Poverty and Inequality with convey

Introduction

The convey package by Guilherme Jacob, Anthony Damico, and Djalma Pessoa implements poverty and inequality indicators for complex survey data. It works with survey::svydesign objects — the same objects that metasurvey wraps inside Survey objects.

This vignette shows how to use convey functions inside workflow() to compute Gini coefficients, at-risk-of-poverty rates, FGT indices, and other distributional measures, all with proper standard errors and CVs.

For the full reference on every measure, see the convey book.

Setup

We use the api dataset from the survey package. The api00 variable (Academic Performance Index score in 2000) serves as our continuous variable for inequality measures, and meals (percent of students eligible for subsidized meals) works as an income-like proxy.

library(metasurvey)
library(survey)
library(convey)
library(data.table)

data(api, package = "survey")
dt <- data.table(apistrat)

svy <- Survey$new(
  data    = dt,
  edition = "2000",
  type    = "api",
  psu     = NULL,
  engine  = "data.table",
  weight  = add_weight(annual = "pw")
)

Preparing the design for convey

Before using any convey function, the underlying design must be prepared with convey_prep(). Build the design with ensure_design() and then replace the estimation-type entry:

svy$ensure_design()
svy$design[["annual"]] <- convey_prep(svy$design[["annual"]])

Inequality Measures

Gini coefficient

The Gini index measures overall inequality on a 0–1 scale:

gini <- workflow(
  list(svy),
  convey::svygini(~api00, na.rm = TRUE),
  estimation_type = "annual"
)

gini
#>                     stat variable     value          se         cv
#>                   <char>   <char>     <num>       <num>      <num>
#> 1: convey::svygini: gini     gini 0.1123906 0.004824568 0.04292681
#>    confint_lower confint_upper  evaluate
#>            <num>         <num>    <char>
#> 1:     0.1029346     0.1218465 Excellent

Atkinson index

The Atkinson index uses an inequality aversion parameter epsilon. Higher epsilon gives more weight to the lower tail:

atk_05 <- workflow(
  list(svy),
  convey::svyatk(~api00, epsilon = 0.5),
  estimation_type = "annual"
)

atk_1 <- workflow(
  list(svy),
  convey::svyatk(~api00, epsilon = 1),
  estimation_type = "annual"
)

rbind(atk_05, atk_1)
#>                        stat variable       value           se         cv
#>                      <char>   <char>       <num>        <num>      <num>
#> 1: convey::svyatk: atkinson atkinson 0.008841101 0.0007781485 0.08801488
#> 2: convey::svyatk: atkinson atkinson 0.017852866 0.0015768947 0.08832726
#>    confint_lower confint_upper  evaluate
#>            <num>         <num>    <char>
#> 1:   0.007315958    0.01036624 Very good
#> 2:   0.014762210    0.02094352 Very good

The QSR compares income at the top 20% with the bottom 20%:

qsr <- workflow(
  list(svy),
  convey::svyqsr(~api00, na.rm = TRUE),
  estimation_type = "annual"
)

qsr
#>                   stat variable    value        se         cv confint_lower
#>                 <char>   <char>    <num>     <num>      <num>         <num>
#> 1: convey::svyqsr: qsr      qsr 1.565964 0.0355218 0.02268367      1.496342
#>    confint_upper  evaluate
#>            <num>    <char>
#> 1:      1.635585 Excellent

Generalized entropy index

The GEI family includes the Theil index (alpha = 1) and the mean log deviation (alpha = 0):

theil <- workflow(
  list(svy),
  convey::svygei(~api00, epsilon = 1),
  estimation_type = "annual"
)

mld <- workflow(
  list(svy),
  convey::svygei(~api00, epsilon = 0),
  estimation_type = "annual"
)

rbind(theil, mld)
#>                   stat variable      value          se         cv confint_lower
#>                 <char>   <char>      <num>       <num>      <num>         <num>
#> 1: convey::svygei: gei      gei 0.01749577 0.001533703 0.08766137    0.01448977
#> 2: convey::svygei: gei      gei 0.01801415 0.001605559 0.08912763    0.01486731
#>    confint_upper  evaluate
#>            <num>    <char>
#> 1:    0.02050177 Very good
#> 2:    0.02116099 Very good

Poverty Measures

For poverty measures we use meals (percent of students receiving subsidized meals) as an income-like variable. We define a poverty threshold at 50%.

At-risk-of-poverty threshold

svyarpt() computes the at-risk-of-poverty threshold (60% of the median by default):

arpt <- workflow(
  list(svy),
  convey::svyarpt(~meals, na.rm = TRUE),
  estimation_type = "annual"
)

arpt
#>                     stat variable value       se         cv confint_lower
#>                   <char>   <char> <num>    <num>      <num>         <num>
#> 1: convey::svyarpt: arpt     arpt    27 2.051721 0.07598967       22.9787
#>    confint_upper  evaluate
#>            <num>    <char>
#> 1:       31.0213 Very good

At-risk-of-poverty rate

svyarpr() computes the proportion of units below the ARPT:

arpr <- workflow(
  list(svy),
  convey::svyarpr(~meals, na.rm = TRUE),
  estimation_type = "annual"
)

arpr
#>                     stat variable     value         se         cv confint_lower
#>                   <char>   <char>     <num>      <num>      <num>         <num>
#> 1: convey::svyarpr: arpr     arpr 0.2974169 0.02696583 0.09066677     0.2445648
#>    confint_upper  evaluate
#>            <num>    <char>
#> 1:     0.3502689 Very good

