Skip to main content

Bayesian analysis of capture-recapture data with hidden Markov models: Theory and case studies in R and NIMBLE

6 Covariates

WORK IN PROGRESS

6.1 Covariate selection with reversible jump MCMC

RJMCMC in Gimenez, Grégoire, and Lenormand (2009) on Common blackbirds or Gimenez et al. (2009) on White stork.

As an illustration, we use data on the white stork Ciconia ciconia population in Baden Wurttemberg (Germany), consisting of 321 capture histories of individuals ringed as chicks between 1956 and 1971. From the 60’s to the 90’s, all Western European stork populations were declining Bairlein (1991). This trend was likely the result of reduced food availability Schaub, Kania, and U. (2005) caused by severe droughts observed in the wintering ground of storks in the Sahel region. This hypothesis has been examined in several studies (Kanyamibwa et al. (1990) and Barbraud, Barbraud, and Barbraud (1999)).

Check out https://r-nimble.org/nimbleExamples/RJMCMC_example.html and https://r-nimble.org/variable-selection-in-nimble-using-reversible-jump-mcmc.

Somewhere explain how to use if-else in model code to consider alternative models, w/ some covariate in/out. Avoids rewriting all models, we see what’s changed, and it avoids errors. Example:

if(covariate){
logit(survival[t]) <- beta[1] + beta[2] *x[t]
}else{
logit(survival[t]) <- beta[1]
}#ifelse

then specify “covariate=TRUE/FALSE”.

6.2 Missing values

Work on missing values by Bonner and Schwarz (2006) (see Gimenez et al. (2009)) and Langrock and King (2013) and Worthington, King, and Buckland (2015). See also Rose et al. (2018).

6.3 Sex uncertainty

Pradel et al. (2008) and Genovart, Pradel, and Oro (2012)

6.4 Nonlinearities

Splines à la Gimenez et al. (2006), possibly w/ jagam https://rdrr.io/cran/mgcv/src/R/jagam.r.