closedp               package:Rcapture               R Documentation

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_D_e_s_c_r_i_p_t_i_o_n:

     This function fits various loglinear models for closed populations
     in capture-recapture experiments: M0, Mt, Mh Chao, Mh Poisson2, Mh
     Darroch, Mth Chao, Mth Poisson2, Mth Darroch, Mb and Mbh.

_U_s_a_g_e:

     closedp(X, dfreq=FALSE, neg=TRUE)

     ## S3 method for class 'closedp':
     print(x, ...)

     ## S3 method for class 'closedp':
     boxplot(x, ...)

_A_r_g_u_m_e_n_t_s:

       X: The table of the observed capture histories in one of the two
          accepted formats. In the default format, it has one row per
          unit captured in the experiment. In this case, the number of
          columns in the table represents the number of capture
          occasions in the experiment (noted t). In the alternative
          format, it contains one row per capture history followed by
          its frequency. In that case, 'X' has t+1 columns. The first t
          columns of 'X', identifying the capture histories, must
          contain only zeros and ones. The number one indicates a
          capture. 

   dfreq: This argument specifies the format of the data matrix 'X'. By
          default, it is set to FALSE, which means that 'X' has one row
          per unit. If it is set to TRUE, then the matrix 'X' contains
          frequencies in its last column.

     neg: If this option is set to TRUE, negative eta parameters in
          Chao's models are set to zero. 

       x: An object, produced by the 'closedp' function, to print or to
          plot.

     ...: Further arguments passed to or from other methods.

_D_e_t_a_i_l_s:

     Chao's models estimate a lower bound for the abundance, both with
     (Mth Chao) and without a time effect (Mh Chao). The estimate
     obtained under Mh Chao is Chao's (1987) moment estimator. Rivest
     and Baillargeon (2007) exhibit a loglinear model underlying this
     estimator and provide a generalization to Mth. For these two
     models, a small deviance means that there is an heterogeneity in
     capture probabilities; it does not mean that the lower bound
     estimates are unbiased. For Darroch's models, the column for
     heterogeneity in the design matrix is defined as k^2/2 where k is
     the number of captures;  these models for Mh and Mth are
     considered by Darroch et al. (1993) and Agresti (1994). For
     Poisson2 models, the column for heterogeneity in the design matrix
     is 2^k-1. Poisson models with an exponent's base different than 2
     can be fitted with the 'closedp.h' function. These models are
     discussed in Rivest and Baillargeon (2007);  they typically yield
     smaller corrections for heterogeneity than Darroch's model since
     the capture probabilities are bounded from below under these
     models.

     The 'boxplot.closedp' function produces boxplots of the Pearson
     residuals of the ten loglinear models.

     To perform a bias correction on the abundance estimates, use the
     'closedp.bc' function.

_V_a_l_u_e:

       n: The number of captured units

       t: The number of capture occasions in the data matrix 'X'

 results: A table containing, for each model, the estimated population
          size, the standard error of estimation, the deviance, the
          number of degrees of freedom and the Akaike criteria.

   glmM0: The 'glm' object obtained from fitting the M0 model.

   glmMt: The 'glm' object obtained from fitting the Mt model.

  glmMhC: The 'glm' object obtained from fitting the Mh Chao model.

  glmMhP: The 'glm' object obtained from fitting the Mh Poisson model.

  glmMhD: The 'glm' object obtained from fitting the Mh Darroch model.

 glmMthC: The 'glm' object obtained from fitting the Mth Chao model.

 glmMthP: The 'glm' object obtained from fitting the Mth Poisson model.

 glmMthD: The 'glm' object obtained from fitting the Mth Darroch model.

   glmMb: The 'glm' object obtained from fitting the Mb model.

  glmMbh: The 'glm' object obtained from fitting the Mbh model.

   parM0: Capture-recapture parameters estimates for model M0 : the
          abundance N and p, the capture probability at any capture
          occasion.

   parMt: Capture-recapture parameters estimates for model Mt : N and
          p1 to pt, the capture probabilities for each capture
          occasion.

  parMhC: Capture-recapture parameters estimates for model MhC : N and
          p, the average probability of capture.

  parMhP: Capture-recapture parameters estimates for model MhP : N and
          p, the average probability of capture.

  parMhD: Capture-recapture parameters estimates for model MhD : N and
          p, the average probability of capture.

 parMthC: Capture-recapture parameters estimates for model MthC : N and
          p1 to pt, the average probabilities of capture for each
          occasion.

 parMthP: Capture-recapture parameters estimates for model MthP : N and
          p1 to pt, the average probabilities of capture for each
          occasion.

 parMthD: Capture-recapture parameters estimates for model MthD : N and
          p1 to pt, the average probabilities of capture for each
          occasion.

   parMb: Capture-recapture parameters estimates for model Mb : N, p,
          the probability of first capture at any capture occasion, and
          c, the recapture probability at any capture occation.

  parMbh: Capture-recapture parameters estimates for model Mbh : N, p
          and c.

  negMhC: The position of the eta parameters set to zero in the
          loglinear parameter vector of model MhC.

 negMthC: The position of the eta parameters set to zero in the
          loglinear parameter vector of model MthC.

_N_o_t_e:

     This function uses the 'glm' function of the 'stats' package.

_A_u_t_h_o_r(_s):

     Sophie Baillargeon sbaillar@mat.ulaval.ca and Louis-Paul Rivest
     lpr@mat.ulaval.ca

_R_e_f_e_r_e_n_c_e_s:

     Agresti, A. (1994). Simple capture-recapture models permitting
     unequal catchability and variable sampling effort. _Biometrics_,
     50, 494-500.

     Baillargeon, S. and Rivest, L.P. (2007). The Rcapture package:
     Loglinear models for capture-recapture in R. _Journal of
     Statistical Software_, to appear (available online at <URL:
     http://www.jstatsoft.org/>).

     Chao, A. (1987). Estimating the population size for
     capture-recapture data with unequal catchabililty.  _ Biometrics_,
     45, 427-438

     Darroch, S.E.,  Fienberg, G.,  Glonek, B. and Junker, B. (1993). A
     three sample multiple capture-recapture approach to the census
     population estimation with heterogeneous catchability. _Journal of
     the American Statistical Association_, 88, 1137-1148

     Rivest, L.P. and Levesque, T. (2001) Improved log-linear model
     estimators of abundance in capture-recapture experiments.
     _Canadian Journal of Statistics_, 29, 555-572.

     Rivest, L.P. and Baillargeon, S. (2007). Applications and
     extensions of Chao moment estimator for the size of a closed
     population. _Biometrics_, to appear.

_S_e_e _A_l_s_o:

     'uifit', 'closedp.bc', 'closedp.Mtb', 'closedp.mX', 'closedp.h'

_E_x_a_m_p_l_e_s:

     data(hare)
     hare.closedp<-closedp(hare)
     hare.closedp
     boxplot(hare.closedp)

     data(mvole)
     period3<-mvole[,11:15]
     closedp(period3)

