t_y2: Multivariate Ratio Estimator of Total for Complex Sample

In williamsbenjamin/blendR: Blending a Probablilty Sample and a Non-Probability Sample in a Capture-Recapture Setting

Description

Make an Estimate of Total Using a Weighted Combination of t_p and t_y2 from Liu et al (2017) for a Complex Sample Setting.

Usage

t_y2(data, delta, captured, survey_design, na_remove = T, capture_units,
  total_from_capture)

Arguments

data	A data frame, each row is an observation from the recapture sample. If the row refers to a unit which is also in the capture sample, the data frame contains the information gathered from the recapture sample. If the row refers to a unit only in the recapture sample, those columns for recapture sample data contain zeros. The data frame should contain a variable delta, see below, and and sample design information.
delta	Name of variable from given data frame. For every unit in the recapture sample, delta is the value of the variable of interest observed in the recapture sample minus the value observed in the capture sample. If the unit in the recapture sample is not also a member of the capture sample, delta =0
captured	Name of indicator variable of unit being in capture sample, from given data frame
survey_design	A complex survey design specified with survey::svydesign()
na_remove	Remove NA's? Logical
capture_units	Total number of units in the capture sample
total_from_capture	Total of variable of interest from all units in the capture sample

Details

This estimator is defined by: t_y2 = t_{y*} + \frac{n_1}{\hat{n}_1}(\hat{t}_y - \hat{t}_{y*}) = t_{y*} + n_1\hat{bar{δ}}. This amounts to a ratio estimator of δ over \hat{n_1} with auxiliary information n_1 added to t_{y*}. δ = y_i - r_iy*_i, \hat{t}_y = ∑{i=1}^{N}w_i z_i y_i, z_i is a sampling indicator, w_i is the sampling weight, y_i is the value of the variable of interest observed in the Recapture sample, y*_i is the value of the variable of interest observed in the Capture sample. There are N units in the population. y*_i is the value of the variable of interest recorded in the recapture sample. t_{y*} = ∑{i =1}^{N}r_iy*_i r_i is an indicator of whether the unit is a member of the recapture sample.

Value

Estimate of Total and Standard Error of Estimate

total	Estimate of total of variable of interest in population
se	Standard error of estimate of total

Examples

 s_design <- survey::svydesign(id = ~psu,
                               strat = ~stratum,
                               prob = ~prob,
                               nest = T,
                               data = red_snapper_sampled)
t_y2(data = red_snapper_sampled,
     delta = delta_catch,
     survey_design = s_design,
     captured = captured_indicator,
     capture_units = nrow(self_reports),
     total_from_capture = sum(self_reports$number_kept)
     )

williamsbenjamin/blendR documentation built on March 18, 2021, 4:07 a.m.