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I am modeling tree mortality using a binomial model in R. Mortality data are collected by two visits to an individual site. On the second visit observers record all trees that died over the measurement interval. The measurement interval is anywhere from 5-10 years. Therefore, the longer the measurement interval, the higher the likelihood of observing mortality. Finally, the data are collected from across the Eastern US, and so spatial auto-correlation of residuals must be dealt with.

I am approaching this using the gamm function within the mgcv package in R. I include an uninformative random effect (all observations have the same level of the random effect). The model looks like this:

mod <- gamm(mortality ~ x1 + x2, 
            family=binomial, 
            random = random = list(rand.eff = ~1), 
            correlation = corExp(form = ~longitude + latitude, nugget=T),
            data=data)

However, this does not account for the effect of the duration of the measurement interval. How can I incorporate this information into this model?

kjetil b halvorsen
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colin
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  • offset doesn't work, e.g. http://stats.stackexchange.com/questions/58368/predicting-with-gam-using-an-offset ? – Florian Hartig Sep 01 '16 at 21:39
  • @FlorianHartig can you explain what the offset is doing in this example? Its not clear to me how it relates to this temporal problem. Currently the model fits a bernoulli distribution to the predicted probability values, say pr, as: bern(pr), where pr is calculated as the inverse logit of the linear combination of predictions. I want the bernoulli distribution to instead be calculated as bern(1 - (1 - pr)^ t)), where t is the measurement interval. This way the predictors predict things on a standardized time interval, and the model accounts for the varying measurement interval. – colin Sep 02 '16 at 01:19
  • I'm just saying that it is common to include things like time interval / area via an offset. What you propose is more exact I suppose, but I'm not sure it's possible with gamm. – Florian Hartig Sep 02 '16 at 12:45
  • @FlorianHartig ah. This is what I feared! I usually do this in a bayesian framework where models are very flexible, but accounting for spatial autocorrelation with a model like this in JAGS, with 50k observations, would take a prohibitively long time to run in JAGS. – colin Sep 02 '16 at 13:06
  • There is a CRAN package geoRglm for spatially correlated generalized linear models, you could look into that – kjetil b halvorsen Aug 27 '17 at 12:42

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