Package {heaping}

Type:	Package
Title:	Correction of Heaping on Individual Level
Version:	0.2.0
Description:	Provides methods for correcting heaping (digit preference) in survey data at the individual record level. Age heaping, where respondents disproportionately report ages ending in 0 or 5, is a common phenomenon that can distort demographic analyses. Unlike traditional smoothing methods that only correct aggregated statistics, this package corrects individual values by replacing a calculated proportion of heaped observations with draws from fitted truncated distributions (log-normal, normal, or uniform). Supports 5-year and 10-year heaping patterns, single heap correction, survey weights, and optional covariate-conditional (model-based) correction via quantile regression forests or linear models to preserve relationships. A multiple-imputation wrapper repeats the correction to propagate the added uncertainty into downstream inference.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://github.com/matthias-da/heaping
BugReports:	https://github.com/matthias-da/heaping/issues
Encoding:	UTF-8
LazyData:	true
LazyDataCompression:	xz
Depends:	R (≥ 3.5.0)
Imports:	fitdistrplus, EnvStats, stats
Suggests:	VIM, ranger, data.table, ggplot2, simPop, testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder:	knitr
RoxygenNote:	7.3.3
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-07-13 11:09:03 UTC; matthias
Author:	Matthias Templ [aut, cre], Bernhard Meindl [ctb]
Maintainer:	Matthias Templ <matthias.templ@gmail.com>
Repository:	CRAN
Date/Publication:	2026-07-13 12:50:02 UTC

heaping: Correction of Heaping on Individual Level

Description

Provides methods for correcting heaping (digit preference) in survey data at the individual record level. Age heaping, where respondents disproportionately report ages ending in 0 or 5, is a common phenomenon that can distort demographic analyses.

Main Functions

correctHeaps

Correct regular age heaping patterns (5-year or 10-year intervals)

correctSingleHeap

Correct a specific single age heap

correctHeapsMI

Produce multiple corrected datasets for multiple-imputation inference

Methodology

Unlike traditional smoothing methods that only correct aggregated statistics, this package corrects individual values by replacing a calculated proportion of heaped observations with draws from fitted truncated distributions (log-normal, normal, or uniform).

The correction ratio is determined by comparing the (optionally weighted) count at each heap to the mean of neighboring ages. Records exceeding this expected count are selected and treated as untrusted; the replacement distribution is then fitted to the remaining (trusted) records and used to draw truncated replacements. Survey weights are supported via the weight argument.

Model-Based Correction

When a model formula and dataModel are supplied, an imputation model for age given the covariates is fitted on the trusted records and used to draw covariate-conditional replacements for the heaped records, preserving relationships with other variables. The engine is selectable via model.engine: a quantile regression forest (ranger, the default) or a linear model. VIM is used only to impute missing covariates.

Multiple Imputation

correctHeapsMI repeats the correction m times with distinct seeds to produce m corrected datasets. Pooling an estimate across them with Rubin's rules propagates the correction uncertainty into downstream standard errors and confidence intervals.

Author(s)

Matthias Templ matthias.templ@fhnw.ch

References

Templ, M. (2026). Correction of heaping on individual level. Journal TBD.

Templ, M., Meindl, B., Kowarik, A., Alfons, A., Dupriez, O. (2017). Simulation of Synthetic Populations for Survey Data Considering Auxiliary Information. Journal of Statistical Software, 79(10), 1-38. doi:10.18637/jss.v079.i10

See Also

Useful links:

• https://github.com/matthias-da/heaping

• Report bugs at https://github.com/matthias-da/heaping/issues

Bachi's Index of Age Heaping

Description

Bachi's index involves applying the Whipple method repeatedly to determine the extent of preference for each terminal digit (0-9). It equals the sum of positive deviations from 10 percent.

Usage

bachi(x, ageMin = 23, ageMax = 77, weight = NULL)

Arguments

Details

Calculate Bachi's index to measure digit preference in age data.

The theoretical range is 0 to 90:

• 0: no digit preference (each digit represents 10

• 90: maximum heaping (all ages end in same digit)

For populations with no age heaping, each digit should appear in approximately 10

Value

A single numeric value representing Bachi's index.

Author(s)

Matthias Templ

References

Bachi, R. (1951). The tendency to round off age returns: measurement and correction. Bulletin of the International Statistical Institute, 33(4), 195-222.

