saSampleAlloc: Optimal Allocation Using Simulated Annealing

In jlisic/saAlloc: Optimal Allocation of Sampling Units to Form Strata using Simulated Annealing

Description

This function exchanges sample allocations between strata to minimize the CV of a set of known administrative variables. This is accomplished by through simulated annealing, where proposed changes in allocations are accepted or rejected based on a penalized objective function. The penalized objective function takes the form of the sum of an L2 norm and a penalty function. The first L2 norm is the vector of differences between the CVs for the current allocation and the target CVs. The penalty function is the dot product between a vector of penalty values and the vector of CVs for the current allocation.

Usage

saSampleAlloc(
  total,
  S2,
  targetCV,
  sampleSize,
  strataSize, 
  locationAdjustment,
  scaleAdjustment,
  iterations=100,
  p = 2,                   # l2 norm of the penalty function
  penalty = -1,            # negative penalties are ignored
  cooling = 0,
  preserveSatisfied=TRUE,
  fpc = TRUE
   )

Arguments

total	(Required) A matrix where each row is a replicate population total and each column is a characteristic of the sampling population used for allocation. When replicates are used, the average CV of each characteristic is used in the objective function.
S2	(Required) A matrix where each row identifies a stratum (in order) and each column is a characteristic of the sampling population used for allocation. The values of this matrix is the variance estimate for each sampling unit within each stratum (S^2). When replicates are used for total, a variance must also be provided for each replicate. This is done by appending each replicate matrix of variances to the S2 matrix in the same order it appears in total.
targetCV	(Required) A vector of target CVs. This vector must be of equal length to the number of columns of total.
sampleSize	(Required) sample size, either an integer valued scalar that will be equally split between strata, or a sample size for each strata. When the sample size cannot be split excess sample allocations will be given to strata in increasing order.
strataSize	(Required) strata size, an integer valued array or population sizes by stratum.
locationAdjustment	A constant value added to the population variable for each administrative variable, this is of the same size and layout of S2.
scaleAdjustment	A constant value multiplied by the population variable (before the location adjustment) for each administrative variable, this is of the same size and layout of S2.
iterations	Number of iterations of the allocation.
p	The exponent for the penalty function, fractional exponents are available.
penalty	The penalty vector used for each of the CV targets penalties. Penalties with negative elements are ignored. A scalar value may be used, and will be repeated for all CVs.
cooling	Cooling Schedule (0 = exchange only).
preserveSatisfied	TRUE implies that any constraint that is met for an accepted state is kept, FALSE allows for met CVs to be violated by accepted states.
fpc	TRUE use a finite population correction factor (fpc), FALSE do not use a fpc.

Value

accept	Matrix with three columns and a row for each iteration, "change": change in objective function, "U": uniform random variable, "accepted": 1 - accepted, 0 - not accepted "selected": index of PSU, "from": current stratum of selected PSU , "to": candidate stratum of selected PSU, "n_h": sample size (h is the index or label associated with strata), column names or numbers if not presented
cost	Objective Function
label	Final Label
sampleSize	Final Sample Size

Examples

# data set with 100 observations and four 
# characteristics split between two strata
x <- matrix(rnorm( 100*4 ),ncol=4)  

total <- colSums(x)

S2 <- apply( x, 2, var)

# run minCV for a sample size of 20
b <- saSampleAlloc(
  total,
  S2,
  strataSize=rep(50,2),
  targetCV=c(0.08, 0.10, 0.05, 0.08),
  sampleSize=20
)

summary(b)

jlisic/saAlloc documentation built on May 19, 2019, 12:47 p.m.