Latent class recapture models with flexible behavioural response


  • Alessio Farcomeni Università di Roma “La Sapienza”



Capture history, Equality constraints, Population size


We propose a class of models for population size estimation in capture-recapture studies, allowing for flexible behavioural and time response, observed heterogeneity and unobserved heterogeneity. The latter is taken into account by means of discrete random variables. The conditional likelihood is maximized through an efficient EM based on the Aitchinson-Silvey algorithm.


J. AITCHISON, S. D. SILVEY (1958). Maximum-likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, pp. 813–828.

H. AKAIKE (1973). Information theory as an extension of the maximum likelihood principle. In B. N. Petrov, C. F. (eds.), Second International symposium on information theory. Akademiai Kiado, Budapest, pp. 267–281.

J. M. ALHO (1990). Logistic regression in capture-recapture models. Biometrics, 46, pp. 623–635.

D. ALUNNI FEGATELLI, L. TARDELLA (2013). Improved inference on capture recapture models with behavioural effects. Statistical Methods & Applications, 22, pp. 45–66.

S. C. AMSTRUP, T. L. MCDONALD, B. F. J. MANLY (eds.) (2003). Handbook of Capture- Recapture Analysis. John Wiley, London.

D. R. ANDERSON, K. P. BURNHAM, G. C. WHITE (1994). Aic model selection in overdispersed capture-recapture data. Ecology, 75, pp. 1780–1793.

F. BARTOLUCCI, A. FARCOMENI (2009). A multivariate extension of the dynamic logit model for longitudinal data based on a latent Markov heterogeneity structure. Journal of the American Statistical Association, 104, pp. 816–831.

F. BARTOLUCCI, A. FARCOMENI (2015). Information matrix for hidden Markov models with covariates. Statistics and Computing, 25, pp. 515–526.

F. BARTOLUCCI, A. FARCOMENI, F. PENNONI (2014). Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates (with discussion). TEST, 23, pp. 433–486.

F. BARTOLUCCI, A. FORCINA (2006). A class of latent marginal models for capture-recapture data with continuous covariates. Journal of the American Statistical Association, 101, pp. 786–794.

S. BASU, N. EBRAHIMI (2001). Bayesian capture-recapture methods for error detection and estimation of population size: Heterogeneity and dependence. Biometrika, 88, pp. 269–279.

D. BÖHNING (2008). A simple variance formula for population size estimators by conditioning. Statistical Methodology, 5, pp. 410–423.

K. P. BURNHAM, G. C. WHITE, D. R. ANDERSON (1995). Model selection strategy in the analysis of capture-recapture data. Biometrics, 51, pp. 888–898.

A. CHAO (2001). An overview of closed capture-recapture models. Journal of Agricultural, Biological and Environmental Statistics, 6, no. 2, pp. 158–175.

A. CHAO, P. K. TSAY, L. S.-H., W.-Y. SHAU, D.-Y. CHAO (2003). Tutorial in biostatistics: the applications of capture-recapture models to epidemiological data. Statistics in Medicine, 20, pp. 3123–3157.

B. A. COULL, A. AGRESTI (1999). The use of mixed logit models to reflect heterogeneity in capture-recapture studies. Biometrics, 55, pp. 294–301.

B. A. COULL, A. AGRESTI (2000). Random effects modeling of multiple binomial responses using the multivariate binomial logit-normal distribution. Biometrics, 56, pp. 73–80.

R. J. EVANS, A. FORCINA (2013). Two algorithms for fitting constrained marginal models. Computational statistics & Data analysis, 66, pp. 1–7.

A. FARCOMENI (2011). Recapture models under equality constraints for the conditional capture probabilities. Biometrika, 98, pp. 237–242.

A. FARCOMENI (2015). A general class of recapture models based on the conditional capture probabilities. Biometrics, p. available online.

A. FARCOMENI, L. GRECO (2015). Robust Methods for Data Reduction. Chapman & Hall/CRC Press.

A. FARCOMENI, D. SCACCIATELLI (2013). Heterogeneity and behavioural response in continuous time capture-recapture, with application to street cannabis use in Italy. Annals of Applied Statistics, 7, pp. 2293–2314.

A. FARCOMENI, L. TARDELLA (2010). Reference Bayesian methods for alternative recapture models with heterogeneity. TEST, 19, pp. 187–208.

A. FARCOMENI, L. TARDELLA (2012). Identifiability and inferential issues in capture-recapture experiments with heterogeneous detection probabilities. Electronic Journal of Statistics, 6, pp. 2602–2626.

A. FARCOMENI, L. VENTURA (2012). An overview of robust methods in medical research. Statistical Methods in Medical Research, 21, pp. 111–133.

R. FEWSTER, P. JUPP (2009). Inference on population size in binomial detectability models. Biometrika, 96, pp. 805–820.

H. HOLZMANN, A. MUNK, W. ZUCCHINI (2006). On identifiability in capturerecapture models. Biometrics, 62, no. 3, pp. 934–936.

R. HUGGINS (1989). On the statistical analysis of capture experiments. Biometrika, 76, pp. 133–140.

P. LAPLACE (1783). Sur les naissances, les marriages, et les morts. Paris. W. A. Link (2003). Nonidentifiability of population size from capture-recapture data with heterogeneous detection probabilities. Biometrics, 59, no. 4, pp. 1123–1130.

C.-X. MAO (2008). On the nonidentifiability of population sizes. Biometrics, 64, no. 3, pp. 977–979.

C. X. MAO, N. YOU (2009). On comparison of mixture models for closed population capture-recapture studies. Biometrics, 65, pp. 547–553.

D. OAKES (1999). Direct calculation of the information matrix via the EM algorithm. Journal of the Royal Statistical Society (Series B), 61, pp. 479–482.

D. L. OTIS, K. P. BURNHAM, G. C. WHITE, D. R. ANDERSON (1978). Statistical Inference From Capture Data on Closed Animal Populations. Wildlife Monographs.

C. G. PETERSEN (1896). The yearly immigration of young plaice into the Limfjord from the German sea. Tech. rep., Danish Biological Station.

S. PLEDGER (2005). The performance of mixture models in heterogeneous closed population capture-recapture. Biometrics, 61, pp. 868–876.

K. H. POLLOCK (2000). Capture-recapture models. Journal of the American Statistical Association, 95, pp. 293–296.

F. RAMSEY, D. USNER (2003). Persistence and heterogeneity in habitat association studies using radio tracking. Biometrics, 59, pp. 331–339.

J. A. ROYLE (2009). Analysis of capture-recapture models with individual covariates using data augmentation. Biometrics, 65, pp. 267–276.

L. SANATHANAN (1972). Estimating the size of a multinomial population. Annals of Mathematical Statistics, 43, pp. 142–152.

G. SCHWARZ (1978). Estimating the dimension of a model. Annals of Statistics, 6, pp. 461–464.

J. Thandrayen, Y. Wang (2010). Capture-recapture analysis with a latent class model allowing for local dependence and observed heterogeneity. Biometrical Journal, 52.

H.-C. YANG, A. CHAO (2005). Modeling animals’ behavioral response by Markov chain models for capture-recapture experiments. Biometrics, 61, pp. 1010–1017.




How to Cite

Farcomeni, A. (2015). Latent class recapture models with flexible behavioural response. Statistica, 75(1), 5–17.