See Also

myers for Myers' index, whipple for Whipple's index.

Other heaping indices: coale_li(), heaping_indices(), jdanov(), kannisto(), myers(), noumbissi(), spoorenberg(), whipple()

Examples

# No heaping
set.seed(42)
age_uniform <- sample(23:77, 10000, replace = TRUE)
bachi(age_uniform)  # Should be close to 0

# Strong heaping on 0 and 5
age_heaped <- sample(seq(25, 75, by = 5), 5000, replace = TRUE)
bachi(age_heaped)  # Should be high

Coale-Li Age Heaping Index

Description

The Coale-Li index was developed to detect age heaping in populations with high proportions of elderly persons. It compares actual counts at specific ages to smoothed reference values using moving averages.

Usage

coale_li(x, digit = 0, ageMin = 60, ageMax = max(x), terms = 5, weight = NULL)

Arguments

Details

Calculate the Coale-Li index for detecting age heaping at older ages.

The method applies double moving averages to create a smooth reference distribution, then calculates the ratio of observed to expected counts for ages ending in a specified digit.

Interpretation:

• 1.0: no preference for the digit

• >1.0: attraction to the digit (heaping)

• <1.0: avoidance of the digit

This index is particularly useful for evaluating data quality at older ages (60+) where heaping on round numbers is common.

Value

A single numeric value representing the Coale-Li index.

Author(s)

Matthias Templ

References

Coale, A. J. and Li, S. (1991). The effect of age misreporting in China on the calculation of mortality rates at very high ages. Demography, 28(2), 293-301.

See Also

kannisto for Kannisto's index, jdanov for Jdanov's index.

Other heaping indices: bachi(), heaping_indices(), jdanov(), kannisto(), myers(), noumbissi(), spoorenberg(), whipple()

Examples

# Create age data with heaping at older ages
set.seed(42)
age <- c(sample(60:99, 5000, replace = TRUE),
         rep(seq(60, 90, by = 10), each = 200))  # Add heaping on 0s
coale_li(age, digit = 0)  # Should be > 1
coale_li(age, digit = 5)  # Should be closer to 1

Correct Age Heaping

Description

Age heaping can cause substantial bias in important demographic measures and thus should be corrected. This function corrects heaping at regular intervals (every 5 or 10 years) by replacing a proportion of heaped observations with draws from fitted truncated distributions.

Usage

correctHeaps(
  x,
  heaps = "10year",
  method = "lnorm",
  start = 0,
  fixed = NULL,
  model = NULL,
  dataModel = NULL,
  model.engine = "ranger",
  weight = NULL,
  width = NULL,
  case.weights = FALSE,
  seed = NULL,
  na.action = "omit",
  verbose = FALSE,
  sd = NULL
)

correctHeaps2(
  x,
  heaps = "10year",
  method = "lnorm",
  start = 0,
  fixed = NULL,
  model = NULL,
  dataModel = NULL,
  model.engine = "ranger",
  weight = NULL,
  width = NULL,
  case.weights = FALSE,
  seed = NULL,
  na.action = "omit",
  verbose = FALSE,
  sd = NULL
)

Arguments

Details

Correct for age heaping at regular intervals using truncated distributions.

For method “lnorm”, a truncated log-normal distribution is fit to the trusted (non-selected) records. Then for each age heap (at 0, 5, 10, 15, ... or 0, 10, 20, ...) random numbers from a truncated log-normal distribution (with lower and upper bounds) are drawn for the selected records.

The correction range is controlled by width: replacement values are drawn from a truncated distribution on [\,\mathrm{heap}-\mathrm{width},\, \mathrm{heap}+\mathrm{width}\,]. The default half-width is 2 years for 5-year and custom heaps and 5 years for 10-year heaps (a single symmetric window, replacing the earlier two-stage \pm 4 / \pm 5 correction).

The ratio of observations to replace is calculated by comparing the count at each heap age to the arithmetic mean of the two neighboring ages. For example, for age heap 5, the ratio is: count(age=5) / mean(count(age=4), count(age=6)).

Method “norm” uses truncated normal distributions instead. The choice between “lnorm” and “norm” depends on whether the age distribution is right-skewed (use “lnorm”) or more symmetric (use “norm”). Many distributions with heaping problems are right-skewed.

