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標題: 具輔助變量之重複捕獲模型的模擬研究
A simulation study on capture-recapture models with covariates
作者: 杜宇舜
Yu-Shun Tu
關鍵字: 母體總數;重複捕獲;負二項迴歸模型;Population size;Capture-recapture;Negative binomial regression model
引用: [1] Anan, O., Bohning, D., and Maruotti, A. (2017). Population size estimation and heterogeneity in capture–recapture data: a linear regression estimator based on the Conway–Maxwell–Poisson distribution. Statistical Methods and Applications, 26(1), 49-79. [2] Bo ̈hning, D., Suppawattanabodee, B., Kusolvisitkul, W., and Viwatwongkasem, C. (2004). Estimating the number of drug users in Bangkok 2001 : a capture-recapture approach using repeated entries in one list. European Journal of Epidemiology, 19(12), 1075-1083. [3] Bo ̈hning, D., Dietz, E., Kuhnert, R., and Scho ̈n, D. (2005). Mixture models for capture-recapture count data. Statistical Methods and Applications, 14(1), 29-43. [4] Chao, A. (1989). Estimating population size for sparse data in capture-recapture experiments. Biometrics, 45(2), 427-438. [5] Daly, F., and Gaunt, R. E. (2016). The Conway-Maxwell-Poisson distribution: distributional theory and approximation. Alea-latin American Journal of Probability and Mathematical Statistics, 13(2), 635-658. [6] Horvitz, D. G., and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47(260), 663-685. [7] Hanski, I., Kuussaari, M., and Nieminen, M. (1994). Metapopulation structure and migration in the butterfly melitaea cinxia. Ecology, 75(3), 747-762. [8] Lynch, H. J., Thorson J. T., and Shelton, A. O. (2014). Dealing with under- and over-dispersed count data in life history, spatial, and community ecology. Ecology, 95(11), 3173-3180. [9] Huggins, R. M., and Yip, P. S. F. (1996). Estimation of the size of an open population from capture-recapture data using weighted martingale methods. Biometrics, 55(2), 387-395. [10] Sellers, K. F., Swift, A. W., and Weems, K. S. (2017). A flexible distribution class for count data. Journal of Statistical Distributions and Applications, 4(22). [11] Mace, R. D., Minta, S. C., Manley, T. L. and Aune, K. E. (1994). Estimating grizzly bear population size using camera sighting. Wildlife Society Bulletin, 22(1), 74-83. [12] Minka, T. P., Shmueli, G., Kadane, J. B., Borle, S., and Boatwright, P. (2003). Computing with the COM-Poisson distribution. Carnegie Mellon University Department of Statistics Technical Report, 776. [13] Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S., and Boatwright, P. (2005). A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution. Journal of the Royal Statistical Society : Series C (Applied Statistics), 54(1), 127-142. [14] van der Heijden, P. G. M., Bustami, R., Cruyff, M. J. L. F., Engbersen, G., and van Houwelingen, H. C. (2003). Point and interval estimation of population size using the truncated Poisson regression model. Statistical Modelling, 3(4), 305-322. [15] van der Heijden, P. G. M., and Cruyff, M. J. L. F. (2008). Point and Interval Estimation of the Population Size Using a Zero-Truncated Negative Binomial Regression Model. Biometrical Journal, 50(6), 1035-1050. [16] Hwang, W. H., and Huang, Y. H. (2007). Measurement errors in continuous-time capture-recapture models. Journal of Statistical Planning and Inference, 137(6), 1888-1899. [17] Hwang, W. H., and Huggins, R. (2005). An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data. Biometrika, 92(1), 229-233. [18] Zelterman, D. (1988). Robust estimation in truncated discrete distributions with applications to capture-recapture experiments. Journal of Statistical Planning and Inference, 18(2), 225-237.

No matter it is in medicine or ecology, the estimation of population size is a very important issue. When the number of times of capture or observation is related to some variables, the literature often uses Poisson regression or negative binomial regression model to fit its count data, and then estimate population size. This paper discusses the feasibility of using the Conway-Maxwell Poisson (CMP) zero truncated regression model to estimate the population size. Under different simulation type, compare the advantages and disadvantages of various modes. We also used a set of capture-recapture experimental data from Hong Kong Bird Reserve to compare the utility of various methods.
Rights: 同意授權瀏覽/列印電子全文服務,2018-08-01起公開。
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