svrep provides methods for creating, updating, and analyzing replicate weights for surveys. Functions from svrep can be used to implement adjustments to replicate designs (e.g. nonresponse weighting class adjustments) and analyze their effect on the replicate weights and on estimates of interest. Facilitates the creation of bootstrap and generalized bootstrap replicate weights.

You can install the released version of svrep from CRAN with:

You can install the development version from GitHub with:

When using the ‘svrep’ package, please make sure to cite it in any resulting publications. This is appreciated by the package maintainer and helps to incentivize ongoing development, maintenance, and support.

Schneider B. (2023). “svrep: Tools for Creating, Updating, and Analyzing Survey Replicate Weights”. R package version 0.6.0.

When using the ‘svrep’ package, please also cite the ‘survey’ package and R itself, since they are essential to the use of ‘svrep’. Call `citation('svrep')`

, `citation('survey')`

, and `citation('base')`

for more information and to generate BibTex entries for citing these packages as well as R.

Suppose we have data from a survey selected using a complex sampling method such as cluster sampling. To represent the complex survey design, we can create a survey design object using the survey package.

```
library(survey)
library(svrep)
data(api, package = "survey")
set.seed(2021)
# Create a survey design object for a sample
# selected using a single-stage cluster sample without replacement
dclus1 <- svydesign(
data = apiclus1,
ids = ~dnum,
weights = ~pw,
fpc = ~fpc
)
```

To help us estimate sampling variances, we can create bootstrap replicate weights. The function `as_bootstrap_design()`

creates bootstrap replicate weights appropriate to common complex sampling designs, using bootstrapping methods from the ‘survey’ package as well as additional methods such as the Rao-Wu-Yue-Beaumont method (a generalization of the Rao-Wu bootstrap).

```
# Create replicate-weights survey design
orig_rep_design <- dclus1 |> as_bootstrap_design(
replicates = 500,
type = "Rao-Wu-Yue-Beaumont"
)
print(orig_rep_design)
#> Call: as_bootstrap_design(dclus1, replicates = 500, type = "Rao-Wu-Yue-Beaumont")
#> Survey bootstrap with 500 replicates.
```

For especially complex survey designs (e.g., systematic samples), the generalized survey bootstrap can be used.

```
# Load example data for a stratified systematic sample
data('library_stsys_sample', package = 'svrep')
# First, ensure data are sorted in same order as was used in sampling
library_stsys_sample <- library_stsys_sample[
order(library_stsys_sample$SAMPLING_SORT_ORDER),
]
# Create a survey design object
design_obj <- svydesign(
data = library_stsys_sample,
strata = ~ SAMPLING_STRATUM,
ids = ~ 1,
fpc = ~ STRATUM_POP_SIZE
)
# Convert to generalized bootstrap replicate design
gen_boot_design_sd2 <- as_gen_boot_design(
design = design_obj,
variance_estimator = "SD2",
replicates = 500
)
#> For `variance_estimator='SD2', assumes rows of data are sorted in the same order used in sampling.
```

For relatively simple designs, we can also use the random-groups jackknife.

```
# Create random-group jackknife replicates
# for a single-stage survey with many first-stage sampling units
rand_grp_jk_design <- apisrs |>
svydesign(data = _,
ids = ~ 1,
weights = ~ pw) |>
as_random_group_jackknife_design(
replicates = 20
)
```

In social surveys, unit nonresponse is extremely common. It is also somewhat common for respondent cases to be classified as “ineligible” for the survey based on their response. In general, sampled cases are typically classified as “respondents”, “nonrespondents”, “ineligible cases”, and “unknown eligibility” cases.

```
# Create variable giving response status
orig_rep_design$variables[['response_status']] <- sample(
x = c("Respondent", "Nonrespondent",
"Ineligible", "Unknown eligibility"),
prob = c(0.6, 0.2, 0.1, 0.1),
size = nrow(orig_rep_design),
replace = TRUE
)
table(orig_rep_design$variables$response_status)
#>
#> Ineligible Nonrespondent Respondent Unknown eligibility
#> 16 32 119 16
```

It is common practice to adjust weights when there is non-response or there are sampled cases whose eligibility for the survey is unknown. The most common form of adjustment is “weight redistribution”: for example, weights from non-respondents are reduced to zero, and weights from respondents are correspondingly increased so that the total weight in the sample is unchanged. In order to account for these adjustments when estimating variances for survey statistics, the adjustments are repeated separately for each set of replicate weights. This process can be easily implemented using the `redistribute_weights()`

function.

```
# Adjust weights for unknown eligibility
ue_adjusted_design <- redistribute_weights(
design = orig_rep_design,
reduce_if = response_status %in% c("Unknown eligibility"),
increase_if = !response_status %in% c("Unknown eligibility")
)
```

By supplying column names to the `by`

argument of `redistribute_weights()`

, adjustments are conducted separately in different groups. This can be used to conduct nonresponse weighting class adjustments.

```
nr_adjusted_design <- redistribute_weights(
design = ue_adjusted_design,
reduce_if = response_status == "Nonrespondent",
increase_if = response_status == "Respondent",
by = c("stype")
)
```