Method “unif” draws from truncated uniform distributions around the age heaps, providing a simpler baseline approach.

Method “kernel” uses kernel density estimation to sample replacement values, providing a nonparametric alternative that adapts to the local data distribution.

Repeated calls of this function mimic multiple imputation, i.e., repeating this procedure m times provides m corrected datasets that properly reflect the uncertainty from the correction process. Use the seed parameter to ensure reproducibility.

Value

If verbose = FALSE, a numeric vector of the same length as x with heaping corrected. If verbose = TRUE, a list with:

corrected

the corrected numeric vector

n_changed

total number of values changed

changes_by_heap

named vector of changes per heap age

ratios

named vector of heaping ratios per heap age

method

method used

seed

seed used (if any)

n_fallback

number of model-based draws that fell back to the marginal distribution because no fitted conditional quantile lay within the heap window (0 for the simple, non-model arm)

weighted

logical; whether weighted counts were used

Author(s)

Matthias Templ, Bernhard Meindl

References

Templ, M. (2026). Correction of heaping on individual level. Journal TBD.

Templ, M., Meindl, B., Kowarik, A., Alfons, A., Dupriez, O. (2017). Simulation of Synthetic Populations for Survey Data Considering Auxiliary Information. Journal of Statistical Software, 79(10), 1-38. doi:10.18637/jss.v079.i10

See Also

correctSingleHeap for correcting a single specific heap.

Other heaping correction: correctHeapsMI(), correctSingleHeap()

Examples

# Create artificial age data with log-normal distribution
set.seed(123)
age <- rlnorm(10000, meanlog = 2.466869, sdlog = 1.652772)
age <- round(age[age < 93])

# Artificially introduce 5-year heaping by relabelling (misreporting)
# a share of records to the nearest multiple of five
k <- sample(length(age), round(0.3 * length(age)))
age5 <- age
age5[k] <- round(age5[k] / 5) * 5

# Correct with reproducible results
age5_corrected <- correctHeaps(age5, heaps = "5year", method = "lnorm", seed = 42)

# Get diagnostic information
result <- correctHeaps(age5, heaps = "5year", verbose = TRUE, seed = 42)
print(result$n_changed)
print(result$ratios)

# Use kernel method for nonparametric correction
age5_kernel <- correctHeaps(age5, heaps = "5year", method = "kernel", seed = 42)

# Custom heap positions (e.g., heaping at 12, 18, 21)
custom_heaps <- c(12, 18, 21)
age_custom <- correctHeaps(age5, heaps = custom_heaps, method = "lnorm", seed = 42)

Multiple-Imputation Heaping Correction

Description

Run correctHeaps m times with distinct, deterministically derived seeds to produce m corrected datasets for multiple-imputation inference. Because each corrected value is a random draw from a (truncated) predictive distribution, a single correction understates the uncertainty it introduces. Computing an estimate on each of the m datasets and pooling with Rubin's rules propagates that correction uncertainty into downstream standard errors and confidence intervals.

Usage

correctHeapsMI(x, m = 50, ..., seed = NULL)

## S3 method for class 'heapingMI'
print(x, ...)

Arguments

Details

Child seeds are drawn once from the (optionally user-supplied) seed, so the whole set of m imputations is reproducible while the individual imputations differ from one another. Any further arguments in ... (e.g. heaps, method, weight, model, dataModel, model.engine) are passed unchanged to correctHeaps.

Value

An object of class heapingMI: a list with

imputations

a list of m corrected numeric vectors

m

the number of imputations

seeds

the integer seeds used for the individual imputations

Author(s)

Matthias Templ

See Also

correctHeaps for a single correction.

Other heaping correction: correctHeaps(), correctSingleHeap()

Examples

set.seed(123)
age <- round(rlnorm(2000, meanlog = 2.466869, sdlog = 1.652772))
age <- age[age < 93]
# introduce 5-year heaping by relabelling a share of records
k <- sample(length(age), round(0.3 * length(age)))
age5 <- age
age5[k] <- round(age5[k] / 5) * 5

# Five corrected datasets for multiple-imputation inference
mi <- correctHeapsMI(age5, m = 5, heaps = "5year", seed = 42)
mi

# Pool a simple estimate (the mean) across imputations
means <- sapply(mi$imputations, mean)
mean(means)        # point estimate
var(means)         # between-imputation variance (cost of correction)

Correct a Single Age Heap

Description

While correctHeaps corrects regular heaping patterns, this function allows correction of a single specific heap value. This is useful when heaping occurs at irregular intervals or when only a particular age shows excessive heaping.

