assign_hadamard_rows: Row Assignment for Successive Difference Replication

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

Row Assignment for Successive Difference Replication

Description

Creates a row assignment matrix: for each row of a dataset of size n, assigns two rows of a Hadamard matrix.

Usage

assign_hadamard_rows(
  n,
  hadamard_order,
  number_of_cycles = ceiling(n/hadamard_order),
  use_first_row = TRUE,
  circular = TRUE
)

Arguments

n	The sample size of the data.
hadamard_order	The order of the Hadamard matrix (i.e., the number of rows/columns)
number_of_cycles	The number of cycles to use in the row assignment. Must be at least as large as n/hadamard_order. Only applies when n exceeds the number of available rows in the Hadamard matrix. The number of available rows is hadamard_order when use_first_row = TRUE, and hadamard_order - 1 when use_first_row = FALSE.
use_first_row	Whether to use the first row of the Hadamard matrix. The first row of a Hadamard matrix is often all 1's, and so using the first row to create replicate factors leads to the creation of a replicate whose weights exactly match the full-sample weights. Thus, using the first row of the Hadamard matrix may be undesirable for practical purposes, even if it is valid for the purpose of variance estimation.
circular	TRUE or FALSE. Only applies when the number of available rows in the Hadamard matrix is at least as large as n. Whether to make a circular row assignment, so that the resulting successive-difference replication variance estimator is equivalent to the SD2 variance estimator rather than the SD1 variance estimator (see Ash 2014). The number of available rows is hadamard_order when use_first_row = TRUE, and hadamard_order - 1 when use_first_row = FALSE.

Details

Implements row-assignment methods described in Ash (2014) and in Fay and Train (1995). The row-assignment method depends on the number of available rows of the Hadamard matrix used. The number of available rows is hadamard_order when use_first_row = TRUE, and hadamard_order - 1 when use_first_row = FALSE.

When the number of available Hadamard rows is at least as large as n, then the row assignment is as follows. Let i=1,\dots,n be the index for the data that will receive row assignments, and let a_j denote row j of a Hadamard matrix. For i < n, the assignments are entries a_i and a_{i+1} when use_first_row = TRUE, and when use_first_row = FALSE, the assignments are entries a_{i+1} and a_{i+2}. The assignment for i=n depends on whether circular = TRUE. If circular=TRUE, then the assignment for i=n is entries a_i and a_1 if use_first_row = TRUE, and entries a_{i+1} and a_2 if use_first_row = FALSE.

When the number of available Hadamard rows is less than n, then the row assignment method is the method denoted as RA1 in Ash (2014). This method uses the argument number_of_cycles and does not use the argument circular.

Value

A matrix with n rows and two columns. Each row gives the assignment of two rows of a Hadamard matrix to the row of data.

References

Ash, S. (2014). "Using successive difference replication for estimating variances." Survey Methodology, Statistics Canada, 40(1), 47-59.

bschneidr/svrep documentation built on June 14, 2025, 10 p.m.