make_sdr_replicate_factors: Create matrix of replicate factors to use for Successive...

In bschneidr/svrep: Tools for Creating, Updating, and Analyzing Survey Replicate Weights

Create matrix of replicate factors to use for Successive Difference Replication Method

Description

Create matrix of replicate factors to use for Successive Difference Replication Method

Usage

make_sdr_replicate_factors(
  n,
  target_number_of_replicates,
  use_normal_hadamard = FALSE
)

Arguments

n	The number of sampling units
target_number_of_replicates	The target number of replicates to create. This will determine the order of the Hadamard matrix to use when creating replicate factors. The actual number of replicates will be a multiple of 4. If use_normal_hadamard = FALSE, then the actual number of replicates will be 4 \times 2^k for some integer k, which means that the actual number of replicates might be much larger than the target.
use_normal_hadamard	Whether to use a normal Hadamard matrix: that is, a matrix whose first row and first column only have entries equal to 1.

Value

A matrix of replicate factors, with n rows and the number of columns corresponding to the order of the Hadamard matrix used (which is greater than or equal to target_number_of_replicates).

Examples

# Note that one of the replicates has every factor equal to 1
# Also note that this matches Table 1 in Ash (2014)
make_sdr_replicate_factors(
  n = 4,
  target_number_of_replicates = 4,
  use_normal_hadamard = TRUE
)

# Note the difference when using a non-normal Hadamard matrix
rep_factors <- make_sdr_replicate_factors(
  n = 4,
  target_number_of_replicates = 4,
  use_normal_hadamard = FALSE
)
print(rep_factors)

# These replicate factors are equivalent
# to the SD2 variance estimator
tcrossprod(rep_factors - 1)

# Compare to the quadratic form of the SD2 estimator
sd2_quad_form <- make_quad_form_matrix(
  variance_estimator = "SD2",
  cluster_ids        = matrix(1:4, ncol = 1),
  sort_order         = matrix(1:4, ncol = 1)
)
print(sd2_quad_form)

bschneidr/svrep documentation built on Feb. 11, 2025, 4:24 a.m.