In order to assess whether weighting adjustments have an impact on the estimates we care about, we want to compare the estimates from the different sets of weights. The function `svyby_repwts()`

makes it easy to compare estimates from different sets of weights.

```
# Estimate overall means (and their standard errors) from each design
overall_estimates <- svyby_repwts(
rep_designs = list('original' = orig_rep_design,
'nonresponse-adjusted' = nr_adjusted_design),
formula = ~ api00,
FUN = svymean
)
print(overall_estimates, row.names = FALSE)
#> Design_Name api00 se
#> nonresponse-adjusted 641.2030 25.54368
#> original 644.1694 23.06284
# Estimate domain means (and their standard errors) from each design
domain_estimates <- svyby_repwts(
rep_designs = list('original' = orig_rep_design,
'nonresponse-adjusted' = nr_adjusted_design),
formula = ~ api00,
by = ~ stype,
FUN = svymean
)
print(domain_estimates, row.names = FALSE)
#> Design_Name stype api00 se
#> nonresponse-adjusted E 649.9188 25.56366
#> original E 648.8681 22.31347
#> nonresponse-adjusted H 603.5390 45.26079
#> original H 618.5714 37.39448
#> nonresponse-adjusted M 616.3260 36.27983
#> original M 631.4400 31.03957
```

We can even test for differences in estimates from the two sets of weights and calculate confidence intervals for their difference.

```
estimates <- svyby_repwts(
rep_designs = list('original' = orig_rep_design,
'nonresponse-adjusted' = nr_adjusted_design),
formula = ~ api00,
FUN = svymean
)
vcov(estimates)
#> nonresponse-adjusted original
#> nonresponse-adjusted 652.4793 585.5253
#> original 585.5253 531.8947
diff_between_ests <- svycontrast(
stat = estimates,
contrasts = list(
"Original vs. Adjusted" = c(-1,1)
)
)
print(diff_between_ests)
#> contrast SE
#> Original vs. Adjusted 2.9664 3.6501
confint(diff_between_ests)
#> 2.5 % 97.5 %
#> Original vs. Adjusted -4.187705 10.12056
```

When adjusting replicate weights, there are several diagnostics which can be used to ensure that the adjustments were carried out correctly and that they do more good than harm. The function `summarize_rep_weights()`

helps by allowing you to quickly summarize the replicate weights.

For example, when carrying out nonresponse adjustments, we might want to verify that all of the weights for nonrespondents have been set to zero in each replicate. We can use the `summarize_rep_weights()`

to compare summary statistics for each replicate, and we can use its `by`

argument to group the summaries by one or more variables.

```
summarize_rep_weights(
rep_design = nr_adjusted_design,
type = 'specific',
by = "response_status"
) |>
subset(Rep_Column %in% 1:2)
#> response_status Rep_Column N N_NONZERO SUM MEAN CV MIN MAX
#> 1 Ineligible 1 16 16 608.1360 38.00850 1.2415437 0.5632079 120.38814
#> 2 Ineligible 2 16 16 739.2634 46.20397 0.7578107 0.5422029 77.44622
#> 501 Nonrespondent 1 32 0 0.0000 0.00000 NaN 0.0000000 0.00000
#> 502 Nonrespondent 2 32 0 0.0000 0.00000 NaN 0.0000000 0.00000
#> 1001 Respondent 1 119 119 6236.0577 52.40385 1.0431318 0.6072282 151.10496
#> 1002 Respondent 2 119 119 6426.4544 54.00382 0.8345243 0.5971008 102.40567
#> 1501 Unknown eligibility 1 16 0 0.0000 0.00000 NaN 0.0000000 0.00000
#> 1502 Unknown eligibility 2 16 0 0.0000 0.00000 NaN 0.0000000 0.00000
```

At the end of the adjustment process, we can inspect the number of rows and columns and examine the variability of the weights across all of the replicates.

```
nr_adjusted_design |>
subset(response_status == "Respondent") |>
summarize_rep_weights(
type = 'overall'
)
#> nrows ncols degf_svy_pkg rank avg_wgt_sum sd_wgt_sums min_rep_wgt max_rep_wgt
#> 1 119 500 29 30 5625.555 1257.982 0.5305136 367.826
```

When we rake or poststratify to estimated control totals rather than to “true” population values, we may need to account for the variance of the estimated control totals to ensure that calibrated estimates appropriately reflect sampling error of both the primary survey of interest and the survey from which the control totals were estimated. The ‘svrep’ package provides two functions which accomplish this. The function `calibrate_to_estimate()`

requires the user to supply a vector of control totals and its variance-covariance matrix, while the function `calibrate_to_sample()`

requires the user to supply a dataset with replicate weights to use for estimating control totals and their sampling variance.

