| as_random_group_jackknife_design {svrep} | R Documentation |
Convert a survey design object to a random-groups jackknife design
Description
Forms a specified number of jackknife replicates based on grouping primary sampling units (PSUs) into random, (approximately) equal-sized groups.
Usage
as_random_group_jackknife_design(
design,
replicates = 50,
var_strat = NULL,
var_strat_frac = NULL,
sort_var = NULL,
adj_method = "variance-stratum-psus",
scale_method = "variance-stratum-psus",
group_var_name = ".random_group",
compress = TRUE,
mse = getOption("survey.replicates.mse")
)
Arguments
design |
A survey design object created using the 'survey' (or 'srvyr') package,
with class |
replicates |
The number of replicates to create
for each variance stratum. The total number of replicates
created is the number of variance strata times |
var_strat |
Specifies the name of a variable
in the data that defines variance strata to use
for the grouped jackknife. If |
var_strat_frac |
Specifies the sampling fraction
to use for finite population corrections in each
value of |
sort_var |
(Optional) Specifies the name of a variable
in the data which should be used to sort the data before
assigning random groups. If a variable is specified for
|
adj_method |
Specifies how to calculate the
replicate weight adjustment factor.
Available options for
See the section "Adjustment and Scale Methods" for details. |
scale_method |
Specifies how to calculate the
scale factor for each replicate.
Available options for
See the section "Adjustment and Scale Methods" for details. |
group_var_name |
(Optional) The name of a new variable created to save
identifiers for which random group each PSU was grouped into
for the purpose of forming replicates.
Specify |
compress |
Use a compressed representation of the replicate weights matrix. This reduces the computer memory required to represent the replicate weights and has no impact on estimates. |
mse |
If |
Value
A replicate design object, with class svyrep.design, which can be used with the usual functions,
such as svymean() or svyglm().
Use weights(..., type = 'analysis') to extract the matrix of replicate weights.
Use as_data_frame_with_weights() to convert the design object to a data frame with columns
for the full-sample and replicate weights.
Formation of Random Groups
Within each value of VAR_STRAT,
the data are sorted by first-stage sampling strata,
and then the PSUs in each stratum are randomly arranged.
Groups are then formed by serially placing PSUs
into each group.
The first PSU in the VAR_STRAT is placed into the first group,
the second PSU into the second group, and so on.
Once a PSU has been assigned to the last group,
the process begins again by assigning the next PSU to the first group,
the PSU after that to the second group, and so on.
The random group that each observation is assigned to
can be saved as a variable in the data
by using the function argument group_var_name.
Adjustment and Scale Methods
The jackknife replication variance estimator based on R replicates takes the following form:
v(\hat{\theta}) = \sum_{r=1}^{R} (1 - f_r) \times c_r \times \left(\hat{\theta}_r - \hat{\theta}\right)^2
where r indexes one of the R sets of replicate weights,
c_r is a corresponding scale factor for the r-th replicate,
and 1 - f_r is an optional finite population correction factor
that can potentially differ across variance strata.
To form the replicate weights, the PSUs are divided into \tilde{H} variance strata,
and the \tilde{h}-th variance stratum contains G_{\tilde{h}}
random groups. The number of replicates R equals the total number
of random groups across all variance strata:
R = \sum_{\tilde{h}}^{\tilde{H}} G_{\tilde{h}}. In other words,
each replicate corresponds to one of the random groups from one of the variance strata.
The weights for replicate r corresponding to random group g within
variance stratum \tilde{h} is defined as follows.
If case i
is not in variance stratum \tilde{h}, then w_{i}^{(r)} = w_i.
If case i is in variance stratum \tilde{h} but in random group g,
then w_{i}^{(r)} = a_{\tilde{h}g} w_i.
Otherwise, if case i is in
in random group g of variance stratum \tilde{h}, then w_{i}^{(r)} = 0.
The R function argument adj_method determines how
the adjustment factor a_{\tilde{h} g} is calculated.
When adj_method = "variance-units", then
a_{\tilde{h} g} is calculated based on G_{\tilde{h}},
which is the number of random groups in variance stratum \tilde{h}.
When adj_method = "variance-stratum-psus", then
a_{\tilde{h} g} is calculated based on n_{\tilde{h}g},
which is the number of PSUs in random group g in variance stratum \tilde{h},
as well as n_{\tilde{h}}, the total number of PSUs in variance stratum \tilde{h}.
If adj_method = "variance-units", then:
a_{\tilde{h}g} = \frac{G_{\tilde{h}}}{G_{\tilde{h}} - 1}
If adj_method = "variance-stratum-psus", then:
a_{\tilde{h}g} = \frac{n_{\tilde{h}}}{n_{\tilde{h}} - n_{\tilde{h}g}}
The scale factor c_r for replicate r
corresponding to random group g within variance stratum \tilde{h} is
calculated according to the function argument scale_method.
If scale_method = "variance-units", then:
c_r = \frac{G_{\tilde{h}} - 1}{G_{\tilde{h}}}
If scale_method = "variance-stratum-psus", then:
c_r = \frac{n_{\tilde{h}} - n_{\tilde{h}g}}{n_{\tilde{h}}}
The sampling fraction f_r used for finite population correction 1 - f_r
is by default assumed to equal 0. However, the user can supply a sampling fraction
for each variance stratum using the argument var_strat_frac.
When variance units in a variance stratum
have differing numbers of PSUs,
the combination adj_method = "variance-stratum-psus"
and scale_method = "variance-units" is
recommended by Valliant, Brick, and Dever (2008),
corresponding to their method "GJ2".
The random-groups jackknife method often referred to as "DAGJK"
corresponds to the options var_strat = NULL,
adj_method = "variance-units", and scale_method = "variance-units".
The DAGJK method will yield upwardly-biased variance estimates for totals
if the total number of PSUs is not a multiple of the total number of replicates (Valliant, Brick, and Dever 2008).
References
See Section 15.5 of Valliant, Dever, and Kreuter (2018) for an introduction to the grouped jackknife and guidelines for creating the random groups.
- Valliant, R., Dever, J., Kreuter, F. (2018). "Practical Tools for Designing and Weighting Survey Samples, 2nd edition." New York: Springer.
See Valliant, Brick, and Dever (2008)
for statistical details related to the
adj_method and scale_method arguments.
- Valliant, Richard, Michael Brick, and Jill Dever. 2008. "Weight Adjustments for the Grouped Jackknife Variance Estimator." Journal of Official Statistics. 24: 469–88.
See Chapter 4 of Wolter (2007) for additional details of the jackknife, including the method based on random groups.
- Wolter, Kirk. 2007. "Introduction to Variance Estimation." New York, NY: Springer New York. https://doi.org/10.1007/978-0-387-35099-8.
Examples
library(survey)
# Load example data
data('api', package = 'survey')
api_strat_design <- svydesign(
data = apistrat,
id = ~ 1,
strata = ~stype,
weights = ~pw
)
# Create a random-groups jackknife design
jk_design <- as_random_group_jackknife_design(
api_strat_design,
replicates = 15
)
print(jk_design)