Modelling the covariance structure in marginal multivariate count models: Hunting in Bioko Island.

The main goal of this article is to present a flexible statistical modelling framework to deal with multivariate count data along with longitudinal and repeated measures structures. The covariance structure for each response variable is defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. In order to specify the joint covariance matrix for the multivariate response vector, the generalized Kronecker product is employed. We take into account the count nature of the data by means of the power dispersion function associated with the Poisson–Tweedie distribution. Furthermore, the score information criterion is extended for selecting the components of the matrix linear predictor. We analyse a data set consisting of prey animals (the main hunted species, the blue duiker Philantomba monticola and other taxa) shot or snared for bushmeat by 52 commercial hunters over a 33-month period in Pico Basilé, Bioko Island, Equatorial Guinea. By taking into account the severely unbalanced repeated measures and longitudinal structures induced by the hunters and a set of potential covariates (which in turn affect the mean and covariance structures), our method can be used to indicate whether there was statistical evidence of a decline in blue duikers and other species hunted during the study period. Determining whether observed drops in the number of animals hunted are indeed true is crucial to assess whether species depletion effects are taking place in exploited areas anywhere in the world. We suggest that our method can be used to more accurately understand the trajectories of animals hunted for commercial or subsistence purposes and establish clear policies to ensure sustainable hunting practices

Bayesian multiple imputation for large-scale categorical data with structural zeros

We propose an approach for multiple imputation of items missing at random in large-scale surveys with exclusively categorical variables that have structural zeros. Our approach is to use mixtures of multinomial distributions as imputation engines, accounting for structural zeros by conceiving of the observed data as a truncated sample from a hypothetical population without structural zeros. This approach has several appealing features: imputations are generated from coherent, Bayesian joint models that automatically capture complex dependencies and readily scale to large numbers of variables. We outline a Gibbs sampling algorithm for implementing the approach, and we illustrate its potential with a repeated sampling study using public use census microdata from the state of New York, USA.National Science Foundatio

Bayesian estimation of a cancer population by capture-recapture with individual capture heterogeneity and small sample

BACKGROUND: Cancer incidence and prevalence estimates are necessary to inform health policy, to predict public health impact and to identify etiological factors. Registers have been used to estimate the number of cancer cases. To be reliable and useful, cancer registry data should be complete. Capture-recapture is a method for estimating the number of cases missed, originally developed in ecology to estimate the size of animal populations. Capture recapture methods in cancer epidemiology involve modelling the overlap between lists of individuals using log-linear models. These models rely on assumption of independence of sources and equal catchability between individuals, unlikely to be satisfied in cancer population as severe cases are more likely to be captured than simple cases. METHODS: To estimate cancer population and completeness of cancer registry, we applied M(th) models that rely on parameters that influence capture as time of capture (t) and individual heterogeneity (h) and compared results to the ones obtained with classical log-linear models and sample coverage approach. For three sources collecting breast and colorectal cancer cases (Histopathological cancer registry, hospital Multidisciplinary Team Meetings, and cancer screening programmes), individual heterogeneity is suspected in cancer population due to age, gender, screening history or presence of metastases. Individual heterogeneity is hardly analysed as classical log-linear models usually pool it with between-“list” dependence. We applied Bayesian Model Averaging which can be applied with small sample without asymptotic assumption, contrary to the maximum likelihood estimate procedure. RESULTS: Cancer population estimates were based on the results of the M(h) model, with an averaged estimate of 803 cases of breast cancer and 521 cases of colorectal cancer. In the log-linear model, estimates were of 791 cases of breast cancer and 527 cases of colorectal cancer according to the retained models (729 and 481 histological cases, respectively). CONCLUSIONS: We applied M(th) models and Bayesian population estimation to small sample of a cancer population. Advantage of M(th) models applied to cancer datasets, is the ability to explore individual factors associated with capture heterogeneity, as equal capture probability assumption is unlikely. M(th) models and Bayesian population estimation are well-suited for capture-recapture in a heterogeneous cancer population. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12874-015-0029-7) contains supplementary material, which is available to authorized users

Integrated methodology for multiple systems estimation and record linkage using a missing data formulation

Capture–recapture, Heterogeneity, Data fusion, EM algorithm, Fellegi–Sunter linkage, Missing data,