The Analysis of Mark-recapture Data with Individual Heterogeneity via the H-likelihood
Abstract
Mark-recapture methods play a key role in ecological studies monitoring wild animal populations. One consideration in analyzing mark-recapture data is individual variation in the detection rate. Classical methods for modelling heterogeneity require numerical integration and may be computationally intensive. This thesis presents a novel approach based on the h-likelihood to remedy such difficulties by avoiding numerical integration.
First, I present the h-likelihood approach for fitting the fundamental model describing individual heterogeneity in mark-recapture studies. The conditional likelihood approach allows the model to be regarded as a generalized linear mixed model (GLMM). I construct the h-likelihood for the model in the context of this GLMM. The population size is estimated via the Horvitz-Thompson estimator.
Second, I extend my approach to fit advanced models accounting for individual heterogeneity along with variation over time and individuals’ trap responses. The conditional likelihood approach enables these models to be treated as vector GLMMs. The approach from the first project is adapted to fit these models with multi-dimensional response variables. The Horvitz-Thompson estimator is again employed to estimate the population size.
Finally, I develop the h-likelihood approach to fit more flexible models describing individual heterogeneity. As standard models assume a linear relationship, I apply the structure of generalized additive models through B-spline, which can be considered as a GLMM with the conditional likelihood penalized for roughness. Again, I apply the h-likelihood to fit this model and to estimate the population size using the Horvitz-Thompson estimator.