using derived parameter from latent state as a covariate

[Dilsad Dagtekin]

Hi everyone!

I am trying to do a capture-recapture model in nimble. Model works fine and all, however, I have population size covariate in the model and I thought it could also be calculated with the same model and used in the same model, could be useful to account for uncertainty in that variable.

 But when I tried it out I got an error saying:

"The graph has cycles; topological sorting is only possible in acyclic graphs, Invalid value"

So, I was wondering if it is possible to use a derived parameter (population size) from latent state (z, true survival) in a model as a covariate in the same model in nimble? 

The relevant code snippet is below (the model is rather big, if need be I can send it):

for (t in 1:(n.occasions-1)){    

logit(phi_jpost[t]) <- alpha_phi + beta1*cov1[t] + beta2*cov2[t] + beta3t*popsize_out[t]
 }

 ### LIKELIHOOD ##
  for (i in 1:M){
    ## Define latent state at first occasion ##
    z[i,1] <- 1   # Make sure that all M individuals are in state 1 at t=1
    for (t in 2:n.occasions){
     
      ## State process: draw S(t) given S(t-1) ##
      z[i,t] ~ dcat(ps[z[i,t-1], i, t-1, 1:6])}

  
      # total jpost

      z_jpost[i, t-1] <- equals(z[i,t], 2)
     
      # total jpre
      z_jpre[i, t-1] <- equals(z[i,t], 3)
     
      # total apost
      z_apost[i, t-1] <- equals(z[i,t], 4)
     
      # total apre

      z_apre[i, t-1] <- equals(z[i,t], 5)

} # i

} # t

for (t in 1:n.occasions){
    N_jpost[t] <- sum(z_jpost[1:M,t])   

    N_jpre[t] <- sum(z_jpre[1:M,t])
    N_apost[t] <- sum(z_apost[1:M,t])
    N_apre[t] <- sum(z_apre[1:M,t])

    popsize_out[t] <-  N_jpost[t] + N_jpre[t] + N_apost[t] + N_apre[t]
  }

Any help is appreciated.

Cheers,

Dilsad

[Quresh Latif]

I have tried using latent states or parameters derived from latent states as covariates in a couple different contexts. Sometimes it has worked and sometimes it hasn't. The main thing to remember is that it needs to make sense for information to flow both from the latent state to the dependent parameter and back the other way. If it doesn't make sense for information to flow in both directions, the model will choke or you will get wonky estimates. In this case, it looks to me like 'z' is a latent state representing the realization of survival probability, so you can't then use 'z' to inform survival probability. If you are trying to do this, you have a cycle in your model graph, which is why you are getting that error.

[Dilsad Dagtekin]

Hi Quresh,

Thanks for your reply, that's what I thought so as well. 

Best,

Dilsad

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A. Dilsad Dagtekin

PhD Student at Population Ecology Research Group

University of Zurich, Department of Evolutionary Biology and Environmental Studies 

dilsad....@ieu.uzh.ch | www.popecol.org

Ecology and Evol. Biology Society of Turkey: www.ekoevo.org
ITU Alumni '16 & '18 | AFS Alumni '12