var.strata {stratification}

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, n_h is increased if the input rh is lower than the anticipated response rate in the strata.bh object, and n_h is decreased if the input rh is higher than the anticipated response rate given when creating the strata.bh object. The modification of n_h 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, n_h cannot be increased since it is equal to N_h. 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 n_h, 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)