Frequentist analysis of hierarchical models for population dynamics and demographic data

Hierarchical models include random effects or latent state variables. This class of models includes state–space models for population dynamics, which incorporate process and sampling variation, and models with random individual or year effects in capture–mark–recapture models, for example. This paper reviews methods for frequentist analysis of hierarchical models and gives an example of a non-Gaussian, potentially nonlinear analysis of Lapwing data using the Monte Carlo kernel likelihood (MCKL) method for maximum-likelihood estimation and bridge sampling for calculation of likelihood values given estimated parameters. The Lapwing example uses the state–space model as part of an integrated population model, which combines survey data with ring-recovery demographic data. The methods reviewed include filtering methods, such as the Kalman filter and sequential Monte Carlo (or particle filtering) methods, Monte Carlo expectation maximization, data cloning, and MCKL. The latter methods estimate the maximum-likelihood parameters but omit a normalizing constant from the likelihood that is needed for model comparisons, such as the Akaike information criterion and likelihood ratio tests. The methods reviewed for normalizing constant calculation include filtering, importance sampling, likelihood ratios from importance sampling, and bridge sampling. For the Lapwing example, a novel combination of MCKL parameter estimation, bridge sampling likelihood calculation, and profile likelihood confidence intervals for an integrated population model is presented to illustrate the feasibility of these methods. A complementary view of Bayesian and frequentist analysis is taken.