As an example, suppose we have a survey measuring vaccination status of adults in Louisville, Kentucky. For variance estimation, we use 100 bootstrap replicates.

```
data("lou_vax_survey")
# Load example data
lou_vax_survey <- svydesign(
data = lou_vax_survey,
ids = ~ 1,
weights = ~ SAMPLING_WEIGHT
) |>
as_bootstrap_design(
replicates = 100,
mse = TRUE
)
# Adjust for nonresponse
lou_vax_survey <- lou_vax_survey |>
redistribute_weights(
reduce_if = RESPONSE_STATUS == "Nonrespondent",
increase_if = RESPONSE_STATUS == "Respondent"
) |>
subset(RESPONSE_STATUS == "Respondent")
```

To reduce nonresponse bias or coverage error for the survey, we can rake the survey to population totals for demographic groups estimated by the Census Bureau in the American Community Survey (ACS). To estimate the population totals for raking purposes, we can use microdata with replicate weights.

```
# Load microdata to use for estimating control totals
data("lou_pums_microdata")
acs_benchmark_survey <- survey::svrepdesign(
data = lou_pums_microdata,
variables = ~ UNIQUE_ID + AGE + SEX + RACE_ETHNICITY + EDUC_ATTAINMENT,
weights = ~ PWGTP,
repweights = "PWGTP\\d{1,2}",
type = "successive-difference",
mse = TRUE
)
```

We can see that the distribution of race/ethnicity among respondents differs from the distribution of race/ethnicity in the ACS benchmarks.

```
# Compare demographic estimates from the two data sources
estimate_comparisons <- data.frame(
'Vax_Survey' = lou_vax_survey |>
svymean(x = ~ RACE_ETHNICITY) |>
coef(),
'ACS_Benchmark' = acs_benchmark_survey |>
svymean(x = ~ RACE_ETHNICITY) |>
coef()
)
rownames(estimate_comparisons) <- gsub(x = rownames(estimate_comparisons),
"RACE_ETHNICITY", "")
print(estimate_comparisons)
#> Vax_Survey ACS_Benchmark
#> Black or African American alone, not Hispanic or Latino 0.16932271 0.19949824
#> Hispanic or Latino 0.03386454 0.04525039
#> Other Race, not Hispanic or Latino 0.05776892 0.04630955
#> White alone, not Hispanic or Latino 0.73904382 0.70894182
```

There are two options for calibrating the sample to the control totals from the benchmark survey. With the first approach, we supply point estimates and their variance-covariance matrix to the function `calibrate_to_estimate()`

.

```
# Estimate control totals and their variance-covariance matrix
control_totals <- svymean(
x = ~ RACE_ETHNICITY + EDUC_ATTAINMENT,
design = acs_benchmark_survey
)
point_estimates <- coef(control_totals)
vcov_estimates <- vcov(control_totals)
# Calibrate the vaccination survey to the estimated control totals
vax_survey_raked_to_estimates <- calibrate_to_estimate(
rep_design = lou_vax_survey,
estimate = point_estimates,
vcov_estimate = vcov_estimates,
cal_formula = ~ RACE_ETHNICITY + EDUC_ATTAINMENT,
calfun = survey::cal.raking
)
```

With the second approach, we supply the control survey’s replicate design to `calibrate_to_sample()`

.

```
vax_survey_raked_to_acs_sample <- calibrate_to_sample(
primary_rep_design = lou_vax_survey,
control_rep_design = acs_benchmark_survey,
cal_formula = ~ RACE_ETHNICITY + EDUC_ATTAINMENT,
calfun = survey::cal.raking
)
```

After calibration, we can see that the estimated vaccination rate has decreased, and the estimated standard error of the estimated vaccination rate has increased.

```
# Compare the two sets of estimates
svyby_repwts(
rep_design = list(
'NR-adjusted' = lou_vax_survey,
'Raked to estimate' = vax_survey_raked_to_estimates,
'Raked to sample' = vax_survey_raked_to_acs_sample
),
formula = ~ VAX_STATUS,
FUN = svymean,
keep.names = FALSE
)
#> Design_Name VAX_STATUSUnvaccinated VAX_STATUSVaccinated se1 se2
#> 1 NR-adjusted 0.4621514 0.5378486 0.01870176 0.01870176
#> 2 Raked to estimate 0.4732623 0.5267377 0.01901224 0.01901224
#> 3 Raked to sample 0.4732623 0.5267377 0.01900022 0.01900022
```

Once we’re satisfied with the weights, we can create a data frame with the analysis variables and columns of final full-sample weights and replicate weights. This format is easy to export to data files that can be loaded into R or other software later.

```
data_frame_with_final_weights <- vax_survey_raked_to_estimates |>
as_data_frame_with_weights(
full_wgt_name = "RAKED_WGT",
rep_wgt_prefix = "RAKED_REP_WGT_"
)
# Preview first 10 column names
colnames(data_frame_with_final_weights) |> head(10)
#> [1] "RESPONSE_STATUS" "RACE_ETHNICITY" "SEX" "EDUC_ATTAINMENT" "VAX_STATUS" "SAMPLING_WEIGHT"
#> [7] "RAKED_WGT" "RAKED_REP_WGT_1" "RAKED_REP_WGT_2" "RAKED_REP_WGT_3"
```