Interaction between a time trend and an indicator variable

questions concerning analysis/theory using program PRESENCE

Interaction between a time trend and an indicator variable

Postby kbrunk » Fri Nov 09, 2018 3:32 pm

Hello again,

I am building a multi-state multi-season model using the Psi, R, p, delta parameterization. In an earlier stage of my modeling procedure, I have found support for a logarithmic time trend in CR that is additive with state and with land ownership type ("Type," an indicator variable). I am very interested in testing whether this logarithmic time trend is the same or different between the two different land ownership types. I have set up the design matrix like this:


a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15
...
CR0(1) 0 0 0 0 0 0 0 0 0 1 0 0 0.69 Type Int1
CR1(1) 0 0 0 0 0 0 0 0 0 1 1 0 0.69 Type Int1
CR2(1) 0 0 0 0 0 0 0 0 0 1 0 1 0.69 Type Int1
CR0(2) 0 0 0 0 0 0 0 0 0 1 0 0 1.1 Type Int2
CR1(2) 0 0 0 0 0 0 0 0 0 1 1 0 1.1 Type Int2
CR2(2) 0 0 0 0 0 0 0 0 0 1 0 1 1.1 Type Int2
CR0(3) 0 0 0 0 0 0 0 0 0 1 0 0 1.39 Type Int3
CR1(3) 0 0 0 0 0 0 0 0 0 1 1 0 1.39 Type Int3
CR2(3) 0 0 0 0 0 0 0 0 0 1 0 1 1.39 Type Int3
CR0(4) 0 0 0 0 0 0 0 0 0 1 0 0 1.61 Type Int4
CR1(4) 0 0 0 0 0 0 0 0 0 1 1 0 1.61 Type Int4
CR2(4) 0 0 0 0 0 0 0 0 0 1 0 1 1.61 Type Int4
...

Where the last column (Int1, Int2, etc.) is the product of the log time trend and the indicator variable Type for each transition. When I run this model, it is exactly 2 deltaAIC from the additive model that doesn't include the interaction term, leading me to believe that either there is absolutely no support for the interaction model over the additive OR that I am setting up the interaction wrong and being penalized 2 AIC for running exactly the same model with an extra nonsense variable. I'd be super happy for any feedback!

Thanks!

KB
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Re: Interaction between a time trend and an indicator variab

Postby jhines » Fri Nov 09, 2018 4:21 pm

The design matrix looks OK to me. Perhaps you don't have sufficient data to estimate the interaction? By that I don't mean necessarily lots of sites, but you'll need sites where there is breeding (state=2) and non-breeding for both land ownership types. One option I highly recommend with the more complicated models is to try different starting values. There is an option in the run dialog screen allowing you to run the model with a bunch of random starting values. You might try 10 or 20 sets of starting values to see if it converges on different estimates. If you're still concerned, I'd be happy to take a look if you send me the most recent backup zipfile.

Jim
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Re: Interaction between a time trend and an indicator variab

Postby kbrunk » Fri Nov 09, 2018 5:09 pm

Oh, I see. That makes a lot of sense, I didn't fully think about the data requirements for an interaction effect. There are definitely very few instances of nonbreeding within one of the land ownership types, and that may be the source of my issue.

Just from looking at the individual site estimates, it seems there is a decline in CR over time in one ownership type, with smaller probabilities of transitioning to state 2 for sites that had lower states in the previous year, which is pretty intuitive for my population. The other ownership type constantly has a probability of 1 for transitions to state 2, no matter the state in the previous year.

Is it possible to do a post-hoc analysis to see if the trend in predicted transition probability mentioned above has a slope that is significantly different than zero? I realize this is definitely less desirable than evaluating support for an interaction effect, but I want to somehow quantitatively judge whether this trend is ecologically meaningful.
kbrunk
 
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Re: Interaction between a time trend and an indicator variab

Postby jhines » Tue Nov 13, 2018 9:13 am

I don't see how to do a post-hoc analysis on trend of one of the types since you would need the estimates for the model that you're having trouble with. Did you try the random starting values option? Since the model where the interaction term worked, it might be better to try specifying the final values from that model as starting values for the model with interaction. The starting value for the interaction should be a large number, since you suspect that CR for the other type is near 1.0.
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Re: Interaction between a time trend and an indicator variab

Postby kbrunk » Wed Nov 14, 2018 4:26 pm

Hey Jim,

I tried the random initial values option with 20 sets of values and got the same results as before (2 delta AIC from the additive model), and then I tried supplying initial values the way you mentioned and still got the same results. I'd be really bummed not to be able to consider this interaction, and would be super excited to try them if you have any other ideas.

Thanks a ton!

KB
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Posts: 12
Joined: Fri Oct 12, 2018 11:51 am


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