| derived {secr} | R Documentation |
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).
derived(object, sessnum = NULL, groups = NULL, alpha = 0.05,
se.esa = FALSE, se.D = TRUE, loginterval = TRUE,
distribution = NULL)
esa(object, sessnum = 1, beta = NULL, real = NULL)
object |
secr object output from secr.fit |
sessnum |
index of session in object$capthist for which output required |
groups |
indices defining group(s) (see Details) |
alpha |
alpha level for confidence intervals |
se.esa |
logical for whether to calculate SE(mean(esa)) |
se.D |
logical for whether to calculate SE(D-hat) |
loginterval |
logical for whether to base interval on log(D) |
distribution |
character string for distribution of the number of individuals detected |
beta |
vector of fitted parameters on transformed (link) scale |
real |
vector of 'real' parameters |
The derived estimate of density is a Horvitz-Thompson-like estimate:
D-hat = sum( a_i (theta-hat)^–1)
where (theta-hat) is the estimate of effective sampling area for animal i with detection parameter vector theta.
A non-null value of the argument distribution overrides the value
in object$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$capthist (or each of its components, in the case of a
multi-session dataset).
The effective sampling area 'esa' reported by derived is equal
to the mean of the a_i (theta-hat).
A 100(1–alpha)% asymptotic confidence interval is reported for density. By default, this is asymmetric about the estimate because the variance is computed by backtransforming from the log scale. You may also choose a symmetric interval (variance obtained on natural scale).
esa is used by derived to compute individual-specific
effective sampling areas:
a_i = integral p.(X; z_i, theta_i) dX
where p.(X) is the probability an individual at X is detected at least once and the z_i are optional individual covariates. Integration is over the area A of the habitat mask.
The vector of detection parameters for esa may be specified via
beta or real, with the former taking precedence. If
neither is provided then the fitted values in object$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.
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 |
Murray Efford murray.efford@otago.ac.nz
Borchers, D. L. and Efford, M. G. (2007) Supplements to Biometrics paper. Available online at 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.
predict.secr, print.secr, secr.fit
## 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))