Calibrate weights from a primary survey to estimated totals from a control survey, with replicate-weight adjustments that account for variance of the control totals

Calibrate the weights of a primary survey to match estimated totals from a control survey, using adjustments to the replicate weights to account for the variance of the estimated control totals. The adjustments to replicate weights are conducted using the method proposed by Opsomer and Erciulescu (2021). This method can be used to implement general calibration as well as post-stratification or raking specifically (see the details for the calfun parameter).

Usage

calibrate_to_sample(
  primary_rep_design,
  control_rep_design,
  cal_formula,
  calfun = survey::cal.linear,
  bounds = list(lower = -Inf, upper = Inf),
  verbose = FALSE,
  maxit = 50,
  epsilon = 1e-07,
  variance = NULL,
  control_col_matches = NULL
)

Arguments

primary_rep_design: A replicate design object for the primary survey, created with either the survey or srvyr packages.
control_rep_design: A replicate design object for the control survey.
cal_formula: A formula listing the variables to use for calibration. All of these variables must be included in both primary_rep_design and control_rep_design.
calfun: A calibration function from the survey package, such as cal.linear, cal.raking, or cal.logit. Use cal.linear for ordinary post-stratification, and cal.raking for raking. See calibrate for additional details.
bounds: Parameter passed to grake for calibration. See calibrate for details.
verbose: Parameter passed to grake for calibration. See calibrate for details.
maxit: Parameter passed to grake for calibration. See calibrate for details.
epsilon: Parameter passed to grake for calibration.
After calibration, the absolute difference between each calibration target and the calibrated estimate will be no larger than epsilon times (1 plus the absolute value of the target). See calibrate for details.
variance: Parameter passed to grake for calibration. See calibrate for details.
control_col_matches: Optional parameter to specify which control survey replicate is matched to each primary survey replicate. If the \(i-th\) entry of control_col_matches equals \(k\), then replicate \(i\) in primary_rep_design is matched to replicate \(k\) in control_rep_design. Entries of NA denote a primary survey replicate not matched to any control survey replicate. If this parameter is not used, matching is done at random.

Value

A replicate design object, with full-sample weights calibrated to totals from control_rep_design, and replicate weights adjusted to account for variance of the control totals. If primary_rep_design had fewer columns of replicate weights than control_rep_design, then the number of replicate columns and the length of rscales will be increased by a multiple k, and the scale will be updated by dividing by k.

The element control_column_matches indicates, for each replicate column of the calibrated primary survey, which column of replicate weights it was matched to from the control survey. Columns which were not matched to control survey replicate column are indicated by NA.

The element degf will be set to match that of the primary survey to ensure that the degrees of freedom are not erroneously inflated by potential increases in the number of columns of replicate weights.

Details

With the Opsomer-Erciulescu method, each column of replicate weights from the control survey is randomly matched to a column of replicate weights from the primary survey, and then the column from the primary survey is calibrated to control totals estimated by perturbing the control sample's full-sample estimates using the estimates from the matched column of replicate weights from the control survey.

If there are fewer columns of replicate weights in the control survey than in the primary survey, then not all primary replicate columns will be matched to a replicate column from the control survey.

If there are more columns of replicate weights in the control survey than in the primary survey, then the columns of replicate weights in the primary survey will be duplicated k times, where k is the smallest positive integer such that the resulting number of columns of replicate weights for the primary survey is greater than or equal to the number of columns of replicate weights in the control survey.

Because replicate columns of the control survey are matched at random to primary survey replicate columns, there are multiple ways to ensure that this matching is reproducible. The user can either call set.seed before using the function, or supply a mapping to the argument control_col_matches.

Syntax for Common Types of Calibration

For ratio estimation with an auxiliary variable X, use the following options:
- cal_formula = ~ -1 + X
- variance = 1,
- cal.fun = survey::cal.linear

For post-stratification, use the following option:

- cal.fun = survey::cal.linear

For raking, use the following option:

- cal.fun = survey::cal.raking

References

Opsomer, J.D. and A. Erciulescu (2021). "Replication variance estimation after sample-based calibration." Survey Methodology, 47: 265-277.

Examples

if (FALSE) {

# Load example data for primary survey ----

  suppressPackageStartupMessages(library(survey))
  data(api)

  primary_survey <- svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc) |>
    as.svrepdesign(type = "JK1")

# Load example data for control survey ----

  control_survey <- svydesign(id = ~ 1, fpc = ~fpc, data = apisrs) |>
    as.svrepdesign(type = "JK1")

# Calibrate totals for one categorical variable and one numeric ----

  calibrated_rep_design <- calibrate_to_sample(
    primary_rep_design = primary_survey,
    control_rep_design = control_survey,
    cal_formula = ~ stype + enroll,
  )

# Inspect estimates before and after calibration ----

  ##_ For the calibration variables, estimates and standard errors
  ##_ from calibrated design will match those of the control survey

    svytotal(x = ~ stype + enroll, design = primary_survey)
    svytotal(x = ~ stype + enroll, design = control_survey)
    svytotal(x = ~ stype + enroll, design = calibrated_rep_design)

  ##_ Estimates from other variables will be changed as well

    svymean(x = ~ api00 + api99, design = primary_survey)
    svymean(x = ~ api00 + api99, design = control_survey)
    svymean(x = ~ api00 + api99, design = calibrated_rep_design)

# Inspect weights before and after calibration ----

  summarize_rep_weights(primary_survey, type = 'overall')
  summarize_rep_weights(calibrated_rep_design, type = 'overall')

# For reproducibility, specify how to match replicates between surveys ----

  column_matching <- calibrated_rep_design$control_col_matches
  print(column_matching)

  calibrated_rep_design <- calibrate_to_sample(
    primary_rep_design = primary_survey,
    control_rep_design = control_survey,
    cal_formula = ~ stype + enroll,
    control_col_matches = column_matching
  )
}