Usage

correctSingleHeap(
  x,
  heap,
  before = 2,
  after = 2,
  method = "lnorm",
  fixed = NULL,
  weight = NULL,
  seed = NULL,
  na.action = "omit",
  verbose = FALSE,
  sd = NULL
)

Arguments

Details

Correct a specific age heap in a vector containing ages.

Value

A numeric vector of the same length as x with the specified heap corrected, or a list with diagnostics if verbose = TRUE.

Author(s)

Matthias Templ, Bernhard Meindl

See Also

correctHeaps for correcting regular heaping patterns.

Other heaping correction: correctHeaps(), correctHeapsMI()

Examples

# Create artificial age data
set.seed(123)
age <- rlnorm(10000, meanlog = 2.466869, sdlog = 1.652772)
age <- round(age[age < 93])

# Artificially introduce a heap at age 23 by relabelling (misreporting)
# half of the nearby ages 21-25 to 23
k <- which(age %in% 21:25)
k <- sample(k, round(0.5 * length(k)))
age23 <- age
age23[k] <- 23

# Correct with reproducible results
age23_corrected <- correctSingleHeap(age23, heap = 23, before = 5, after = 5,
                                     method = "lnorm", seed = 42)

# Get diagnostic information
result <- correctSingleHeap(age23, heap = 23, before = 5, after = 5,
                            verbose = TRUE, seed = 42)
print(result$n_changed)

Calculate All Heaping Indices

Description

This function calculates all available heaping indices for a given age vector, providing a comprehensive assessment of data quality.

Usage

heaping_indices(x, weight = NULL)

Arguments

Details

Convenience function to calculate multiple heaping indices at once.

Value

A named list with all heaping indices:

whipple_standard

Standard Whipple index (100 = no heaping)

whipple_modified

Modified Whipple index (0 = no heaping)

myers

Myers' blended index (0 = no heaping)

bachi

Bachi's index (0 = no heaping)

spoorenberg

Total Modified Whipple index (0 = no heaping)

noumbissi_0

Noumbissi's index for digit 0 (1 = no heaping)

noumbissi_5

Noumbissi's index for digit 5 (1 = no heaping)

Author(s)

Matthias Templ

See Also

Other heaping indices: bachi(), coale_li(), jdanov(), kannisto(), myers(), noumbissi(), spoorenberg(), whipple()

Examples

set.seed(42)
# Uniform ages (no heaping)
age_uniform <- sample(20:70, 10000, replace = TRUE)
heaping_indices(age_uniform)

# Heaped ages
age_heaped <- sample(seq(20, 70, by = 5), 5000, replace = TRUE)
heaping_indices(age_heaped)

Jdanov's Old-Age Heaping Index

Description

Jdanov's index is designed to detect age heaping at very old ages (typically 95+), where data quality is often poorest. It applies the Whipple principle to specific old-age values.

Usage

jdanov(x, Agei = c(95, 100, 105), weight = NULL)

Arguments

Details

Calculate Jdanov's index for detecting heaping at very old ages.

The index compares counts at specified old ages to the surrounding 5-year age groups, similar to the standard Whipple approach but focused on the oldest ages where heaping is most problematic.

Interpretation:

• 100: no heaping

• >100: preference for the specified ages

• 500: maximum heaping (all ages at specified values)

Value

A single numeric value representing Jdanov's index.

Author(s)

Matthias Templ

References

Jdanov, D. A., Scholz, R. D., and Shkolnikov, V. M. (2008). Official population statistics and the Human Mortality Database estimates of populations aged 80+ in Germany and nine other European countries. Demographic Research, 19, 1169-1196.

See Also

kannisto for Kannisto's index, coale_li for Coale-Li index.

