Balanced Sampling

It's unbelievably fast!

I installed it immediately and the results in terms of execution times are exciting!

I can't survive without it! It solved all my problems in terms of time of computation.

It's really fast. It's C++

The implementations are written in C++ and make use of the excellent Rcpp package.

# How fast is it?
# Let's check with N = 100 000 
# and 5 balancing variables
N = 100000;        # population size
n = 100;           # sample size
p = rep(n/N,N);    # inclusion probabilities
# matrix of 5 auxiliary variables
X = cbind(p,runif(N),runif(N),runif(N),runif(N)); 
system.time(cube(p,X));  
   user  system elapsed 
  0.228   0.008   0.237 

N = 100000;                      # A population of size 100 000
n = 50;                          # Sample size
p = rep(n/N,N);                  # Inclusion probabilities
X = cbind(runif(N),runif(N));    # Auxiliary variables

system.time(lpm2(p,X));
   user  system elapsed 
 45.605   0.048  45.659 
 
system.time(lpm2_kdtree(p,X));
   user  system elapsed 
  0.372   0.004   0.375 

# For no ties it gives identical results!
  
set.seed(12345);
s1 = lpm2(p,X);

set.seed(12345);
s2 = lpm2_kdtree(p,X);

print(sum(s1!=s2))
 0

New kd-tree implementation of LPM2! It's much faster.

Thanks to Jonathan Lisic for providing this new implementation of lpm2! Now available in the R package SamplingBigData (imported to BalancedSampling).

Spatially balanced sample. It's representative.

If the inclusion probabilities are equal, then a well spread sample is representative in the auxiliary variables, i.e. the distribution in the sample is very close to the distribution in the population. The image shows a spatially balanced sample (red dots) selected with the local pivotal method.

set.seed(1234567);
N = 1000;                     # population size
n = 100;                      # sample size
p = rep(n/N,N);               # inclusion probabilities
X = cbind(runif(N),runif(N)); # matrix of auxiliary variables
s = lpm1(p,X);                # select sample

plot(X[,1],X[,2],xlab="x",ylab="y",pch=19,col="gray");
points(X[s,1],X[s,2],pch=19,col="red"); 

Spatially balanced sampling is efficient! For any smooth relationship.

set.seed(12345);
N = 200;           # population size
n = 40;            # sample size
p = rep(n/N,N);    # inclusion probabilities
x = runif(N,0,10); # auxiliary variable
# target variable related to x
y = 4 + 2 * x + 2 * x^2 + rnorm(N,0,1);

nrs = 1000;
ht1 = ht2 = rep(0,nrs);
for(i in 1:nrs){
  # spatially balanced
  s = lpm2(p,cbind(x));
  ht1[i] = sum(y[s]/p[s]);
  # simple random
  s = sample(N,n);
  ht2[i] = sum(y[s]/p[s]);
}
res = cbind(ht1,ht2);
colnames(res) = c("Spatially balanced sampling","Simple random sampling");
boxplot(res);