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Interactions in Logit, HB and Latent Class

Dear Forum,

I have a question regarding interactions. Using the Interaction Search tool in Lighthouse studio, I found several interactions in both the basic 2LL test and the modified 2LL test (by using the HB utilities file). I have a few questions regarding these interactions:

1. I want to know which levels that are interacting have the most significant statistical significance in the basic 2LL test and modified 2LL test. I looked at the "RUNS" tab of the interaction search, which gives me the effects and t ratios per level and interaction.
- Within a significant interaction effect between attributes, I can find effect scores and t ratios of interactions between specific levels. Are only the ones above 1.96 significant to at least the 95% confidence? What does the effect tell me?
- Within a non significant interaction effect between attributes, I can still find some interactions between specific levels that are above 1.96. Does this mean that this interaction between levels is significant, although the interaction between attributes is not significant?

2. The 2LL P-Value for Interaction Effect within the modified 2LL test shows two interactions that are significant (95% confidence). However, when looking at the individual t ratios, no significant interacting levels can be found. Furthermore, when clicking on the "Charts" tab of the Interaction search, no interactions are found. How is it so that the  2LL P-Value still reports for a significant interaction?

3. I want to know if there are specific interactions within my Latent Classes I have estimated. I want to do this the same way as the basic 2LL test and the modified 2LL test (so with Logit and HB estimates). From what I understand:
- I have the estimated utilities from the Latent Class report (as a logit)
- By including Latent Classes in the HB utility report as a segment, I now have HB utility values.
How do I now use these utility values for finding interactions in Latent Classes?

I understand this is a pretty large post, but since all my questions are centred around interactions, I assumed these would be the best way. I am looking forward to your answers.

Kind regards,

Joost
asked Oct 28 by Joost (140 points)

1 Answer

0 votes
Joost,

Let me answer your sets of questions one at a time, inline with your question, in CAPS below:  

1. I want to know which levels that are interacting have the most significant statistical significance in the basic 2LL test and modified 2LL test. I looked at the "RUNS" tab of the interaction search, which gives me the effects and t ratios per level and interaction.  CORRECT
- Within a significant interaction effect between attributes, I can find effect scores and t ratios of interactions between specific levels. Are only the ones above 1.96 significant to at least the 95% confidence? YES What does the effect tell me? THE EFFECT IS THE COEFFICIENT THAT CAPTURES THE UTILITY OF THE TWO INTERACTING LEVELS, OVER AND ABOVE THEIR SEPARATE MAIN EFFECTS.  INTERPRETING THE COMBINATION OF TWO LEVELS WOULD REQUIRE SUMMING THEIR MAIN EFFECTS AND THE INTERACTION EFFECT.
- Within a non significant interaction effect between attributes, I can still find some interactions between specific levels that are above 1.96. Does this mean that this interaction between levels is significant, although the interaction between attributes is not significant? THINK OF THE TEST OF THE INTERACTION BETWEEN THE ATTRIBUTES AS BEING AN OMNIBUS TEST.  YOU DON'T EVEN LOOK AT THE INTERACTIONS BETWEEN LEVELS UNLESS THE INTERACTION BETWEEN THE ATTRIBUTE IS SIGNIFICANT.  THINK OF IT, AN INTERACTION BETWEEN TWO 5-LEVEL ATTRIBUTES PRODUCES 16 INTERACTION TERMS, AND THE CHANCES OF EXPERIMENTWISE ERROR RISE ACCORDINGLY IF YOU ONLY LOOK AT THE 16 SPECIFIC INTERACTIONS.
answered Oct 28 by Keith Chrzan Platinum Sawtooth Software, Inc. (79,575 points)
And see CAPS below for the rest of your questions:

2. The 2LL P-Value for Interaction Effect within the modified 2LL test shows two interactions that are significant (95% confidence). However, when looking at the individual t ratios, no significant interacting levels can be found. Furthermore, when clicking on the "Charts" tab of the Interaction search, no interactions are found. How is it so that the  2LL P-Value still reports for a significant interaction? IT DEPENDS.  MAYBE SEND ME YOUR OUTPUT SO I CAN TAKE A LOOK - KEITH@SAWTOOTHSOFTWARE.COM

3. I want to know if there are specific interactions within my Latent Classes I have estimated. I want to do this the same way as the basic 2LL test and the modified 2LL test (so with Logit and HB estimates). From what I understand:
- I have the estimated utilities from the Latent Class report (as a logit)
- By including Latent Classes in the HB utility report as a segment, I now have HB utility values. I'M NOT SURE WHY THE HB RESULTS COME IN HERE.  IF YOU WANT TO EXAMINE INTERACTIONS IN THE LATENT CLASS ANALYSIS, SPECIFY THEM ON YOUR ANALYSIS RUN AND INTERPRET THEM AS YOU DID FOR THE AGGREGATE LOGIT.  
How do I now use these utility values for finding interactions in Latent Classes?
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