Estimating second language productive vocabulary size: A Capture-Recapture approach

This study provides validity evidence for the Capture-Recapture (CR) method, borrowed from ecology, as a measure of second language (L2) productive vocabulary size (PVS). Two separate “captures” of productive vocabulary were taken using written word association tasks (WAT). At Time 1, 47 bilinguals provided at least 4 associates to each of 30 high-frequency stimulus words in English, their first language (L1), and in French, their L2. A few days later (Time 2), this procedure was repeated with a different set of stimulus words in each language. Since the WAT was used, both Lex30 and CR PVS scores were calculated in each language. Participants also completed an animacy judgment task assessing the speed and efficiency of lexical access. Results indicated that, in both languages, CR and Lex30 scores were significantly positively correlated (evidence of convergent validity). CR scores were also significantly larger in the L1, and correlated significantly with the speed of lexical access in the L2 (evidence of construct validity). These results point to the validity of the technique for estimating relative L2 PVS. However, CR scores are not a direct indication of absolute vocabulary size. A discussion of the method’s underlying assumptions and their implications for interpretation are provided.

Estimating the size of the population of persons who inject drugs in the island of Montréal, Canada, using a six-source capture-recapture model

BACKGROUND: To plan and implement services to persons who inject drugs (PWID), knowing their number is essential. For the island of Montréal, Canada, the only estimate, of 11,700 PWID, was obtained in 1996 through a capture-recapture method. Thirteen years later, this study was undertaken to produce a new estimate. METHODS: PWID were defined as individuals aged 14-65 years, having injected recently and living on the island of Montréal. The study period was 07/01/2009 to 06/30/2010. An estimate was produced using a six-source capture-recapture log-linear regression method. The data sources were two epidemiological studies and four drug dependence treatment centres. Model selection was conducted in two steps, the first focusing on interactions between sources and the second, on age group and gender as covariates and as modulators of interactions. RESULTS: A total of 1480 PWID were identified in the six capture sources. They corresponded to 1132 different individuals. Based on the best-fitting model, which included age group and sex as covariates and six two-source interactions (some modulated by age), the estimated population was 3910 PWID (95% confidence intervals (CI): 3180-4900) which represents a prevalence of 2.8 (95% CI: 2.3-3.5) PWID per 1000 persons aged 14-65 years. CONCLUSIONS: The 2009-2010 estimate represents a two-third reduction compared to the one for 1996. The multisource capture-recapture method is useful to produce estimates of the size of the PWID population. It is of particular interest when conducted at regular intervals thus allowing for close monitoring of the injection phenomenon.

Mixture models for capture-recapture count data

The contribution investigates the problem of estimating the size of a population, also known as the missing cases problem. Suppose a registration system is targeting to identify all cases having a certain characteristic such as a specific disease (cancer, heart disease, ...), disease related condition (HIV, heroin use, ...) or a specific behavior (driving a car without license). Every case in such a registration system has a certain notification history in that it might have been identified several times (at least once) which can be understood as a particular capture-recapture situation. Typically, cases are left out which have never been listed at any occasion, and it is this frequency one wants to estimate. In this paper modelling is concentrating on the counting distribution, e.g. the distribution of the variable that counts how often a given case has been identified by the registration system. Besides very simple models like the binomial or Poisson distribution, finite (nonparametric) mixtures of these are considered providing rather flexible modelling tools. Estimation is done using maximum likelihood by means of the EM algorithm. A case study on heroin users in Bangkok in the year 2001 is completing the contribution.

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

A capture-recapture approach for screening using two diagnostic tests with availability of disease status for the test positives only

The article considers screening human populations with two screening tests. If any of the two tests is positive, then full evaluation of the disease status is undertaken; however, if both diagnostic tests are negative, then disease status remains unknown. This procedure leads to a data constellation in which, for each disease status, the 2 x 2 table associated with the two diagnostic tests used in screening has exactly one empty, unknown cell. To estimate the unobserved cell counts, previous approaches assume independence of the two diagnostic tests and use specific models, including the special mixture model of Walter or unconstrained capture-recapture estimates. Often, as is also demonstrated in this article by means of a simple test, the independence of the two screening tests is not supported by the data. Two new estimators are suggested that allow associations of the screening test, although the form of association must be assumed to be homogeneous over disease status. These estimators are modifications of the simple capture-recapture estimator and easy to construct. The estimators are investigated for several screening studies with fully evaluated disease status in which the superior behavior of the new estimators compared to the previous conventional ones can be shown. Finally, the performance of the new estimators is compared with maximum likelihood estimators, which are more difficult to obtain in these models. The results indicate the loss of efficiency as minor.

