Description Usage Arguments Details Value Author(s) References See Also Examples

These functions first determine boundaries to stratify a population. Then, in a second independent step, the sample sizes are calculated given a CV or the CV is computed given the total sample size. The function `strata.cumrootf`

uses the cumulative root frequency method by Dalenius and Hodges (1959) and `strata.geo`

uses the geometric method by Gunning and Horgan (2004). A model can be specified for the relationship between the stratification variable *X* and the survey variable *Y*, but this model has no impact on the first step of boundary determination. It only influences the calculation of the n or of the CV by the use of anticipated means and variances of *Y* instead of the empirical means and variances of *X*.

1 2 3 4 5 6 7 8 9 | ```
strata.cumrootf(x, n = NULL, CV = NULL, Ls = 3, certain = NULL,
alloc = list(q1 = 0.5, q2 = 0, q3 = 0.5), rh = rep(1, Ls),
model = c("none", "loglinear", "linear", "random"),
model.control = list(), nclass = NULL)
strata.geo(x, n = NULL, CV = NULL, Ls = 3, certain=NULL,
alloc = list(q1 = 0.5, q2 = 0, q3 = 0.5), rh = rep(1, Ls),
model = c("none", "loglinear", "linear", "random"),
model.control = list())
``` |

`x` |
A vector containing the values of the stratification variable |

`n` |
A numeric: the target sample size. It has no default value. The argument |

`CV` |
A numeric: the target coefficient of variation. It has no default value. The argument |

`Ls` |
A numeric: the number of sampled strata (take-none and certain strata are not counted in |

`certain` |
A vector giving the position, in the vector |

`alloc` |
A list specifying the allocation scheme. The list must contain 3 numerics for the 3 exponents |

`rh` |
A vector giving the anticipated response rates in each of the |

`model` |
A character string identifying the model used to describe the discrepancy between the stratification variable |

`model.control` |
A list of model parameters (see |

`nclass` |
A numeric for the cumulative root frequency method only: the number of classes (Dalenius and Hodges 1959). The default (see |

The efficiency of the cumulative root frequency method depends on the number of classes `nclass`

(see Dalenius and Hodges (1959) for a description of these classes). However, there is no theory about how to choose the best value for `nclass`

(Hedlin 2000). This is a limit of the method.

`bh ` |
A vector of the |

`nclassh` |
A vector for the cumulative root frequency method only: the number of classes in each stratum (Dalenius and Hodges 1959). |

`Nh ` |
A vector of length |

`nh ` |
A vector of length |

`n ` |
The total sample size ( |

`nhnonint ` |
A vector of length |

`certain.info ` |
A vector giving statistics for the certainty stratum (see |

`opti.nh ` |
The final value of the criteria to optimize (either the total sample size |

`opti.nhnonint ` |
The final value of the criteria to optimize (either the total sample size |

`meanh ` |
A vector of length |

`varh ` |
A vector of length |

`mean ` |
A numeric: the anticipated global mean value of |

`stderr ` |
A numeric: the standard error of the anticipated global mean of |

`CV` |
The anticipated coefficient of variation for the mean of |

`stratumID` |
A factor, having the same length as the input |

`takeall ` |
The number of take-all strata in the final solution. Note: It is possible that |

`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. |

Sophie Baillargeon Sophie.Baillargeon@mat.ulaval.ca and

Louis-Paul Rivest Louis-Paul.Rivest@mat.ulaval.ca

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

Dalenius, T. and Hodges, J.L., Jr. (1959). Minimum variance stratification. *Journal of the American Statistical Association*, **54**, 88-101.

Gunning, P. and Horgan, J.M. (2004). A new algorithm for the construction of stratum boundaries in skewed populations. *Survey Methodology*, **30**(2), 159-166.

Hedlin, D. (2000). A procedure for stratification by an extended Ekman rule. *Journal of Official Statistics*, **61**, 15-29.

`print.strata`

, `plot.strata`

, `strata.LH`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
### Example for strata.cumrootf
res <- matrix(NA, nrow=20, ncol=2)
i <- 1
for ( n in seq(100,2000,100)){
cum <- strata.cumrootf(x=MRTS, CV=0.01, Ls=4, alloc=c(0.5,0,0.5), nclass=n)
res[i,] <- c(n,cum$n)
i <- i + 1
}
plot(res, ylab="suggested sample size n", xlab="number of classes", main=expression(
paste("Example of the effect of nclass on n for the cum",sqrt(f)," method")))
### Example for strata.geo
strata.geo(x=Sweden$REV84, CV=0.05, Ls=5, alloc=c(0.35,0.35,0), model="none")
strata.geo(x=Sweden$REV84, CV=0.05, Ls=5, alloc=c(0.35,0.35,0), model="loglinear",
model.control=list(beta=1.058355, sig2=0.06593083, ph=1))
strata.geo(x=Sweden$REV84, CV=0.05, Ls=5, alloc=c(0.35,0.35,0), rh=0.85,
model="loglinear", model.control=list(beta=1.058355, sig2=0.06593083, ph=1))
# When non-response or a model is added, the stratum boundaries do not change,
# only the nh's do.
### Exemple of how a certainty stratum can be usefull with these methods
strata.cumrootf(x=Sweden$REV84, CV=0.05, Ls=4, alloc=c(0.35,0.35,0), model="none",
nclass=50)
strata.cumrootf(x=sort(Sweden$REV84), CV=0.05, Ls=4, alloc=c(0.35,0.35,0),
certain=282:284, model="none", nclass=50)
# The certainty stratum is used here to ensure that the three large units in the
# Sweden$REV84 population are in the sample, since no take-all stratum can be forced
# in the stratified design with the cumulative root frequency or geometric method.
# We see that this allows to reduce by more than half the suggested sample size n
# (47 vs 19). This example was presented in Baillargeon and Rivest (2011).
``` |

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