R: Estimate size of sub populations.

stratifyPopsize {singleRcapture}

R Documentation

Estimate size of sub populations.

Description

A function that estimates sizes of specific sub populations based on a capture-recapture model for the whole population.

Usage

stratifyPopsize(object, stratas, alpha, ...)

## S3 method for class 'singleRStaticCountData'
stratifyPopsize(object, stratas, alpha, cov = NULL, ...)

Arguments

`object`	an object on which the population size estimates should be based in `singleRcapture` package this is a fitter `singleRStaticCountData` class object.
`stratas`	a specification of sub populations either by: formula – a formula to be applied to `model.frame` extracted from the object . Logical vector with number of entries equal to number of rows in the dataset. A (named) list where each element is a logical vector, names of the list will be used to specify names variable in returned object. Vector of names of explanatory variables. For `singleRStaticCountData` method for this function this specification of `stratas` parameter will result in every level of explanatory variable having its own sub population for each variable specified. If no value was provided the `singleRStaticCountData` method for this function will itself create sub populations based on levels of factor variables in `model.frame`.
`alpha`	significance level for confidence intervals – Either a single numeric value or a vector of length equal to number of sub populations specified in `stratas`. If missing it is set to `.05` in `singleRStaticCountData` method.
`...`	a vector of arguments to be passed to other functions. For `singleRStaticCountData` method for this functions arguments in `...` are passed to either `cov` if argument provided was a function or `vcov` if `cov` argument was missing at call.
`cov`	for `singleRStaticCountData` method an estimate of variance-covariance matrix for estimate of regression parameters. It is possible to pass a function such as for example `sandwich::vcovHC` which will be called as: `foo(object, ...)` and a user may specify additional arguments of a function in `...` argument. If not provided an estimate for covariance matrix will be set by calling appropriate `vcov` method.

Details

In single source capture-recapture models the most frequently used estimate for population size is Horvitz-Thompson type estimate:

\[\hat{N} = \sum_{k=1}^{N}\frac{I_{k}}{\mathbb{P}(Y_{k}>0)} = \sum_{k=1}^{N_{obs}}\frac{1}{1-\mathbb{P}(Y_{k}=0)}\]

where \(I_{k}=I_{Y_{k} > 0}\) are indicator variables, with value 1 if kth unit was observed at least once and 0 otherwise and the inverse probabilistic weights weights for units observed in the data \(\tfrac{1}{\mathbb{P}(Y_{k}>0)}\) are estimated using fitted linear predictors.

The estimates for different sub populations are made by changing the \(I_{k}=I_{Y_{k} > 0}\) indicator variables to refer not to the population as a whole but to the sub populations that are being considered i.e. by changing values from 1 to 0 if kth unit is not a member of sub population that is being considered at the moment.

The estimation of variance for these estimates and estimation of variance for estimate of population size for the whole population follow the same relation as the one described above.

Value