Application of one-list capture-recapture models to scrapie surveillance data in Great Britain

In this paper, we apply one-list capture-recapture models to estimate the number of scrapie-affected holdings in Great Britain. We applied this technique to the Compulsory Scrapie Flocks Scheme dataset where cases from all the surveillance sources monitoring the presence of scrapie in Great Britain, the abattoir survey, the fallen stock survey and the statutory reporting of clinical cases, are gathered. Consequently, the estimates of prevalence obtained from this scheme should be comprehensive and cover all the different presentations of the disease captured individually by the surveillance sources. Two estimators were applied under the one-list approach: the Zelterman estimator and Chao's lower bound estimator. Our results could only inform with confidence the scrapie-affected holding population with clinical disease; this moved around the figure of 350 holdings in Great Britain for the period under study, April 2005-April 2006. Our models allowed the stratification by surveillance source and the input of covariate information, holding size and country of origin. None of the covariates appear to inform the model significantly. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Estimating cumulative exposure of wildlife to non-lethal disturbance using spatially explicit capture-recapture models

Impact assessments often focus on short-term behavioral responses of animals to human disturbance. However, the cumulative effects caused by repeated behavioral disruptions are of management concern because these effects have the potential to influence individuals' survival and reproduction. We need to estimate individual exposure rates to disturbance to determine cumulative effects. We present a new approach to estimate the spatial exposure of minke whales to whalewatching boats in Faxaflõi Bay, Iceland. We used recent advances in spatially explicit capture-recapture modeling to estimate the probability that whales would encounter a disturbance (i.e., whalewatching boat). We obtained spatially explicit individual encounter histories of individually identifiable animals using photo-identification. We divided the study area into 1-km2 grid cells and considered each cell a spatially distinct sampling unit. We used capture history of individuals to model and estimate spatial encounter probabilities of individual minke whales across the study area, accounting for heterogeneity in sampling effort. We inferred the exposure of individual minke whales to whalewatching vessels throughout the feeding season by estimating individual whale encounters with vessels using the whale encounter probabilities and spatially explicit whalewatching intensity in the same area, obtained from recorded whalewatching vessel tracks. We then estimated the cumulative time whales spent with whalewatching boats to assess the biological significance of whalewatching disturbances. The estimated exposure levels to boats varied considerably between individuals because of both temporal and spatial variations in the activity centers of whales and the whalewatching intensity in the area. However, although some whales were repeatedly exposed to whalewatching boats throughout the feeding season, the estimated cumulative time they spent with boats was very low. Although whalewatching boat interactions caused feeding disruptions for the whales, the estimated low cumulative exposure indicated that the whalewatching industry in its current state likely is not having any long-term negative effects on vital rates.

Estimating the number of whales entering trade using DNA profiling and capture-recapture analysis of market products

Surveys of commercial markets combined with molecular taxonomy (i.e. molecular monitoring) provide a means to detect products from illegal, unregulated and/or unreported (IUU) exploitation, including the sale of fisheries bycatch and wild meat (bushmeat). Capture-recapture analyses of market products using DNA profiling have the potential to estimate the total number of individuals entering the market. However, these analyses are not directly analogous to those of living individuals because a ‘market individual’ does not die suddenly but, instead, remains available for a time in decreasing quantities, rather like the exponential decay of a radioactive isotope. Here we use mitochondrial DNA (mtDNA) sequences and microsatellite genotypes to individually identify products from North Pacific minke whales (Balaenoptera acutorostrata ssp.) purchased in 12 surveys of markets in the Republic of (South) Korea from 1999 to 2003. By applying a novel capture-recapture model with a decay rate parameter to the 205 unique DNA profiles found among 289 products, we estimated that the total number of whales entering trade across the five-year survey period was 827 (SE, 164; CV, 0.20) and that the average ‘half-life’ of products from an individual whale on the market was 1.82 months (SE, 0.24; CV, 0.13). Our estimate of whales in trade (reflecting the true numbers killed) was significantly greater than the officially reported bycatch of 458 whales for this period. This unregulated exploitation has serious implications for the survival of this genetically distinct coastal population. Although our capture-recapture model was developed for specific application to the Korean whale-meat markets, the exponential decay function could be modified to improve the estimates of trade in other wildmeat or fisheries markets or abundance of living populations by noninvasive genotyping.