# lpm1: Local pivotal method 1 In BalancedSampling: Balanced and Spatially Balanced Sampling

## Description

Select spatially balanced samples with prescribed inclusion probabilities from a finite population. Euclidean distance is used in the `x` space.

## Usage

 `1` ```lpm1(prob,x) ```

## Arguments

 `prob` vector of length N with inclusion probabilities `x` matrix of (standardized) auxiliary variables of N rows and q columns

## Value

Returns a vector of selected indexes in 1,2,...,N. If the inclusion probabilities sum to n, where n is integer, then the sample size is fixed (n).

## References

Grafstr<c3><b6>m, A., Lundstr<c3><b6>m, N.L.P. and Schelin, L. (2012). Spatially balanced sampling through the Pivotal method. Biometrics 68(2), 514-520.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```## Not run: # Example 1 set.seed(12345); 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]); # plot population points(X[s,1],X[s,2], pch=19); # plot sample # Example 2 # check inclusion probabilities set.seed(12345); p = c(0.2, 0.25, 0.35, 0.4, 0.5, 0.5, 0.55, 0.65, 0.7, 0.9); # prescribed inclusion probabilities N = length(p); # population size X = cbind(runif(N),runif(N)); # some artificial auxiliary variables ep = rep(0,N); # empirical inclusion probabilities nrs = 10000; # repetitions for(i in 1:nrs){ s = lpm1(p,X); ep[s]=ep[s]+1; } print(ep/nrs); ## End(Not run) ```

BalancedSampling documentation built on May 2, 2019, 1:04 p.m.