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:

`install.packages("svrep")`

You can install the development version from GitHub with:

```
# install.packages("devtools")
::install_github("bschneidr/svrep") devtools
```

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
<- svydesign(data = apiclus1,
dclus1 id = ~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
<- as_bootstrap_design(dclus1, replicates = 500,
orig_rep_design 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
<- svydesign(
design_obj data = library_stsys_sample,
strata = ~ SAMPLING_STRATUM,
ids = ~ 1,
fpc = ~ STRATUM_POP_SIZE
)
# Convert to generalized bootstrap replicate design
<- as_gen_boot_design(
gen_boot_design_sd2 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.
```

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
$variables[['response_status']] <- sample(
orig_rep_designx = c("Respondent", "Nonrespondent",
"Ineligible", "Unknown eligibility"),
prob = c(0.6, 0.2, 0.1, 0.1),
size = nrow(orig_rep_design),
replace = TRUE
)
table(orig_rep_design$variables$response_status)
#>
#> Ineligible Nonrespondent Respondent Unknown eligibility
#> 26 30 111 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
<- redistribute_weights(
ue_adjusted_design 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.

```
<- redistribute_weights(
nr_adjusted_design 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
<- svyby_repwts(
overall_estimates 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 636.0485 23.74044
#> original 644.1694 23.06284
# Estimate domain means (and their standard errors) from each design
<- svyby_repwts(
domain_estimates 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 634.0529 24.16837
#> original E 648.8681 22.31347
#> nonresponse-adjusted H 654.9667 25.25871
#> original H 618.5714 37.39448
#> nonresponse-adjusted M 637.7941 32.72545
#> 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.

```
<- svyby_repwts(
estimates rep_designs = list('original' = orig_rep_design,
'nonresponse-adjusted' = nr_adjusted_design),
formula = ~ api00, FUN = svymean
)
vcov(estimates)
#> nonresponse-adjusted original
#> nonresponse-adjusted 563.6085 527.2104
#> original 527.2104 531.8947
<- svycontrast(stat = estimates,
diff_between_ests contrasts = list(
"Original vs. Adjusted" = c(-1,1)
))print(diff_between_ests)
#> contrast SE
#> Original vs. Adjusted 8.1209 6.4096
confint(diff_between_ests)
#> 2.5 % 97.5 %
#> Original vs. Adjusted -4.441618 20.68336
```

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
#> 1 Ineligible 1 26 26 1107.164 42.58325 0.8568075
#> 2 Ineligible 2 26 26 1343.087 51.65720 0.7022211
#> 501 Nonrespondent 1 30 0 0.000 0.00000 NaN
#> 502 Nonrespondent 2 30 0 0.000 0.00000 NaN
#> 1001 Respondent 1 111 111 5737.029 51.68495 1.1101252
#> 1002 Respondent 2 111 111 5822.631 52.45613 0.8325374
#> 1501 Unknown eligibility 1 16 0 0.000 0.00000 NaN
#> 1502 Unknown eligibility 2 16 0 0.000 0.00000 NaN
#> MIN MAX
#> 1 0.5503606 117.64198
#> 2 0.5510743 78.71338
#> 501 0.0000000 0.00000
#> 502 0.0000000 0.00000
#> 1001 0.6608875 148.85960
#> 1002 0.5585803 100.33251
#> 1501 0.0000000 0.00000
#> 1502 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
#> 1 111 500 27 28 5234.807 1221.695 0.5329224 348.5783
```

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
<- svydesign(ids = ~ 1, weights = ~ SAMPLING_WEIGHT,
lou_vax_survey data = lou_vax_survey) |>
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")
<- survey::svrepdesign(
acs_benchmark_survey 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
<- data.frame(
estimate_comparisons 'Vax_Survey' = svymean(x = ~ RACE_ETHNICITY, design = acs_benchmark_survey) |> coef(),
'ACS_Benchmark' = svymean(x = ~ RACE_ETHNICITY, design = lou_vax_survey) |> coef()
)rownames(estimate_comparisons) <- gsub(x = rownames(estimate_comparisons),
"RACE_ETHNICITY", "")
print(estimate_comparisons)
#> Vax_Survey
#> Black or African American alone, not Hispanic or Latino 0.19949824
#> Hispanic or Latino 0.04525039
#> Other Race, not Hispanic or Latino 0.04630955
#> White alone, not Hispanic or Latino 0.70894182
#> ACS_Benchmark
#> Black or African American alone, not Hispanic or Latino 0.16932271
#> Hispanic or Latino 0.03386454
#> Other Race, not Hispanic or Latino 0.05776892
#> White alone, not Hispanic or Latino 0.73904382
```

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
<- svymean(x = ~ RACE_ETHNICITY + EDUC_ATTAINMENT,
control_totals design = acs_benchmark_survey)
<- coef(control_totals)
point_estimates <- vcov(control_totals)
vcov_estimates
# Calibrate the vaccination survey to the estimated control totals
<- calibrate_to_estimate(
vax_survey_raked_to_estimates 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()`

.

```
<- calibrate_to_sample(
vax_survey_raked_to_acs_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
#> 1 NR-adjusted 0.4621514 0.5378486 0.02088585
#> 2 Raked to estimate 0.4732623 0.5267377 0.02119417
#> 3 Raked to sample 0.4732623 0.5267377 0.02117422
#> se2
#> 1 0.02088585
#> 2 0.02119417
#> 3 0.02117422
```

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.

```
<- vax_survey_raked_to_estimates |>
data_frame_with_final_weights 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"
#> [5] "VAX_STATUS" "SAMPLING_WEIGHT" "RAKED_WGT" "RAKED_REP_WGT_1"
#> [9] "RAKED_REP_WGT_2" "RAKED_REP_WGT_3"
```

```
# Write the data to a CSV file
write.csv(
x = data_frame_with_final_weights,
file = "survey-data_with-updated-weights.csv"
)
```