Other heaping indices: bachi(), coale_li(), heaping_indices(), kannisto(), myers(), noumbissi(), spoorenberg(), whipple()

Examples

# Create old-age data with heaping
set.seed(42)
age <- c(sample(90:110, 2000, replace = TRUE),
         rep(c(95, 100, 105), each = 100))  # Add heaping
jdanov(age)  # Should be > 100

# No heaping
age_uniform <- sample(90:110, 2000, replace = TRUE)
jdanov(age_uniform)  # Should be close to 100

Kannisto's Age Heaping Index

Description

Kannisto's index compares the count at a specific age to a geometric mean of surrounding ages, providing a measure of heaping that is robust to exponentially declining populations at old ages.

Usage

kannisto(x, Agei = 90, weight = NULL)

Arguments

Details

Calculate Kannisto's index for detecting heaping at a specific old age.

Unlike other indices that use arithmetic means, Kannisto's index uses geometric means of neighboring ages, which is more appropriate for old-age populations where counts decline exponentially.

The index is calculated as the ratio of the count at age Agei to the geometric mean of counts at ages Agei-2 through Agei+2.

Interpretation:

• 1.0: no heaping at the specified age

• >1.0: heaping (attraction to the age)

• <1.0: avoidance of the age

Value

A single numeric value representing Kannisto's index.

Author(s)

Matthias Templ

References

Kannisto, V. (1999). Assessing the information on age at death of old persons in national vital statistics. Validation of Exceptional Longevity, Odense Monographs on Population Aging, 6, 235-249.

See Also

jdanov for Jdanov's index, coale_li for Coale-Li index.

Other heaping indices: bachi(), coale_li(), heaping_indices(), jdanov(), myers(), noumbissi(), spoorenberg(), whipple()

Examples

# Create old-age data with heaping at 90
set.seed(42)
age <- c(sample(85:95, 2000, replace = TRUE),
         rep(90, 200))  # Add heaping at 90
kannisto(age, Agei = 90)  # Should be > 1

# No heaping
age_uniform <- sample(85:95, 2000, replace = TRUE)
kannisto(age_uniform, Agei = 90)  # Should be close to 1

Myers' Blended Index of Age Heaping

Description

Myers' index measures preferences for each of the ten possible terminal digits (0-9) as a blended index. It is based on the principle that in the absence of age heaping, the aggregate population of each age ending in one of the digits 0 to 9 should represent 10 percent of the total population.

Usage

myers(x, ageMin = 23, ageMax = 82, weight = NULL)

Arguments

Details

Calculate Myers' blended index to measure digit preference in age data.

The index uses a blending technique that weights earlier ages more for digit preference calculation and later ages more for avoidance, creating a balanced measure across the age range.

The theoretical range is 0 to 90:

• 0: no digit preference (perfect data)

• 90: all ages reported with same terminal digit (maximum heaping)

Value

A single numeric value representing Myers' blended index.

Author(s)

Matthias Templ

References

Myers, R. J. (1940). Errors and bias in the reporting of ages in census data. Transactions of the Actuarial Society of America, 41, 395-415.

Myers, R. J. (1954). Accuracy of age reporting in the 1950 United States Census. Journal of the American Statistical Association, 49(268), 826-831.

See Also

bachi for Bachi's index, whipple for Whipple's index.

Other heaping indices: bachi(), coale_li(), heaping_indices(), jdanov(), kannisto(), noumbissi(), spoorenberg(), whipple()

Examples

# No heaping (uniform ages)
set.seed(42)
age_uniform <- sample(23:82, 10000, replace = TRUE)
myers(age_uniform)  # Should be close to 0

# Strong heaping on ages ending in 0 or 5
age_heaped <- sample(seq(25, 80, by = 5), 5000, replace = TRUE)
myers(age_heaped)  # Should be high

Noumbissi's Digit Heaping Index

Description

Noumbissi's method improves on Whipple's method by extending its basic principle to all ten digits. It compares the count of ages ending in a specific digit to the count in 5-year age groups centered on that digit.

Usage

noumbissi(
  x,
  digit = 0,
  ageMin = 20 + digit,
  ageMax = ageMin + 30,
  weight = NULL
)

Arguments

Details

Calculate Noumbissi's index for a specific terminal digit.

The index compares the number of persons reporting ages ending in a specific digit to one-fifth of the population in the 5-year age groups centered on those ages.

Interpretation:

• 1.0: no preference for the digit

• >1.0: preference (attraction) to the digit

• <1.0: avoidance of the digit

Value

A single numeric value representing Noumbissi's index for the specified digit.

