derived                 package:secr                 R Documentation

_D_e_r_i_v_e_d _P_a_r_a_m_e_t_e_r_s _o_f _F_i_t_t_e_d _S_E_C_R _M_o_d_e_l

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

     Compute derived parameters of spatially explicit capture-recapture
     model.  Density is a derived parameter when a model is fitted by
     maximizing the conditional likelihood. So also is the effective
     sampling area (in the sense of Borchers and Efford 2008).

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

     derived(object, sessnum = NULL, groups = NULL, alpha = 0.05, 
         se.esa = FALSE, se.D = TRUE, loginterval = FALSE, 
         distribution = NULL)
     esa(object, sessnum = 1, beta = NULL, real = NULL)

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

  object: 'secr' object output from 'secr.fit' 

 sessnum: index of session in object$capthist for which output required 

  groups: indices defining group(s) (see Details) 

   alpha: alpha level for confidence intervals 

  se.esa: logical for whether to calculate SE(mean(esa)) 

    se.D: logical for whether to calculate SE(D-hat) 

loginterval: logical for whether to obtain interval for log(D) 

distribution: character string for distribution of the number of
          individuals detected 

    beta: vector of fitted parameters on transformed (link) scale 

    real: vector of 'real' parameters 

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

     The derived estimate of density is a Horvitz-Thompson-like
     estimate:

                   D-hat = sum( a_i (theta-hat)^-1)

     where (theta-hat) is the estimate of effective sampling area for
     animal i with detection parameter vector theta.

     A non-null value of the argument 'distribution' overrides the
     value in 'object$details'. The sampling variance of D-hat from
     'secr.fit' by default is spatially unconditional ('distribution' =
     'Poisson'). For sampling variance conditional on the population of
     the habitat mask (and therefore dependent on the mask area),
     specify 'distribution' = 'binomial'. The equation for the
     conditional variance includes a factor (1 - a/A) that disappears
     in the unconditional (Poisson) variance (Borchers and Efford
     2007). Thus the conditional variance is always less than the
     unconditional variance. The unconditional variance may in turn be
     an overestimate or (more likely) an underestimate if the true
     spatial variance is non-Poisson.

     Derived parameters may be estimated for population subclasses
     (groups) defined by the user with the 'groups' argument. Each
     named factor in 'groups' should appear in the covariates dataframe
     of object$capthist (or each of its components, in the case of a
     multi-session dataset).

     The effective sampling area 'esa' reported by 'derived' is equal
     to the mean of the a_i (theta-hat).

     A 100(1-alpha)% asymptotic confidence interval is reported for
     density. By default, this is symmetrical about the estimate
     because the variance is computed on the natural scale. You may
     also choose an asymmetric (lognormal) interval. 

     'esa' is used by 'derived' to compute individual-specific
     effective sampling areas: 

                a_i = integral p.(X; z_i, theta_i) dX

     where p.(X) is the probability an individual at X is detected at
     least once and the z_i are optional individual covariates.
     Integration is over the area A of the habitat mask.

     The vector of detection parameters for 'esa' may be specified via
     'beta' or 'real', with the former taking precedence. If neither is
     provided then the fitted values in 'object$fit$par' are used.
     Specifying 'real' parameter values bypasses the various linear
     predictors. Strictly, the 'real' parameters are for a naive
     capture (animal not detected previously).

     The computation of sampling variances is relatively slow and may
     be suppressed with 'se.esa' and 'se.D' as desired.

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

     Dataframe with one row for each derived parameter ('esa', 'D') and
     columns as below

       estimate     estimate of derived parameter
       SE.estimate  standard error of the estimate
       lcl          lower 100(1-alpha)% confidence limit
       ucl          upper 100(1-alpha)% confidence limit
       varcomp1     variance due to variation in n (Huggins' s^2)
       varcomp2     variance due to uncertainty in estimates of detection parameters

     For a multi-session or multi-group analysis the value is a list
     with one component for each session and group.

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

     Murray Efford murray.efford@otago.ac.nz

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

     Borchers, D. L. and Efford, M. G. (2007) Supplements to Biometrics
     paper. Available online at <URL: http://www.otago.ac.nz/density>.

     Borchers, D. L. and Efford, M. G. (2008) Spatially explicit
     maximum likelihood methods for capture-recapture studies.
     _Biometrics_, *64*, 377-385.

     Huggins, R. M. (1989) On the statistical analysis of capture
     experiments. _Biometrika_ *76*, 133-140.

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

     'predict.secr', 'print.secr', 'secr.fit'

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

     ## extract derived parameters from a model fitted previously
     ## by maximizing the conditional likelihood 
     data(secrdemo)
     derived (secrdemo.CL)

     ## what happens when sampling variance is conditional on mask N?
     derived(secrdemo.CL, distribution = 'binomial')

     ## fitted g0, sigma
     esa(secrdemo.CL)
     ## force different g0, sigma
     esa(secrdemo.CL, real = c(0.2, 25))

