Profile Likelihood Confidence Intervals

Description

Compute profile likelihood confidence intervals for ‘beta’ or ‘real’ parameters of a spatially explicit capture-recapture model,

Usage

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## S3 method for class 'secr'
 confint(object, parm, level = 0.95, newdata = NULL,
tracelevel = 1, tol = 0.0001, bounds = NULL, ...)

Arguments

object

secr model object

parm

numeric or character vector of parameters

level

confidence level (1 – alpha)

newdata

optional dataframe of values at which to evaluate model

tracelevel

integer for level of detail in reporting (0,1,2)

tol

absolute tolerance (passed to uniroot)

bounds

numeric vector of outer starting values – optional

...

other arguments (not used)

Details

If parm is numeric its elements are interpreted as the indices of ‘beta’ parameters; character values are interpreted as ‘real’ parameters. Different methods are used for beta parameters and real parameters. Limits for the j-th beta parameter are found by a numerical search for the value satisfying -2(l_j(beta_j) - l) = q, where l is the maximized log likelihood, l_j(beta_j) is the maximized profile log likelihood with beta_j fixed, and q is the 100(1-alpha) quantile of the chi-square distribution with one degree of freedom. Limits for real parameters use the method of Lagrange multipliers (Fletcher and Faddy 2007), except that limits for constant real parameters are backtransformed from the limits for the relevant beta parameter.

If bounds is provided it should be a 2-vector or matrix of 2 columns and length(parm) rows.

Value

A matrix with one row for each parameter in parm, and columns giving the lower (lcl) and upper (ucl) 100*level

Note

Calculation may take a long time, so probably you will do it only after selecting a final model.

The R function uniroot is used to search for the roots of -2(l_j(beta_j) - l) = q within a suitable interval. The interval is anchored at one end by the MLE, and at the other end by the MLE inflated by a small multiple of the asymptotic standard error (1, 2, 4 or 8 SE are tried in turn, using the smallest for which the interval includes a valid solution).

A more efficient algorithm was proposed by Venzon and Moolgavkar (1988); it has yet to be implemented in secr, but see plkhci in the package Bhat for another R implementation.

References

Evans, M. A., Kim, H.-M. and O'Brien, T. E. (1996) An application of profile-likelihood based confidence interval to capture–recapture estimators. Journal of Agricultural, Biological and Experimental Statistics 1, 131–140.

Fletcher, D. and Faddy, M. (2007) Confidence intervals for expected abundance of rare species. Journal of Agricultural, Biological and Experimental Statistics 12, 315–324.

Venzon, D. J. and Moolgavkar, S. H. (1988) A method for computing profile-likelihood-based confidence intervals. Applied Statistics 37, 87–94.

Examples

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## Not run: 
## Limits for the constant real parameter "D"
confint(secrdemo.0, "D")   

## End(Not run)

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