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Optimal allocation of sample sizes

FillStrata.Rd

This function finds an optimal allocation by filling up strata one unit at a time. This approach works when the variance function of n decreases smoothly (The derivative should be strictly increasing).

Usage

FSmatrix(s2, N, ...)

FStotnAlloc(s2, N, totn, ...)

FSvarAlloc(s2, N, varLimits, group, ...)

FScvAlloc(s2, N, totY, cvLimits, group, ...)

FScvAlloc2(s2, N, totYgroup, cvLimits, group, ...)

FSvarLimits(totY, cvLimits, group, ...)

FStotVar(s2, N, min_n, group, ...)

FStotCV(s2, N, totY, min_n, group, ...)

FillStrata(
  s2,
  N,
  totVar = function(s2, n, N) {
     s2 * N * (N - n)/n
 },
  nullcorrection = 1e+20,
  totn = min(sum(max_n_exact), 20000),
  min_n = NULL,
  use_n = NULL,
  corrSumVar = FALSE,
  dotprint = totn > 1000,
  varLimits = NULL,
  group = rep("All", length(s2)),
  intern = FALSE,
  max_n = N,
  totY = NULL,
  cvLimits = NULL,
  totYgroup = NULL,
  groupNames = NULL,
  returnGroupN = FALSE,
  returnGroupn = FALSE,
  returnTable = FALSE,
  returnTotYgroup = FALSE,
  returnVarLimits = FALSE,
  returnMulti = FALSE,
  returnMatrix = FALSE,
  totnGroup = NULL,
  min_nGroup = NULL
)

Arguments

s2

An estimate for the variance within each strata. For example s2 = c(35, 3, 2, 30, 7)

N

The population size within each strata. For example N = c(100, 100, 500, 50, 150)

...

Additional arguments to be passed to the function.

totn

The total desired sample size

varLimits

The desired maximum variance for each group. Note: When varLimits is given, a different output value is returned - the sample size that fulfills the required group variance for totVar. If varLimits = Inf, the output is the group sum of totVar with "n = min_n".

group

A vector or dummy matrix giving the groups to be used with varLimits

totY

Estimate of total Y in each stratum.

cvLimits

The desired maximum CV for each group. This can be a single value or a vector of values.

totYgroup

Estimate of total Y in each group. Alternative instead of totY.

min_n

A minimum sample size in each stratum. This can be a single number used in all strata or a vector of numbers (one for each stratum).

totVar

The function for calculating the total variance from s2, n (sample size) and N as inputs. The function should be able to handle vectors as inputs and give a vector as an output.

nullcorrection

Variance at n=0 is set to nullcorrection times variance at n=1. A large value is needed by the algorithm (not Inf).

use_n

Matrix with the same number of columns as there are strata. Each column should contain the desired sample size choices (will accept missing values)

corrSumVar

Logical value giving if the corrected variance should be used. Default is FALSE.

dotprint

Condition to invoke printing of "---------#--------...." during calculations. Default is set for when totn > 1000.

intern

Logical value giving if the function is being used internally within this or another function or not. Default is set to FALSE.

max_n

A maximum sample size in each stratum. This can be a single number used in all strata or a vector of numbers (one for each stratum).

groupNames

Alternative instead of finding group names from other input.

returnGroupN

Logical on whether to return the population group size.

returnGroupn

Logical on whether to return the sample group size.

returnTable

Logical on whether to return the table

returnTotYgroup

Logical on whether to return the total Y values

returnVarLimits

Logical on whether to return the Y limits

returnMulti

Logical on whether to return the multi

returnMatrix

Logical on whether to return the matrix

totnGroup

Maximal total sample size within group (override cvLimits)

min_nGroup

Minimal total sample size within group (override cvLimits)

Value

The output from FSmatrix (FillStrata with returnMatrix=TRUE) is a two-dimensional list.

Column:Strata

Output values according to each strata.

Column:Group

Output values according to each group as specified by input.

Column:All

Output by treating all strata as a single group.

Row:n

Allocated sample size

Row:N

Population size

Row:totVar

Total variance

Row:totY

Total Y

Row:cv

CV (%)

Row:varLimits

As input (only Group)

Row:cvLimits

As input or computed from varLimits (only Group)

The output from FillStrata is a list with two elements when varLimits or cvLimits is not used.

filledstrata

Strata is filled sequentially according to this vector.

sumVar

Total variance for all values of total n.

When returnTable=TRUE and when varLimits or cvLimits is used (FStotnAlloc, FSvarAlloc, FScvAlloc, FScvAlloc2) the output is the allocated sample size in each strata.

Other elements of the FSmatrix-output can be obtained by setting other return-parameters to TRUE or by using varLimits=Inf or cvLimits=Inf.

Examples


# Examples with 5 strata based on FSmatrix
  s2    = c(35, 3, 2, 30, 7)         # Variance estimate
  N     = c(100, 100, 500, 50, 150)  # N in each strata
  names(N) = paste("st",1:5,sep="")  # Strata-names
  totY  = c(8800,900,5500,400,300)   # Totals in each strata
  g     = c("grA","grA","grB","grB","grB") # Two groups
 
# Total sample size of 200 chosen in advance
  m = FSmatrix(s2=s2,N=N,totn=200,group=g)
  # Three ways of getting allocated n in each strata
  m[,1]$n
#> st1 st2 st3 st4 st5 
#>  55  16  66  26  37 
  m[1,]$Strata
#> st1 st2 st3 st4 st5 
#>  55  16  66  26  37 
  m[[1,1]]
#> st1 st2 st3 st4 st5 
#>  55  16  66  26  37 
  
# Alloc from varLimits
  vL = c(5000,10000)   # variance limits for groups 
  m = FSmatrix(s2=s2,N=N,varLimits=vL,group=g)
  m[[1,1]] # Allocated n in each strata
#> st1 st2 st3 st4 st5 
#>  52  15  72  28  41 
  m[3,] # Total variance in strata, group (less than limits) and all.
#> $Strata
#>      st1      st2      st3      st4      st5 
#> 3230.769 1700.000 5944.444 1178.571 2791.463 
#> 
#> $Group
#>      grA      grB 
#> 4930.769 9914.479 
#> 
#> $All
#>      all 
#> 14845.25 
#> 
  
#  Calculate CV from totY in strata from known allocation (20%)
  m = FSmatrix(s2=s2,N=N,totY=totY,max_n=round(N/5),group=g)
  m[5,] # CV in strata, group and all.
#> $Strata
#>       st1       st2       st3       st4       st5 
#>  1.344564  3.849002  1.149919 19.364917 21.602469 
#> 
#> $Group
#>      grA      grB 
#> 1.271013 1.921996 
#> 
#> $All
#>      all 
#> 1.078392 
#>