1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401
|
#' @title Rescale design weights for multilevel analysis
#' @name rescale_weights
#'
#' @description Most functions to fit multilevel and mixed effects models only
#' allow the user to specify frequency weights, but not design (i.e., sampling
#' or probability) weights, which should be used when analyzing complex samples
#' (e.g., probability samples). `rescale_weights()` implements two algorithms,
#' one proposed by \cite{Asparouhov (2006)} and \cite{Carle (2009)}, to rescale
#' design weights in survey data to account for the grouping structure of
#' multilevel models, and one based on the design effect proposed by
#' \cite{Kish (1965)}, to rescale weights by the design effect to account for
#' additional sampling error introduced by weighting.
#' @param data A data frame.
#' @param by Variable names (as character vector, or as formula), indicating
#' the grouping structure (strata) of the survey data (level-2-cluster
#' variable). It is also possible to create weights for multiple group
#' variables; in such cases, each created weighting variable will be suffixed
#' by the name of the group variable. This argument is required for
#' `method = "carle"`, but optional for `method = "kish"`.
#' @param probability_weights Variable indicating the probability (design or
#' sampling) weights of the survey data (level-1-weight), provided as character
#' string or formula.
#' @param nest Logical, if `TRUE` and `by` indicates at least two group
#' variables, then groups are "nested", i.e. groups are now a combination from
#' each group level of the variables in `by`. This argument is not used when
#' `method = "kish"`.
#' @param method String, indicating which rescale-method is used for rescaling
#' weights. Can be either `"carle"` (default) or `"kish"`. See 'Details'. If
#' `method = "carle"`, the `by` argument is required.
#'
#' @return
#' `data`, including the new weighting variable(s). For `method = "carle"`, new
#' columns `rescaled_weights_a` and `rescaled_weights_b` are returned, and for
#' `method = "kish"`, the returned data contains a column `rescaled_weights`.
#' These represent the rescaled design weights to use in multilevel models (use
#' these variables for the `weights` argument).
#'
#' @details
#' - `method = "carle"`
#'
#' Rescaling is based on two methods: For `rescaled_weights_a`, the sample
#' weights `probability_weights` are adjusted by a factor that represents the
#' proportion of group size divided by the sum of sampling weights within each
#' group. The adjustment factor for `rescaled_weights_b` is the sum of sample
#' weights within each group divided by the sum of squared sample weights
#' within each group (see Carle (2009), Appendix B). In other words,
#' `rescaled_weights_a` "scales the weights so that the new weights sum to the
#' cluster sample size" while `rescaled_weights_b` "scales the weights so that
#' the new weights sum to the effective cluster size".
#'
#' Regarding the choice between scaling methods A and B, Carle suggests that
#' "analysts who wish to discuss point estimates should report results based
#' on weighting method A. For analysts more interested in residual
#' between-group variance, method B may generally provide the least biased
#' estimates". In general, it is recommended to fit a non-weighted model and
#' weighted models with both scaling methods and when comparing the models,
#' see whether the "inferential decisions converge", to gain confidence in the
#' results.
#'
#' Though the bias of scaled weights decreases with increasing group size,
#' method A is preferred when insufficient or low group size is a concern.
#'
#' The group ID and probably PSU may be used as random effects (e.g. nested
#' design, or group and PSU as varying intercepts), depending on the survey
#' design that should be mimicked.
#'
#' - `method = "kish"`
#'
#' Rescaling is based on scaling the sample weights so the mean value is 1,
#' which means the sum of all weights equals the sample size. Next, the design
#' effect (_Kish 1965_) is calculated, which is the mean of the squared
#' weights divided by the squared mean of the weights. The scaled sample
#' weights are then divided by the design effect. This method is most
#' appropriate when weights are based on additional variables beyond the
#' grouping variables in the model (e.g., other demographic characteristics),
#' but may also be useful in other contexts.
#'
#' Some tests on real-world survey-data suggest that, in comparison to the
#' Carle-method, the Kish-method comes closer to estimates from a regular
#' survey-design using the **survey** package. Note that these tests are not
#' representative and it is recommended to check your results against a
#' standard survey-design.
#'
#' @references
#' - Asparouhov T. (2006). General Multi-Level Modeling with Sampling
#' Weights. Communications in Statistics - Theory and Methods 35: 439-460
#'
#' - Carle A.C. (2009). Fitting multilevel models in complex survey data
#' with design weights: Recommendations. BMC Medical Research Methodology
#' 9(49): 1-13
#'
#' - Kish, L. (1965) Survey Sampling. London: Wiley.
#'
#' @examplesIf all(insight::check_if_installed(c("lme4", "parameters"), quietly = TRUE))
#' data(nhanes_sample)
#' head(rescale_weights(nhanes_sample, "WTINT2YR", "SDMVSTRA"))
#'
#' # also works with multiple group-variables
#' head(rescale_weights(nhanes_sample, "WTINT2YR", c("SDMVSTRA", "SDMVPSU")))
#'
#' # or nested structures.
