Interactive terms

andyw

New Member
#1
Afternoon all,

I've been running some GLMs using a stepwise backwards deletion routine (main effects, 2 way, 3 way), deleting the least significant terms between each repeat.

I've found some significant interactive terms and just wanted to check that my interpretation of what these mean is correct....

+ if two terms show a significant positive interaction then it means that an increase in one of these terms significantly relates to an increase in the strength of the effect of the other term?
- if two terms show a significant negative interaction then it means that an increase in one of these terms significantly relates to a decrease in the strength of the effect of the other term?

what does it mean if there is a significant 3-way interaction?

as ever, many thanks

x
 

ledzep

Point Mass at Zero
#2
Interaction, simply means the differences of differences. When there is an interaction, this means that the effect of a factor on the response depends on the level of another factor.

Let me have a fictitious example.

Suppose you have response y (say Expenses). Suppose you have significant positive interaction between factors "Age" (Child/Adult) and "Income".(hi/lo)
This means that greater the age, the larger the positive effect of Income will be on y (Expenses).
Equivalently, the greater the income, the larger the positive effect of Age on Expenses.

So, here the effect of age on the Expenses depends on another factor (Income) i.e. there is an interaction between income and age.


what does it mean if there is a significant 3-way interaction?
Ermm..Higher order interaction are bit difficult to interpret. This means that the effect of a factor depends on the combination of the levels of other two factors. In general, higher order interaction are usually ignored (unless really meaningful). I generally don't look at interactions higher than 2-way.