strata.bh: Stratification of a Population Given a Set of Boundaries

In stratification: Univariate Stratification of Survey Populations

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 (b1, b2, ..., bL-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 nh>Nh 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 nh<=Nh 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 Nh, i.e. the number of units in each stratum.
nh	A vector of length L containing the sample sizes nh, 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 [e-mail] and
Louis-Paul Rivest [e-mail]

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.

See Also

print.strata, plot.strata, strata.cumrootf, strata.geo, strata.LH

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.

stratification documentation built on April 7, 2022, 1:13 a.m.