# popsize_simul: Estimate the total population size and capture probabilities... In drpop: Efficient Doubly Robust Population Size Estimation

## Description

Estimate the total population size and capture probabilities using perturbed true nuisance functions.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```popsize_simul( data, n, K = 2, nfolds = 5, pi1, pi2, omega, alpha, margin = 0.005, iter = 100, twolist = TRUE ) ```

## Arguments

 `data` The data frame in capture-recapture format for which total population is to be estimated. The first K columns are the capture history indicators for the K lists. The remaining columns are covariates in numeric format. `n` The true population size. Required to calculate the added error. `K` The number of lists in the data. typically the first `K` rows of data. `nfolds` The number of folds to be used for cross fitting. `pi1` The function to calculate the conditional capture probabilities of list 1 using covariates. `pi2` The function to calculate the conditional capture probabilities of list 2 using covariates. `omega` The standard deviation from zero of the added error. `alpha` The rate of convergence. Takes values in (0, 1]. `margin` The minimum value the estimates can attain to bound them away from zero. `iter` An integer denoting the maximum number of iterations allowed for targeted maximum likelihood method. `twolist` The logical value of whether targeted maximum likelihood algorithm fits only two modes when K = 2.

## Value

A list of estimates containing the following components:

 `psi` A matrix of the estimated capture probability for each list pair, model and method combination. In the absence of covariates, the column represents the standard plug-in estimate. The rows represent the list pair which is assumed to be independent conditioned on the covariates. The columns represent the model and method combinations (PI = plug-in, DR = bias-corrected, TMLE = targeted maximum likelihood estimate)indicated in the columns. `sigma2` A matrix of the efficiency bound `sigma^2` in the same format as `psi`. `n` A matrix of the estimated population size n in the same format as `psi`. `varn` A matrix of the variance for population size estimate in the same format as `psi`. `N` The number of data points used in the estimation after removing rows with missing data.

## References

Das, M., Kennedy, E. H., & Jewell, N.P. (2021). Doubly robust capture-recapture methods for estimating population size. arXiv preprint arXiv:2104.14091

## Examples

 ```1 2 3 4 5 6``` ```simulresult = simuldata(n = 2000, l = 2) data = simulresult\$data psin_estimate = popsize_simul(data = data, pi1 = simulresult\$pi1, pi2 = simulresult\$pi2, alpha = 0.25, omega = 1) ```

drpop documentation built on Oct. 11, 2021, 9:06 a.m.