Author(s)

Matthias Templ

References

Noumbissi, A. (1992). L'indice de Whipple modifie: une application aux donnees du Cameroun, de la Suede et de la Belgique. Population, 47(4), 1038-1041.

See Also

spoorenberg for Total Modified Whipple index, whipple for original Whipple's index.

Other heaping indices: bachi(), coale_li(), heaping_indices(), jdanov(), kannisto(), myers(), spoorenberg(), whipple()

Examples

# No heaping
set.seed(42)
age_uniform <- sample(20:70, 10000, replace = TRUE)
noumbissi(age_uniform, digit = 0)  # Should be close to 1
noumbissi(age_uniform, digit = 5)  # Should be close to 1

# Heaping on digit 0
age_heap0 <- sample(seq(20, 70, by = 10), 5000, replace = TRUE)
noumbissi(age_heap0, digit = 0)  # Should be > 1

Sample Data for Heaping Correction Examples

Description

A stratified random sample of demographic and income data from a synthetic population generated using the simPop package based on EU-SILC data. This dataset can be used to demonstrate and test heaping correction methods.

Usage

samp

Format

A data frame with 25 variables:

db030

Household ID

hsize

Household size

age

Age in years

rb090

Gender

db040

Region (Bundesland)

pid

Person ID

weight

Original sampling weight

pl031

Economic status

pb220a

Citizenship status

pb190

Marital status

pe040

Education level

pl111

Employment status

pgrossIncomeCat

Personal gross income category

pgrossIncome

Personal gross income

py010g

Employee cash or near cash income

py021g

Company car income

py050g

Self-employment income

py080g

Private pension income

py090g

Unemployment benefits

py100g

Old-age benefits

py110g

Survivor benefits

py120g

Sickness benefits

py130g

Disability benefits

py140g

Education-related allowances

.weight

Sampling weight from stratified sampling

Source

Generated using simPop from EU-SILC 2013 public use file. The full synthetic population can be regenerated using the script inst/scripts/create_pop.R.

See Also

eusilc13puf for the original data source.

Examples

data(samp)
head(samp)

# Check age distribution
hist(samp$age, breaks = 50, main = "Age Distribution")

# Introduce artificial heaping and correct it
age_heaped <- round(samp$age / 5) * 5
age_corrected <- correctHeaps(age_heaped, heaps = "5year")

Spoorenberg's Total Modified Whipple Index

Description

The Total Modified Whipple Index extends Noumbissi's approach by summing the absolute deviations from 1 for all ten digits, providing an overall measure of age heaping across all terminal digits.

Usage

spoorenberg(x, ageMin = 20, ageMax = 64, weight = NULL)

Arguments

Details

Calculate the Total Modified Whipple Index (Wtot) proposed by Spoorenberg.

The index is calculated as:

W_{tot} = \sum_{i=0}^{9} |1 - W_i|

where W_i is Noumbissi's index for digit i.

Interpretation:

• 0: no heaping (perfect data)

• Higher values indicate more heaping

• Maximum theoretical value is 16 (if all ages end in one digit)

Value

A single numeric value representing the Total Modified Whipple Index.

Author(s)

Matthias Templ

References

Spoorenberg, T. and Dutreuilh, C. (2007). Quality of age reporting: extension and application of the modified Whipple's index. Population, 62(4), 729-741.

See Also

noumbissi for single-digit index, whipple for original Whipple's index.

Other heaping indices: bachi(), coale_li(), heaping_indices(), jdanov(), kannisto(), myers(), noumbissi(), whipple()

Examples

# No heaping
set.seed(42)
age_uniform <- sample(20:64, 10000, replace = TRUE)
spoorenberg(age_uniform)  # Should be close to 0

# Strong heaping on 0 and 5
age_heaped <- sample(seq(20, 60, by = 5), 5000, replace = TRUE)
spoorenberg(age_heaped)  # Should be high

Sprague Index (Multipliers)

Description

The Sprague method uses multipliers to estimate population counts for each single year of age from 5-year interval data. This is useful for creating smooth single-year age distributions from grouped census data.

Usage

sprague(x)

Arguments

Details

Disaggregate 5-year age group counts into single-year ages using Sprague multipliers.

The input must be population counts for 17 five-year age groups: 0-4, 5-9, 10-14, 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, and 80+.

