dga-package {dga}

Capture-Recapture Estimation using Bayesian Model Averaging

Description

Performs Bayesian model averaging over all decomposable graphical models, each representing a different list dependence structure, with the goal of estimating the number of uncounted elements from the universe of elements that could have been recorded or “captured". The code here is an implementation of the model described in Madigan and York (1997).

Details

Package:	dga
Type:	Package
Version:	1.2
Date:	2015-04-16
License:	GPL >=2

Author(s)

James Johndrow [e-mail], Kristian Lum [e-mail], and Patrick Ball [e-mail]

Maintainer: Kristian Lum [e-mail]

References

Madigan, David, and Jeremy C. York. "Bayesian methods for estimation of the size of a closed population." Biometrika 84.1 (1997): 19-31.

Examples

### This simulated example goes through the whole process for 3 lists.###
library(chron)
# Simulate some data
N <- 1000 # true population size
num.lists <- 3 # number of lists

# simulate 3 lists independently 'capturing'
l1 <- rbinom(N, 1, .2)
l2 <- rbinom(N, 1, .25)
l3 <- rbinom(N, 1, .3)

overlaps <- data.frame(l1, l2, l3)

# simulate dates of recording
dates <- paste(
  rep(2015, N), "-", sample(1:4, N, replace = TRUE), "-",
  sample(1:28, N, replace = TRUE)
)
dates <- chron(dates, format = c(dates = "y-m-d"))

# save true number in each stratum for comparison later
truth <- table((months(dates)))[1:4]

# remove dates of unrecorded elements
dates <- dates[apply(overlaps, 1, sum) > 0]

# remove individuals not recorded on any list
overlaps <- overlaps[apply(overlaps, 1, sum) > 0, ]

# stratify by date
strata <- make.strata(overlaps, dates = dates, date.defs = "monthly")

# check to make sure that all strata are OK
check <- check.strata(strata)

# look at strata, just to make sure
par(mfrow = c(2, 2), mar = rep(1, 4))
for (i in 1:nrow(strata$overlap.counts)) {
  venn3(strata$overlap.counts[i, ],
    main = rownames(strata$overlap.counts)[i],
    cex.main = 1
  )
}


# load the graphs to make the estimates
data(graphs3)

# select expansion factor defining the largest number of unrecorded elements.
# this makes Nmissing <- 0:(sum(Y)*fac)
fac <- 5

# set prior
delta <- 1 / 2^num.lists

# loop over strata to calculate posterior distributions of
# the total population size for each stratum
par(mfrow = c(2, 2), mar = rep(1.75, 4))
# if using Rstudio, make sure your plot window is pretty big here!
for (i in 1:nrow(strata$overlap.counts)) {
  Nmissing <- 0:(sum(strata$overlap.counts[i, ]) * fac)
  Y <- array(strata$overlap.counts[i, ], dim = rep(2, num.lists))
  weights <- bma.cr(Y, Nmissing, delta, graphs3)
  plotPosteriorN(weights, Nmissing + sum(strata$overlap.counts[i, ]),
    main = rownames(strata$overlap.counts)[i]
  )
  points(truth[i], .5 * max(weights), col = "red", pch = 16, cex = 2)
}