var.strata: Anticipated Variances and RRMSE from a Stratified Design for...

In stratification: Univariate Stratification of Survey Populations

Anticipated Variances and RRMSE from a Stratified Design for a Survey Variable Y

Description

var.strata calculates the anticipated means, variances and relative root mean squared error (RRMSE) obtained when applying a stratified design to a survey variable Y. The variable Y can be input or it can be defined from X by a specified loglinear with mortality, heteroscedastic linear or random replacement model.

print.var.strata prints a "var.strata" object, presenting the stratification information into a table.

Usage

var.strata(strata, y = NULL, rh = strata$args$rh, rh.postcorr = 
           FALSE, model = c("none", "loglinear", "linear", "random"), 
           model.control = list())

## S3 method for class 'var.strata'
print(x, ...)

Arguments

strata	An object of class "strata", which represents a stratified design.
y	A vector containing the values of the survey variable Y for every unit of the population, respecting the order of the units in the x-vector used to create strata. The default is that Y is not given.
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 to use the rates given in the strata.bh object.
rh.postcorr	A logical. If TRUE, a posterior correction for non-response is applied. This correction takes into account the non-response in the strata.bh object. It is only available when the stratified design strata had a target CV. The default is FALSE, i.e. no posterior correction is made (see Details).
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.
x	An object of class "var.strata" to print.
...	Additional arguments affecting the print produced.

Details

POSTERIOR CORRECTION FOR NON-RESPONSE (with a target CV only

The optional posterior correction for non-response is done as follows. For each take-some stratum, nh is increased if the input rh is lower than the anticipated response rate in the strata.bh object, and nh is decreased if the input rh is higher than the anticipated response rate given when creating the strata.bh object. The modification of nh is done by multiplying it by strata$args$rh/rh.

The weakness of this posterior correction is that it cannot take into account non-response in a take-all stratum. In that stratum, nh cannot be increased since it is equal to Nh. To correctly account for non-response in a take-all stratum, the boundary of the stratum has to be lowered. This is what the generalized Lavallee-Hidiroglou method does (strata.LH).

Value

nh	A vector of length L containing the integer sample sizes nh, i.e. the number of units to sample in each stratum. This vector can be different than strata$nh if rh.postcorr=TRUE.
n	The total sample size (sum(nh)). This number can be different than strata$n if rh.postcorr=TRUE.
nhnonint	A vector of length L containing the non-integer values of the sample sizes. This vector can be different than strata$nhnonint if rh.postcorr=TRUE.
certain.info	A vector giving statistics for the certainty stratum (see stratification-package). It contains Nc, the number of units chosen a priori to be in the sample, and meanc, the anticipated mean of Y for these units.
meanh	A vector of length L containing the anticipated means of Y in each stratum.
varh	A vector of length L containing the anticipated variances of Y in each stratum.
mean	A numeric: the anticipated global mean value of Y.
RMSE	A numeric: the root mean squared error (or standard error if strata$args$takenone=0) of the anticipated global mean of Y. This is defined as the squared root of: (bias.penalty x bias of the mean)^2 + variance of the mean.
RRMSE	A numeric: the anticipated relative root mean squared error (or coefficient of variation if strata$args$takenone=0) for the mean of Y, i.e. RMSE divided by mean.
relativebias	A numeric: the anticipated relative bias of the estimator, i.e. (bias.penalty x bias of the mean) divided by mean. If strata$args$takenone=0, this numeric is zero.
propbiasMSE	A numeric: the proportion of the MSE attributable to the bias of the estimator, i.e. (bias.penalty x bias of the mean)^2 divided by the MSE of the mean. If strata$args$takenone=0, this numeric is zero.
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 arguments input to the function or used 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

strata.bh, strata.cumrootf, strata.geo, strata.LH

Examples

nomodel <- strata.LH(x=Sweden$REV84, CV=0.05, Ls=3, alloc=c(0.5,0,0.5),
          takeall=1, model="none")
# We can give a vector of the Y values for every unit in the population
var.strata(nomodel, y=Sweden$RMT85) 
# Or specify a model between X and Y
var.strata(nomodel, model="loglinear", model.control=list(beta=1.058355,
           sig2=0.06593083, ph=1))
# Compared to taking into account the model in the optimization
model <- strata.LH(x=Sweden$REV84, CV=0.05, Ls=3, alloc=c(0.5,0,0.5),
         takeall=1, model="loglinear", model.control=list(beta=1.058355,
		     sig2=0.06593083, ph=1))
var.strata(model, y=Sweden$RMT85)

### Examples of posterior correction for non-response
LH <- strata.LH(x=MRTS, CV=0.01, Ls=4, alloc=c(0.5,0,0.5), takeall=1)
LH
# Without non-response in the take-all strata
var.strata(LH, rh.postcorr=TRUE, rh=c(0.85,0.9,0.9,1))
strata.LH(x=MRTS, CV=0.01, Ls=4, alloc=c(0.5,0,0.5), takeall=1, rh=c(0.85,0.9,0.9,1))
# With non-response in the take-all strata
var.strata(LH, rh.postcorr=TRUE, rh=0.9)
strata.LH(x=MRTS, CV=0.01, Ls=4, alloc=c(0.5,0,0.5), takeall=1, rh=0.9)

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