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How to interpret interaction effects?

I have run a Latent class analysis and have also included one interaction term. However, I did not understand how to interpret the following significant utilities within the output of one of the classes:

Output class 1:

Attribute 1; level 1 = 30.12345 (pos. significant utility)
Attribute 2; level 2 = 57.04145 (pos. significant utility)

(Attribute 1; level 1) x (Attribute 2; level 2) = -54.13564 (neg. significant utility)

It looks strange that both levels individually have a significant positive utility, but that in the interaction term that combination has a significant negative utility.

How is that possible?

Thank you in advance.
asked Mar 3 by anonymous

1 Answer

0 votes
An interaction occurs when the whole is different than the sum of its parts.  You can have a positive interaction if the involved attribute levels have a synergy or a reinforcing effect.  You can have a negative interaction if the two together aren't as good as you would expect from their separate utilities.  

Here's an example of a negative interaction:  I like scrambled eggs, maybe they have utility of +5 for me.  And I like chocolate - maybe it has a utility of +8.  But I would NOT like scrambled eggs with chocolate syrup that would have a utility of -22 for me.  The difference between the total value of chocolate scrambled eggs and the sum of chocolate and scrambled eggs is the interaction, which is -22 - (5+8)  = -35.

In your case the total value of A1L1 and L2L2 is 30 + 57 - 54 = 27, so it's not as extreme as the chocolate scrambled eggs example.  Respondents still like A1L1 + A2L2, they just don't like them together as much as you might expect.
answered Mar 3 by Keith Chrzan Gold Sawtooth Software, Inc. (48,225 points)