How to draw a systematic sample from a geographic population?

Question

I have a data frame (df) representing a 100X100 unit square, and after having created a geographic population like this (z= x+y, where x<-df$x, and y<-df$y), I need to extract a systematic sample of size n=100 from it. How can I do it ?

Answer 1

To draw a systematic (iid) sample from a unit square, here is one method:

# set random seed for reproducibility
set.seed(123)
# create a 100X2 matrix of unit square observations
myUnitSquareSample <- cbind("x"=runif(100), "y"=runif(100))

To put this sample in a data.frame together with your z variable:

df <- data.frame("x"=myUnitSquareSample[,"x"],
                 "y"=myUnitSquareSample[,"y"],
                 "z"=rowSums(myUnitSquareSample))

If you already have a pre-existing data.frame, df, say of 10,000 observations. You can employ the sample function, as suggested by @kunal-puri as follows:

# set random seed for reproducibility
set.seed(11111)

# choose the set of 100 rows
mySample <- sample(1:nrow(df), size=100)
# extract sampled observations from df
mySampled.df <- df[mySample,]

It is a good idea to keep the selected set of rows in its own vector in case you need to use it further on in your script.

To extract an evenly spaced sample, try the following:

envelySpacedMat <- expand.grid(y=seq(0, 1, length.out=10), 
                                x=seq(0, 1, length.out=10))

    df <- data.frame("x"=envelySpacedMat[,"x"],
                 "y"=envelySpacedMat[,"y"],
                 "z"=rowSums(envelySpacedMat))

This selects the borders, to avoid this, you can alter the from and to arguments slightly.

If you would like to select 100 observations from an existing data.frame that are more or less evenly spaced, you might try the following:

# select 100 obs roughly evenly dispersed:
obsSystematic <- as.integer(seq(from=1, to=nrow(df), length.out = 100))

mySystematicdf <-df[obsSystematic,]