为分层抽样准备抽样分布的最佳 R 包函数

Question

I'm attempting to prepare a demonstration in R of how the repeated stratified random sampling of a small population results in a near-normal sampling distribution of means. As an example consider the R code below (which works but is very slow due to looping).

#Dummy population made up of dice throws - 18 per row
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
P1 <- as.data.frame(c(5,6,5,1,6,4,2,2,4,4,6,6,5,2,3,5,1,6))
P1$Zn <- 1
names(P1) <- c('Die','Zn')
Dt <- P1

P2 <- as.data.frame(c(2,5,4,5,5,5,3,3,2,5,6,1,2,5,4,3,6,1))
P2$Zn <- 2
names(P2) <- c('Die','Zn')
Dt <- rbind(Dt,P2)

# Empty dataframe to hold random draws
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Smps <- data.frame(Die = numeric(), Zn= numeric(),Drw = numeric())

# Draw stratifed samples one from each row
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
print(paste('Start','at',Sys.time()))
n <- 10000          # number of draws
r <- 2              # number of rows (the strata)
for (j in 1:n){
  # for a 2 strata
  for (i in 1:r){
    #sub set strata
    x <- subset(Dt, Dt$Zn == i)
    # random sample
    y <- x[sample(1:18,1),]
    y$Drw <- j
    #append sample
    Smps <- rbind(Smps,y)
  }
  # report progress
  if(right(j,3) == '000'){
    print(paste(j,'at',Sys.time()))
    flush.console()
  }
}

# Compute the sample means
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mns <-aggregate(Smps[, 1], list(Smps$Drw), mean)

# Density plot of means
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
d <- density(Mns$x)
plot(d,xlab = 'Means', las=1, main = '')
polygon(d, col="blue", border="blue")

I'm expecting there is an R package with a function that does this type of stratified sampling but I am struggling to find the one that works in the manner I can understand. Something that inputs a data frame with a grouping field and the number of samples to be drawn from each group is something I'm expecting has already been written to allow a repeat sampling by a group. Any pointers to examples that work would be appreciated. Ideally, I would like to prepare to say 100,000 stratified samples from a known population with many more strata and then plot the distribution of the means (but quickly)

Answer 1

After a while away from this problem, I found a package called 'fifer' ( https://www.rdocumentation.org/packages/fifer/versions/1.1 ) which seem contained a stratified function in a package but unfortunately, this package does not work on the latest versions of R. I did, however, find a clever stratified function from Ananda Mahto ( https://gist.github.com/mrdwab/6424112 ) which works well but at the cost of having a rather long function in your script rather than the one line of loading a package. My solution to the problem above using this function is below.

#Dummy population made up of dice throws - 18 per row
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
P1 <- as.data.frame(c(5,6,5,1,6,4,2,2,4,4,6,6,5,2,3,5,1,6))
P1$Zn <- 1
names(P1) <- c('Die','Zn')
Dt <- P1

P2 <- as.data.frame(c(2,5,4,5,5,5,3,3,2,5,6,1,2,5,4,3,6,1))
P2$Zn <- 2
names(P2) <- c('Die','Zn')
Dt <- rbind(Dt,P2)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Stratfed function from web
# https://gist.github.com/mrdwab/6424112
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

stratified <- function(df, group, size, select = NULL, 
                       replace = FALSE, bothSets = FALSE) {
  if (is.null(select)) {
    df <- df
  } else {
    if (is.null(names(select))) stop("'select' must be a named list")
    if (!all(names(select) %in% names(df)))
      stop("Please verify your 'select' argument")
    temp <- sapply(names(select),
                   function(x) df[[x]] %in% select[[x]])
    df <- df[rowSums(temp) == length(select), ]
  }
  df.interaction <- interaction(df[group], drop = TRUE)
  df.table <- table(df.interaction)
  df.split <- split(df, df.interaction)
  if (length(size) > 1) {
    if (length(size) != length(df.split))
      stop("Number of groups is ", length(df.split),
           " but number of sizes supplied is ", length(size))
    if (is.null(names(size))) {
      n <- setNames(size, names(df.split))
      message(sQuote("size"), " vector entered as:\n\nsize = structure(c(",
              paste(n, collapse = ", "), "),\n.Names = c(",
              paste(shQuote(names(n)), collapse = ", "), ")) \n\n")
    } else {
      ifelse(all(names(size) %in% names(df.split)),
             n <- size[names(df.split)],
             stop("Named vector supplied with names ",
                  paste(names(size), collapse = ", "),
                  "\n but the names for the group levels are ",
                  paste(names(df.split), collapse = ", ")))
    }
  } else if (size < 1) {
    n <- round(df.table * size, digits = 0)
  } else if (size >= 1) {
    if (all(df.table >= size) || isTRUE(replace)) {
      n <- setNames(rep(size, length.out = length(df.split)),
                    names(df.split))
    } else {
      message(
        "Some groups\n---",
        paste(names(df.table[df.table < size]), collapse = ", "),
        "---\ncontain fewer observations",
        " than desired number of samples.\n",
        "All observations have been returned from those groups.")
      n <- c(sapply(df.table[df.table >= size], function(x) x = size),
             df.table[df.table < size])
    }
  }
  temp <- lapply(
    names(df.split),
    function(x) df.split[[x]][sample(df.table[x],
                                     n[x], replace = replace), ])
  set1 <- do.call("rbind", temp)

  if (isTRUE(bothSets)) {
    set2 <- df[!rownames(df) %in% rownames(set1), ]
    list(SET1 = set1, SET2 = set2)
  } else {
    set1
  }
}


# Empty dataframe to hold random draws
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Smps <- data.frame(Die = numeric(), Zn = numeric())

# Right function for reporting progress
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
right = function(text, num_char) {
  substr(text, nchar(text) - (num_char-1), nchar(text))
}

# Draw stratifed samples one from each row
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
n <- 10000          # number of draws
for (j in 1:n){
    y <- stratified(Dt,"Zn",1)
    y <- cbind(y,j)
    Smps <- rbind(Smps,y)
  # report progress
  if(right(j,3) == '000'){
    print(paste(j,'at',Sys.time()))
    flush.console()
  }
}

# Compute the sample means
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mns <-aggregate(Smps[, 1], list(Smps$j), mean)

# Density plot of means
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
d <- density(Mns$x)
plot(d,xlab = 'Means', las=1, main = '')
polygon(d, col="blue", border="blue")