#' x <- rescale_weights(
#' data = nhanes_sample,
#' probability_weights = "WTINT2YR",
#' by = c("SDMVSTRA", "SDMVPSU"),
#' nest = TRUE
#' )
#' head(x)
#'
#' \donttest{
#' # compare different methods, using multilevel-Poisson regression
#'
#' d <- rescale_weights(nhanes_sample, "WTINT2YR", "SDMVSTRA")
#' result1 <- lme4::glmer(
#' total ~ factor(RIAGENDR) + log(age) + factor(RIDRETH1) + (1 | SDMVPSU),
#' family = poisson(),
#' data = d,
#' weights = rescaled_weights_a
#' )
#' result2 <- lme4::glmer(
#' total ~ factor(RIAGENDR) + log(age) + factor(RIDRETH1) + (1 | SDMVPSU),
#' family = poisson(),
#' data = d,
#' weights = rescaled_weights_b
#' )
#'
#' d <- rescale_weights(
#' nhanes_sample,
#' "WTINT2YR",
#' method = "kish"
#' )
#' result3 <- lme4::glmer(
#' total ~ factor(RIAGENDR) + log(age) + factor(RIDRETH1) + (1 | SDMVPSU),
#' family = poisson(),
#' data = d,
#' weights = rescaled_weights
#' )
#' d <- rescale_weights(
#' nhanes_sample,
#' "WTINT2YR",
#' "SDMVSTRA",
#' method = "kish"
#' )
#' result4 <- lme4::glmer(
#' total ~ factor(RIAGENDR) + log(age) + factor(RIDRETH1) + (1 | SDMVPSU),
#' family = poisson(),
#' data = d,
#' weights = rescaled_weights
#' )
#' parameters::compare_parameters(
#' list(result1, result2, result3, result4),
#' exponentiate = TRUE,
#' column_names = c("Carle (A)", "Carle (B)", "Kish", "Kish (grouped)")
#' )
#' }
#' @export
rescale_weights <- function(data,
probability_weights = NULL,
by = NULL,
nest = FALSE,
method = "carle") {
method <- insight::validate_argument(method, c("carle", "kish"))
# convert formulas to strings
if (inherits(by, "formula")) {
by <- all.vars(by)
}
if (inherits(probability_weights, "formula")) {
probability_weights <- all.vars(probability_weights)
}
# check for existing variable names
if ((method == "carle" && any(c("rescaled_weights_a", "rescaled_weights_b") %in% colnames(data))) ||
(method == "kish" && "rescaled_weights" %in% colnames(data))) {
insight::format_warning("The variable name for the rescaled weights already exists in the data. Returned columns will be renamed into unique names.") # nolint
}
# need probability_weights
if (is.null(probability_weights)) {
insight::format_error("The argument `probability_weights` is missing, but required to rescale weights.")
}
# check if weight has missings. we need to remove them first,
# and add back weights to correct cases later
weight_missings <- which(is.na(data[[probability_weights]]))
weight_non_na <- which(!is.na(data[[probability_weights]]))
if (length(weight_missings) > 0) {
data_tmp <- data[weight_non_na, ]
} else {
data_tmp <- data
}
fun_args <- list(
nest = nest,
probability_weights = probability_weights,
data_tmp = data_tmp,
data = data,
by = by,
weight_non_na = weight_non_na
)
switch(method,
carle = do.call(.rescale_weights_carle, fun_args),
do.call(.rescale_weights_kish, fun_args)
)
}
# rescale weights, method Kish ----------------------------
.rescale_weights_kish <- function(nest, probability_weights, data_tmp, data, by, weight_non_na) {
# sort id
data_tmp$.bamboozled <- seq_len(nrow(data_tmp))
# `nest` is currently ignored
if (isTRUE(nest)) {
insight::format_warning("Argument `nest` is ignored for `method = \"kish\"`.")
}
# check by argument
if (!is.null(by) && !all(by %in% colnames(data_tmp))) {
dont_exist <- setdiff(by, colnames(data_tmp))
insight::format_error(
paste0(
"The following variable(s) specified in `by` don't exist in the dataset: ",
text_concatenate(dont_exist), "."
),
.misspelled_string(colnames(data_tmp), dont_exist, "Possibly misspelled?")
