[R] Nested for loop

[Kirsten Morehouse]

Hi Caitlin and Ben,

Thanks for your responses! My issue is that I'd like to create one
continuous line, rather than 3 lines overlayed.

The code I've attached works for a population of 400 and samples 100 times.
I'd like to extend this to 300 samples and 3 populations. So, the x-axis
would range from 0-300 samples.

What I'm having trouble with is finding a way to change the population
mid-way through the function. I want samples 1-100 to be taken from a
population of 400, samples 101-200 to be taken from a sample of 800 and
samples 201-300 from a population of 300. The end result should look
something like a heart rate monitor.

Aside from the rationale, does what I'm explaining make sense?

Best,

Kirsten

On Mon, Aug 7, 2017 at 3:18 PM, Caitlin <bioprogrammer at gmail.com> wrote:

> Hi.
>
> A nested for loop is not terribly efficient (it's O(n^2)). Can you
> vectorize it? If so, this would be a far more efficient and faster approach.
>
> ~Caitlin
>
> On Saturday, August 5, 2017, Kirsten Morehouse <kmoreho1 at 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
>>
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>>
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