg age*neg by sex separately.

Two way interaction, if one predictor is continuous, which examine the slope change, three way interaction examine the “change of the ‘slope change ‘ “

If all are categorical,

Main effect is change (difference of two levels), two way-interaction is change of change,

Three way interaction is change of change of change

For continuous factor, standardized the factor only change the slope from per unit increase to per one standard deviation increasing, if using z score.  

For categorical data, do not need do it, if you claim this is binary or nominal in the modeling, it will no effect on it. If you don’t claim it is a categorical data, it would be “dangerous” to do so.

However the p-value will not change.

Thank for every one who deliberately guided about 3 way interaction, however, I am still not cleared the mystery that was found in A.F Hayes's book " Introduction to mediation, moderation and conditional process analysis" in the sense that either this result provide 3 way as well as 2 way interaction or not?

Moderation is the same as an interaction effect. In the typical formulation of moderation effects, you would have differences between the two gender subgroups. As Yuanzhang Li point out, this means that the interaction between age and neg is not the same in both genders.