)
} else if (is.null(by)) {
# if `by` = NULL, we create a dummy group
by <- "tmp_kish_by"
data_tmp[[by]] <- 1
}
# split into groups, and calculate weights
out <- lapply(split(data_tmp, data_tmp[by]), function(group_data) {
p_weights <- group_data[[probability_weights]]
# design effect according to Kish
deff <- mean(p_weights^2) / (mean(p_weights)^2)
# rescale weights, so their mean is 1
z_weights <- p_weights * (1 / mean(p_weights))
# divide weights by design effect
group_data$rescaled_weights <- z_weights / deff
group_data
})
# bind data
result <- do.call(rbind, out)
# restore original order
result <- result[order(result$.bamboozled), ]
# add back rescaled weights to original data, but account for missing observations
data$rescaled_weights <- NA_real_
data$rescaled_weights[weight_non_na] <- result$rescaled_weights
# return result
data
}
# rescale weights, method Carle ----------------------------
.rescale_weights_carle <- function(nest, probability_weights, data_tmp, data, by, weight_non_na) {
# sort id
data_tmp$.bamboozled <- seq_len(nrow(data_tmp))
if (is.null(by)) {
insight::format_error("Argument `by` must be specified. Please provide one or more variable names in `by` that indicate the grouping structure (strata) of the survey data (level-2-cluster variable).") # nolint
}
if (!all(by %in% colnames(data_tmp))) {
dont_exist <- setdiff(by, colnames(data_tmp))
insight::format_error(
paste0(
"The following variable(s) specified in `by` don't exist in the dataset: ",
text_concatenate(dont_exist), "."
),
.misspelled_string(colnames(data_tmp), dont_exist, "Possibly misspelled?")
)
}
if (nest && length(by) < 2) {
insight::format_warning(
sprintf(
"Only one group variable selected in `by`, no nested structure possible. Rescaling weights for grout '%s' now.",
by
)
)
nest <- FALSE
}
if (nest) {
out <- .rescale_weights_nested(data_tmp, group = by, probability_weights, nrow(data), weight_non_na)
} else {
out <- lapply(by, function(i) {
x <- .rescale_weights(data_tmp, i, probability_weights, nrow(data), weight_non_na)
if (length(by) > 1) {
colnames(x) <- sprintf(c("pweight_a_%s", "pweight_b_%s"), i)
}
x
})
}
make_unique_names <- any(vapply(out, function(i) any(colnames(i) %in% colnames(data)), logical(1)))
# add weights to data frame
out <- do.call(cbind, list(data, out))
# check if we have to rename columns
if (make_unique_names) {
colnames(out) <- make.unique(colnames(out), sep = "_")
}
out
}
# rescale weights, for one or more group variables ----------------------------
.rescale_weights <- function(x, group, probability_weights, n, weight_non_na) {
# compute sum of weights per group
design_weights <- .data_frame(
group = sort(unique(x[[group]])),
sum_weights_by_group = tapply(x[[probability_weights]], as.factor(x[[group]]), sum),
sum_squared_weights_by_group = tapply(x[[probability_weights]]^2, as.factor(x[[group]]), sum),
n_per_group = as.vector(table(x[[group]]))
)
colnames(design_weights)[1] <- group
x <- merge(x, design_weights, by = group, sort = FALSE)
# restore original order
x <- x[order(x$.bamboozled), ]
x$.bamboozled <- NULL
# multiply the original weight by the fraction of the
# sampling unit total population based on Carle 2009
w_a <- x[[probability_weights]] * x$n_per_group / x$sum_weights_by_group
w_b <- x[[probability_weights]] * x$sum_weights_by_group / x$sum_squared_weights_by_group
out <- data.frame(
rescaled_weights_a = rep(NA_real_, times = n),
rescaled_weights_b = rep(NA_real_, times = n)
)
out$rescaled_weights_a[weight_non_na] <- w_a
out$rescaled_weights_b[weight_non_na] <- w_b
out
}
# rescale weights, for nested groups ----------------------------
.rescale_weights_nested <- function(x, group, probability_weights, n, weight_non_na) {
groups <- expand.grid(lapply(group, function(i) sort(unique(x[[i]]))))
colnames(groups) <- group
# compute sum of weights per group
design_weights <- cbind(
groups,
.data_frame(
sum_weights_by_group = unlist(as.list(tapply(
x[[probability_weights]], lapply(group, function(i) {
as.factor(x[[i]])
}), sum
)), use.names = FALSE),
sum_squared_weights_by_group = unlist(as.list(tapply(
x[[probability_weights]]^2, lapply(group, function(i) {
as.factor(x[[i]])
}), sum
)), use.names = FALSE),
n_per_group = unlist(as.list(table(x[, group])), use.names = FALSE)
)
)
x <- merge(x, design_weights, by = group, sort = FALSE)
# restore original order
x <- x[order(x$.bamboozled), ]
x$.bamboozled <- NULL
# multiply the original weight by the fraction of the
# sampling unit total population based on Carle 2009
w_a <- x[[probability_weights]] * x$n_per_group / x$sum_weights_by_group
w_b <- x[[probability_weights]] * x$sum_weights_by_group / x$sum_squared_weights_by_group
out <- data.frame(
rescaled_weights_a = rep(NA_real_, times = n),
rescaled_weights_b = rep(NA_real_, times = n)
)
out$rescaled_weights_a[weight_non_na] <- w_a
out$rescaled_weights_b[weight_non_na] <- w_b
out
}
|