README.md

Chapter 7: variation in encounter probability

These models introduce alternative encounter functions, individual-, time-, and sex-varying encounter models.

Exponential encounter functions

1. The exponential-encounter-fn.R demonstrates the use of an exponential encounter function + integrated likelihood, marginalizing over s.

2. See exponential-encounter-fn-data-aug.R for a model that uses data augmentation, keeps s in the joint probability (instead of marginalizing), and uses an exponential encounter function.

Heterogeneity in encounter models

1. Individual-level. See individual-heterogeneity-ranefs.R for a model with individual-level normal random effects. Notice that for efficiency, this model uses a non-centered parameterization. For some background see: https://mc-stan.org/docs/2_18/stan-users-guide/reparameterization-section.html

2. Time-varying. See time-varying-p0.R for a model where p0 varies by occasion. This also uses a non-centered parameterization.

3. Sex-varying. See sex-as-individual-covariate.R for a model that allows encounter probability to vary with sex. The challenge here is that sex is only observed for a subset of individuals. The likelihood for unobserved individuals marginalizes over sex (a latent individual-level covariate).