Latent class recapture models with flexible behavioural response

Recapture models based on conditional capture probabilities are explored. These encompass all possible forms of time-dependence and behavioural response to capture. Covariates are used to deal with observed heterogeneity, while unobserved heterogeneity is modeled through flexible random effects with a finite number of support points

Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits (local, global, continuation or reverse continuation), generalised log-odds ratios and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is formulated following the encompassing prior approach. Then, model selection is performed by using Bayes factors which are estimated by an importance sampling method. The approach is illustrated through three applications involving some datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also considered

Heterogeneity and behavioral response in continuous time capture-recapture, with application to street cannabis use in Italy

We propose a general and flexible capture-recapture model in continuous time. Our model incorporates time-heterogeneity, observed and unobserved individual heterogeneity, and behavioral response to capture. Behavioral response can possibly have a delayed onset and a finite-time memory. Estimation of the population size is based on the conditional likelihood after use of the EM algorithm. We develop an application to the estimation of the number of adult cannabinoid users in Italy.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS672 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Information matrix for hidden Markov models with covariates

For a general class of hidden Markov models that may include time-varying covariates, we illustrate how to compute the observed information matrix, which may be used to obtain standard errors for the parameter estimates and check model identifiability. The proposed method is based on the Oakes’ identity and, as such, it allows for the exact computation of the information matrix on the basis of the output of the expectation-maximization (EM) algorithm for maximum likelihood estimation. In addition to this output, the method requires the first derivative of the posterior probabilities computed by the forward-backward recursions introduced by Baum and Welch. Alternative methods for computing exactly the observed information matrix require, instead, to differentiate twice the forward recursion used to compute the model likelihood, with a greater additional effort with respect to the EM algorithm. The proposed method is illustrated by a series of simulations and an application based on a longitudinal dataset in Health Economics

S-estimation of hidden Markov models

A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step with high breakdown S-estimation of location and scatter, performed by using the bisquare multivariate S-estimator. Estimates are obtained by solving a system of estimating equations that are characterized by component specific sets of weights, based on robust Mahalanobis-type distances. Convergence of the resulting algorithm is proved and its finite sample behavior is investigated by means of a brief simulation study and n application to a multivariate time series of daily returns for seven stock markets

Quantile contours and allometric modelling for risk classification of abnormal ratios with an application to asymmetric growth-restriction in preterm infants

We develop an approach to risk classification based on quantile contours and allometric modelling of multivariate anthropometric measurements. We propose the definition of allometric direction tangent to the directional quantile envelope, which divides ratios of measurements into half-spaces. This in turn provides an operational definition of directional quantile that can be used as cutoff for risk assessment. We show the application of the proposed approach using a large dataset from the Vermont Oxford Network containing observations of birthweight (BW) and head circumference (HC) for more than 150,000 preterm infants. Our analysis suggests that disproportionately growth-restricted infants with a larger HC-to-BW ratio are at increased mortality risk as compared to proportionately growth-restricted infants. The role of maternal hypertension is also investigated.Comment: 31 pages, 3 figures, 8 table