Environmental heterogeneity for multiple study sites

[mgroner]

I am running an MSMR analysis on a dataset with 4 sites. At each site, the individuals can be any of several disease states (healthy thru severely diseased). I would like to evaluate the effect of environmental heterogeneity on both the survival and state-transition estimates. I have environmental data for each of the sites. There is no movement between sites, so I am treating 'site' as a fixed effect and I have environmental data for each site. Is this possible in ESURGE? The most recent manual only has an example for 1 site, and at that time, ANODEV could only be run to examine environmental heterogeneity in the first matrix in the 'transition' step. Has this been updated? If it is not possible in ESURGE, could I run this analysis in MARK? Thank you for your help.

[simone77]

Sorry to be late! Based on the information you've provided, it appears that you have four sites with no movement of individuals between them, which can be considered a fixed characteristic or grouping variable with four levels. Additionally, you have dynamic characteristics (referred to as "states") that can change over an individual's lifetime.

You can certainly conduct an analysis to assess the effect of environmental variables on a transition matrix (survival and/or state-change), provided you have a sufficient amount of data to support the complexity of your models. The complexity of your models depends on the structure of your probabilistic matrices (i.e., the number of events and states and how they are related) and the effects you wish to test in your models. These parameters are defined when you prepare your GEPAT and set your model sentences in the GEMACO .

For example, if you have three "alive" states (e.g., ND-Not Diseased, MD-Moderately Diseased, SD-Severely Diseased), you can define an initial state matrix with probabilities of individuals being in each state at their first encounter.


Similarly, you would have a survival matrix with probabilities of surviving or dying between sessions,


As well as a state-change matrix indicating probabilities of transitioning between states.


Finally, in the simplest form, where you have neither misclassification nor incomplete assessment of the states, you would have an event matrix like this (assuming 0=not detected, 1=detected as ND, 2=detected as MD, 3=detected as SD):


In GEMACO, for example, you could run a model in which survival is determined by the departure state and site-specific environmental (not time-varying) variables. Examples of how to prepare a file with the values of the environmental variables and which syntax to use in GEMACO can be found in the manual (and most likely in this forum).

Good luck!

[mgroner]

Hi SImone,
Thank you for your reply.
My understanding is that I need to run ANODEV to determine the proportion of the time-varying effect that is explained by the environmental covariate. I understand how to do this when I have 1 environmental covariate associated with one matrix in GEMACO (e.g., Survival or Transition), but the model I am most interested in (and with the lowest qAICc) includes environmental covariates for both Survival and Transition matrices. Do you have advice about how to calculate ANODEV when I have two model steps with environmental covariates?
Many thanks!
Maya

[simone77]

Hi Maya,

To my understanding (though I welcome any corrections or alternate insights), if you have these models:

model1: ... phi(variable1) psi(variable2) ...
model2: ... phi(constant) psi(variable2) ...
model3: ... phi(time) psi(variable2) ...
model4: ... phi(variable1) psi(constant) ...
model5: ... phi(variable1) psi(time) ...

All else being equal (same structure on the other parameters), the ANODEV procedure to determine the proportion of time variation in phi explained by variable1 is given by:

(deviance(model1) - deviance(model3)) / (deviance(model2) - deviance(model3))

All else being equal (same structure on the other parameters), the ANODEV procedure to determine the proportion of time variation in psi explained by variable2 is given by:

(deviance(model1) - deviance(model5)) / (deviance(model4) - deviance(model5))