Hi Kirsten,
I can run your example code but I can't quite follow your division of sampling.
Can you restate the the task? Below is what I think you are asking for, but I
have the feeling I may be off the mark.
Set A: 400 samples, draw 100 in range of 5 to 15
Set B: 800 samples, draw 100 in range of 5 to 15
Set C: 300 samples, draw 100 in range of 5 to 15
Ben
> On Aug 5, 2017, at 9:21 AM, Kirsten Morehouse <kmore...@swarthmore.edu> wrote:
>
> Hi! Thanks for taking the time to read this.
>
> The code below creates a graph that takes 100 samples that are between 5%
> and 15% of the population (400).
>
> What I'd like to do, however, is add two other sections to the graph. It
> would look something like this:
>
> from 1-100 samples take 100 samples that are between 5% and 15% of the
> population (400). From 101-200 take 100 samples that are between 5% and 15%
> of the population (800). From 201-300 take 100 samples that are between 5%
> and 15% of the population (300).
>
> I assume this would require a nested for loop. Does anyone have advice as
> to how to do this?
>
> Thanks for your time. Kirsten
>
> ## Mark-Recapture
> ## Estimate popoulation from repeated sampling
>
> ## Population size
> N <- 400
> N
>
> ## Vector labeling each item in the population
> pop <- c(1:N)
> pop
>
> ## Lower and upper bounds of sample size
> lower.bound <- round(x = .05 * N, digits = 0)
> lower.bound ## Smallest possible sample size
>
> upper.bound <- round(x = .15 * N, digits = 0)
> upper.bound ## Largest possible sample size
>
> ## Length of sample size interval
> length.ss.interval <- length(c(lower.bound:upper.bound))
> length.ss.interval ## total possible sample sizes, ranging form lower.bound
> to upper.bound
>
> ## Determine a sample size randomly (not a global variable...simply for
> test purposes)
> ## Between lower and upper bounds set previously
> ## Give equal weight to each possible sample size in this interval
> sample(x = c(lower.bound:upper.bound),
> size = 1,
> prob = c(rep(1/length.ss.interval, length.ss.interval)))
>
> ## Specify number of samples to take
> n.samples <- 100
>
> ## Initiate empty matrix
> ## 1st column is population (item 1 thorugh item 400)
> ## 2nd through nth column are all rounds of sampling
> dat <- matrix(data = NA,
> nrow = length(pop),
> ncol = n.samples + 1)
>
> dat[,1] <- pop
>
> dat
>
> ## Take samples of random sizes
> ## Record results in columns 2 through n
> ## 1 = sampled (marked)
> ## 0 = not sampled (not marked)
> for(i in 2:ncol(dat)) {
> a.sample <- sample(x = pop,
> size = sample(x = c(lower.bound:upper.bound),
> size = 1,
> prob = c(rep(1/length.ss.interval,
> length.ss.interval))),
> replace = FALSE)
> dat[,i] <- dat[,1] %in% a.sample
> }
>
> ## How large was each sample size?
> apply(X = dat, MARGIN = 2, FUN = sum)
> ## 1st element is irrelevant
> ## 2nd element through nth element: sample size for each of the 100 samples
>
> ## At this point, all computations can be done using dat
>
> ## Create Schnabel dataframe using dat
> ## Google the Schnabel formula
>
> schnabel.comp <- data.frame(sample = 1:n.samples,
> n.sampled = apply(X = dat, MARGIN = 2, FUN =
> sum)[2:length(apply(X = dat, MARGIN = 2, FUN = sum))]
> )
>
> ## First column: which sample, 1-100
> ## Second column: number selected in that sample
>
>
> ## How many items were previously sampled?
> ## For 1st sample, it's 0
> ## For 2nd sample, code is different than for remaning samples
>
> n.prev.sampled <- c(0, rep(NA, n.samples-1))
> n.prev.sampled
>
> n.prev.sampled[2] <- sum(ifelse(test = dat[,3] == 1 & dat[,2] == 1,
> yes = 1,
> no = 0))
>
> n.prev.sampled
>
> for(i in 4:ncol(dat)) {
> n.prev.sampled[i-1] <- sum(ifelse(test = dat[,i] == 1 &
> rowSums(dat[,2:(i-1)]) > 0,
> yes = 1,
> no = 0))
> }
>
> schnabel.comp$n.prev.sampled <- n.prev.sampled
>
> ## n.newly.sampled: in each sample, how many items were newly sampled?
> ## i.e., never seen before?
> schnabel.comp$n.newly.sampled <- with(schnabel.comp,
> n.sampled - n.prev.sampled)
>
> ## cum.sampled: how many total items have you seen?
> schnabel.comp$cum.sampled <- c(0,
> cumsum(schnabel.comp$n.newly.sampled)[2:n.samples-1])
>
> ## numerator of schnabel formula
> schnabel.comp$numerator <- with(schnabel.comp,
> n.sampled * cum.sampled)
>
> ## denominator of schnable formula is n.prev.sampled
>
> ## pop.estimate -- after each sample (starting with 2nd -- need at least
> two samples)
> schnabel.comp$pop.estimate <- NA
>
> for(i in 1:length(schnabel.comp$pop.estimate)) {
> schnabel.comp$pop.estimate[i] <- sum(schnabel.comp$numerator[1:i]) /
> sum(schnabel.comp$n.prev.sampled[1:i])
> }
>
>
> ## Plot population estimate after each sample
> if (!require("ggplot2")) {install.packages("ggplot2"); require("ggplot2")}
> if (!require("scales")) {install.packages("scales"); require("scales")}
>
>
> small.sample.dat <- schnabel.comp
>
> small.sample <- ggplot(data = small.sample.dat,
> mapping = aes(x = sample, y = pop.estimate)) +
> geom_point(size = 2) +
> geom_line() +
> geom_hline(yintercept = N, col = "red", lwd = 1) +
> coord_cartesian(xlim = c(0:100), ylim = c(300:500)) +
> scale_x_continuous(breaks = pretty_breaks(11)) +
> scale_y_continuous(breaks = pretty_breaks(11)) +
> labs(x = "\nSample", y = "Population estimate\n",
> title = "Sample sizes are between 5% and 15%\nof the population") +
> theme_bw(base_size = 12) +
> theme(aspect.ratio = 1)
>
> small.sample
>
> [[alternative HTML version deleted]]
>
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Ben Tupper
Bigelow Laboratory for Ocean Sciences
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