FGT poverty indices

The Foster-Greer-Thorbecke (FGT) family provides:

FGT(0): headcount ratio (proportion below the line)
FGT(1): poverty gap (average depth of poverty)
FGT(2): severity (squared poverty gap, penalizes extreme poverty)

threshold <- 50

fgt0 <- workflow(
  list(svy),
  convey::svyfgt(~meals, g = 0, abs_thresh = threshold, na.rm = TRUE),
  estimation_type = "annual"
)

fgt1 <- workflow(
  list(svy),
  convey::svyfgt(~meals, g = 1, abs_thresh = threshold, na.rm = TRUE),
  estimation_type = "annual"
)

fgt2 <- workflow(
  list(svy),
  convey::svyfgt(~meals, g = 2, abs_thresh = threshold, na.rm = TRUE),
  estimation_type = "annual"
)

rbind(fgt0, fgt1, fgt2)
#>                    stat variable     value         se         cv confint_lower
#>                  <char>   <char>     <num>      <num>      <num>         <num>
#> 1: convey::svyfgt: fgt0     fgt0 0.5590055 0.03854638 0.06895528     0.4834560
#> 2: convey::svyfgt: fgt1     fgt1 0.2733427 0.02456407 0.08986547     0.2251980
#> 3: convey::svyfgt: fgt2     fgt2 0.1795022 0.02043659 0.11385149     0.1394472
#>    confint_upper  evaluate
#>            <num>    <char>
#> 1:     0.6345550 Very good
#> 2:     0.3214874 Very good
#> 3:     0.2195572      Good

Full Pipeline: Steps + Convey

A complete pipeline with data transformations followed by inequality estimation:

dt_full <- data.table(apistrat)

svy_full <- Survey$new(
  data    = dt_full,
  edition = "2000",
  type    = "api",
  psu     = NULL,
  engine  = "data.table",
  weight  = add_weight(annual = "pw")
)

# Transform: compute a derived variable
svy_full <- step_compute(svy_full,
  api_growth = api00 - api99,
  comment = "API score growth"
)

# Bake the steps
svy_full <- bake_steps(svy_full)

# Prepare for convey
svy_full$ensure_design()
svy_full$design[["annual"]] <- convey_prep(svy_full$design[["annual"]])

# Inequality: Gini on derived variable, Atkinson on api00 (must be positive)
results <- workflow(
  list(svy_full),
  convey::svygini(~api_growth, na.rm = TRUE),
  convey::svyatk(~api00, epsilon = 1),
  estimation_type = "annual"
)

results
#>                        stat variable      value          se         cv
#>                      <char>   <char>      <num>       <num>      <num>
#> 1:    convey::svygini: gini     gini 0.48220882 0.033233109 0.06891850
#> 2: convey::svyatk: atkinson atkinson 0.01785287 0.001576895 0.08832726
#>    confint_lower confint_upper  evaluate
#>            <num>         <num>    <char>
#> 1:    0.41707312    0.54734451 Very good
#> 2:    0.01476221    0.02094352 Very good

Quality assessment

for (i in seq_len(nrow(results))) {
  cv_val <- results$cv[i] * 100
  cat(
    results$stat[i], ":",
    round(cv_val, 1), "% CV -",
    evaluate_cv(cv_val), "\n"
  )
}
#> convey::svygini: gini : 6.9 % CV - Very good 
#> convey::svyatk: atkinson : 8.8 % CV - Very good

Publication table

workflow_table(
  results,
  title = "Inequality of API Score Growth",
  subtitle = "California Schools, 2000"
)

Statistic	variable	Estimate	SE	CI Lower	CI Upper	CV (%)	Quality
Inequality of API Score Growth
California Schools, 2000
:svygini: gini	gini	0.48	0.033	0.42	0.55	6.9	Very good
:svyatk: atkinson	atkinson	0.02	0.002	0.01	0.02	8.8	Very good
metasurvey 0.0.23 \| CI: 95% \| 2026-04-23

Provenance

Provenance is tracked automatically. The full lineage — steps applied, convey estimates computed, and package versions — is available:

prov <- provenance(results)
prov
#> ── Data Provenance ─────────────────────────────────────────────────────────────
#> Loaded: 2026-04-23T01:10:10 
#> Initial rows: 200 
#> 
#> Pipeline:
#>   1. step_1 Compute: api_growth  N=200 [1.0ms]
#> 
#> Estimation:
#>   Type: annual 
#>   Timestamp: 2026-04-23T01:10:10 
#> 
#> Environment:
#>   metasurvey: 0.0.23 
#>   R: 4.5.3 
#>   survey: 4.5
cat("metasurvey version:", prov$environment$metasurvey_version, "\n")
#> metasurvey version: 0.0.23
cat("Steps applied:", length(prov$steps), "\n")
#> Steps applied: 1

References

Jacob, G., Damico, A., & Pessoa, D. (2024). Poverty and Inequality with Complex Survey Data. https://www.convey-r.org/
Lumley, T. (2010). Complex Surveys: A Guide to Analysis Using R. Wiley.