R: Stratification of a Population Given a Set of Boundaries

strata.bh {stratification}

R Documentation

Stratification of a Population Given a Set of Boundaries

Description

The function strata.bh stratifies a population given a set of boundaries. It calculates the stratum sample sizes and the anticipated coefficient of variation or relative root mean squared error.

Usage

strata.bh(x, bh, n = NULL, CV = NULL, Ls = 3, certain = NULL,
          alloc = list(q1 = 0.5, q2 = 0, q3 = 0.5), takenone = 0, 
          bias.penalty = 1, takeall = 0, takeall.adjust = TRUE, 
          rh = rep(1, Ls), model = c("none", "loglinear", "linear",
          "random"), model.control = list())

Arguments

`x`	A vector containing the values of the stratification variable `X` for every unit in the population.
`bh`	A vector of the `L-1` stratum boundaries `(b_1, b_2, \ldots, b_{L-1})` where `L` is the total number of strata (excluding the certainty stratum, if any). Therefore, if `takenone=0` then `L`=`Ls`, and if `takenone=1` then `L`=`Ls`+1.
`n`	A numeric: the target sample size. It has no default value. The argument `n` or the argument `CV` must be input.
`CV`	A numeric: the target coefficient of variation or relative root mean squared error if `takenone`=1. It has no default value. The argument `CV` or the argument `n` must be input.
`Ls`	A numeric: the number of sampled strata (take-none and certain strata are not counted in `Ls`). The default is 3.
`certain`	A vector giving the position, in the vector `x`, of the units that must be included in the sample (see `stratification-package`). By default `certain` is `NULL`, which means that no units are a priori chosen to be in the sample.
`alloc`	A list specifying the allocation scheme. The list must contain 3 numerics for the 3 exponents `q1`, `q2` and `q3` in the general allocation scheme (see `stratification-package`). The default is Neyman allocation (`q1`=`q3`=0.5 and `q2`=0)
`takenone`	A numeric: the number of take-none strata (0 or 1). The default is 0, i.e. no take-none stratum is included.
`bias.penalty`	A numeric between 0 and 1 giving the penalty for the bias in the anticipated mean squared error (MSE) of the survey estimator (see `stratification-package`). This argument is relevant only if `takenone`=1. The default is 1.
`takeall`	A numeric: the number of take-all strata (one of {0, 1, ..., `Ls`-1}). The default is 0, i.e. no take-all stratum is included.
`takeall.adjust`	A logical. If `TRUE` (the default), when `n_h > N_h` for a take-some stratum, the `takeall` argument is increased by one and the allocation is carried out again. This is done as long as `n_h \leq N_h` for every take-some stratum. If `FALSE`, no adjustment is made. Note: in other functions of the package stratification, this adjustment is not optional; it is made automatically (see `stratification-package`).
`rh`	A vector giving the anticipated response rates in each of the `Ls` sampled strata. A single number can be given if the rates do not vary among strata. The default is 1 in each stratum.
`model`	A character string identifying the model used to describe the discrepancy between the stratification variable `X` and the survey variable `Y`. It can be `"none"` if one assumes `Y=X`, `"loglinear"` for the loglinear model with mortality, `"linear"` for the heteroscedastic linear model or `"random"` for the random replacement model (see `stratification-package` for a description of these models). The default is `"none"`.
`model.control`	A list of model parameters (see `stratification-package`). The default values of the parameters correspond to the model `Y=X`.

Value

`Nh`	A vector of length `L` containing the population sizes `N_h`, i.e. the number of units in each stratum.
`nh`	A vector of length `L` containing the sample sizes `n_h`, i.e. the number of units to sample in each stratum. See `stratification-package` for information about the rounding used to get these integer values.
`n`	The total sample size (`sum(nh)`).
`nhnonint`	A vector of length `L` containing the non-integer values of the sample sizes, obtained directly from applying the allocation rule (see `stratification-package`).
`certain.info`	A vector giving statistics for the certainty stratum (see `stratification-package`). It contains `Nc`, the number of units chosen a priori to be in the sample, and `meanc`, the anticipated mean of `Y` for these units.
`opti.nh`	The final value of the criteria to optimize (either the total sample size `n` if a target `CV` was given or the RRMSE if a target `n` was given) calculated with the integer stratum sample sizes `nh`.
`opti.nhnonint`	The final value of the criteria to optimize (either the total sample size `n` if a target `CV` was given or the RRMSE if a target `n` was given) calculated with the non-integer stratum sample sizes `nhnonint`.
`meanh`	A vector of length `L` containing the anticipated means of `Y` in each stratum.
`varh`	A vector of length `L` containing the anticipated variances of `Y` in each stratum.
`mean`	A numeric: the anticipated global mean value of `Y`.
`RMSE`	A numeric: the root mean squared error (or standard error if `takenone`=0) of the anticipated global mean of `Y`. This is defined as the squared root of: (`bias.penalty` x bias of the mean)^2 + variance of the mean.
`RRMSE`	A numeric: the anticipated relative root mean squared error (or coefficient of variation if `takenone`=0) for the mean of `Y`, i.e. `RMSE` divided by `mean`.
`relativebias`	A numeric: the anticipated relative bias of the estimator, i.e. (`bias.penalty` x bias of the mean) divided by `mean`. If `takenone`=0, this numeric is zero.
`propbiasMSE`	A numeric: the proportion of the MSE attributable to the bias of the estimator, i.e. (`bias.penalty` x bias of the mean)^2 divided by the MSE of the `mean`. If `takenone`=0, this numeric is zero.
`stratumID`	A factor, having the same length as the input `x`, which values are either 1, 2, ..., `L` or `"certain"`. The value `"certain"` is given to units a priori chosen to be in the sample. This factor identifies, for each observation, the stratum to which it has been assigned.
`takeall`	The number of take-all strata in the final solution. Note: It is possible that `n_h=N_h` for non take-all strata because the condition for an automatic addition of a take-all stratum is `n_h>N_h`.
`call`	The function call (object of class "call").
`date`	A character string that contains the system date and time when the function ended.
`args`	A list of all the argument values input to the function or set by default.

Author(s)

Sophie Baillargeon Sophie.Baillargeon@mat.ulaval.ca and
Louis-Paul Rivest Louis-Paul.Rivest@mat.ulaval.ca

References

Baillargeon, S. and Rivest L.-P. (2011). The construction of stratified designs in R with the package stratification. Survey Methodology, 37(1), 53-65.

Examples

adjust <- strata.geo(x=USbanks, CV=0.01, Ls=4, alloc=c(0.35,0.35,0))
adjust
adjust$nhnonint
noadjust <- strata.bh(x=USbanks, bh=adjust$bh, CV=0.01, Ls=4,
            alloc=c(0.35,0.35,0), takeall=0, takeall.adjust=FALSE)
noadjust
noadjust$nhnonint
# without the adjustment for a take-all stratum, n is smaller than
# with the adjustment, but the target CV is not reached.

[Package stratification version 2.2-7 Index]