The Sprague multipliers are applied differently depending on the position of the age group:

• Lowest groups (0-4): Uses only following age groups

• Low groups (5-9): Uses mostly following age groups

• Normal groups (10-74): Uses symmetric weighting

• High groups (75-79): Uses mostly preceding age groups

• Highest groups (80+): Returned as-is (open-ended)

The total population is preserved: sum of output equals sum of input.

Value

A named numeric vector with 81 elements: single-year population counts for ages 0, 1, 2, ..., 79, and the 80+ group.

Author(s)

Matthias Templ

References

Calot, G. and Sardon, J.-P. (1998). Methodology for the calculation of Eurostat's demographic indicators. Detailed report by the European Demographic Observatory.

Sprague, T. B. (1880). Explanation of a new formula for interpolation. Journal of the Institute of Actuaries, 22, 270-285.

See Also

whipple for measuring age heaping.

Examples

# Example from World Bank data
x <- data.frame(
  age = as.factor(c(
    "0-4", "5-9", "10-14", "15-19", "20-24",
    "25-29", "30-34", "35-39", "40-44", "45-49",
    "50-54", "55-59", "60-64", "65-69", "70-74", "75-79", "80+"
  )),
  pop = c(
    1971990, 2095820, 2157190, 2094110, 2116580,
    2003840, 1785690, 1502990, 1214170, 796934,
    627551, 530305, 488014, 364498, 259029, 158047, 125941
  )
)

# Apply Sprague multipliers
s <- sprague(x$pop)
head(s, 20)  # First 20 single-year ages

# Verify population is preserved
all.equal(sum(s), sum(x$pop))

Whipple Index (Original and Modified)

Description

The Whipple index is a demographic measure used to detect and quantify age heaping (digit preference) in population data. This function implements both the original (standard) and modified versions of the index.

Usage

whipple(x, method = "standard", weight = NULL)

Arguments

Details

Calculate the original or modified Whipple index to evaluate age heaping.

The original Whipple index is obtained by summing the number of persons in the age range between 23 and 62, and calculating the ratio of reported ages ending in 0 or 5 to one-fifth of the total sample. A linear decrease in the number of persons of each age within the age range is assumed. Therefore, low ages (0-22 years) and high ages (63 years and above) are excluded from analysis since this assumption is not plausible.

The original Whipple index ranges from:

• 0: when digits 0 and 5 are never reported

• 100: no preference for 0 or 5 (perfect data)

• 500: when only digits 0 and 5 are reported (maximum heaping)

For the modified Whipple index, age heaping is calculated for all ten digits (0-9). For each digit, the degree of preference or avoidance is determined, and the modified Whipple index is given by the absolute sum of these (indices - 1), scaled between 0 and 1:

• 0: ages are distributed perfectly equally across all digits

• 1: all age values end with the same digit

Value

A single numeric value representing the Whipple index.

Author(s)

Matthias Templ

References

Shryock, H. S. and Siegel, J. S. (1976). The Methods and Materials of Demography. New York: Academic Press.

Spoorenberg, T. and Dutreuilh, C. (2007). Quality of age reporting: extension and application of the modified Whipple's index. Population, 62(4), 729-741.

See Also

sprague for disaggregating 5-year age groups.

Other heaping indices: bachi(), coale_li(), heaping_indices(), jdanov(), kannisto(), myers(), noumbissi(), spoorenberg()

Examples

# Equally distributed ages (no heaping)
set.seed(42)
age_uniform <- sample(1:100, 5000, replace = TRUE)
whipple(age_uniform)                    # Should be close to 100
whipple(age_uniform, method = "modified")  # Should be close to 0

# Strong heaping on 5 and 10 (ages ending in 0 or 5 only)
age_5year <- sample(seq(0, 100, by = 5), 5000, replace = TRUE)
whipple(age_5year)                     # Should be 500
whipple(age_5year, method = "modified")   # Should be close to 0.8

# Extreme heaping on 10 only (ages ending in 0 only)
age_10year <- sample(seq(0, 100, by = 10), 5000, replace = TRUE)
whipple(age_10year)                    # Should be 500
whipple(age_10year, method = "modified")  # Should be close to 1

# Using weights
weights <- runif(5000)
whipple(age_uniform, weight = weights)