An Interactive Data Tool to Explore State 

and County Model-based Estimates of Adult

Literacy and Numeracy Skills

Tom Krenzke, Weijia Ren, Andreea Erciulescu, Leyla Mohadjer

TomKrenzke@westat.com

Federal Committee on Statistical Methodology Conference

October 25, 2022
PIAAC International Survey of Adult Skills

❯ Program for the International Assessment of Adult Competencies (PIAAC)

❯ Over 35 countries in Cycle 1 (2012 to 2017)

❯ PIAAC in the U.S. (sponsored by the National Center for Education Statistics)

• Surveyed 12,330 U.S. adults ages 16 to 74 living in households over three 

data collections (2012, 2014, 2017) that were combined together

• Included a Background Questionnaire and assessment of literacy and 

numeracy skills (in English)

• Involved a complex sample design for each data collection

• Designed to produce national estimates 

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National Statistics on Adult Literacy and Numeracy Skills by 

Education Attainment Group

ISCED: International Standard Classification of Education

Source: U.S. Department of Education, National Center for Education Statistics, U.S. Program for the 

International Assessment of Adult Competencies (PIAAC), 2017. 3

0

50

100

150

200

250

300

350

ISCED 2

and below

ISCED 3

and 4a-b

ISCED 5a-b

and 6

Mean Literacy By 

Education Attainment: 

PIAAC 2017

0

50

100

150

200

250

300

350

ISCED 2

and below

ISCED 3

and 4a-b

ISCED 5a-b

and 6

Mean Numeracy By 

Education Attainment: 

PIAAC 2017
PIAAC Small Area Estimation

❯ Small area estimation (SAE) includes a variety of statistical techniques 

to predict survey outcomes for smaller areas

❯ U.S. PIAAC in Cycle 1 had sample in most states, but only 185 counties

❯ Methodology was built upon previous work relating to a previous 

national assessment with one outcome – Mohadjer, et al (2009)

❯ Eight outcomes were estimated

• 2 components: Literacy/numeracy 

• 4 types: average scores, percentage at or below Level 1 (low 

proficiency), at Level 2 (medium proficiency), at or above Level 3 

(high proficiency)

❯ Three sets of model-based estimates were developed

• Set 1. State and county (released in 2020)

• Set 2. State by group (new) – age and education attainment groups

• Set 3. County by group (new) – age and education attainment groups

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Set 1: PIAAC SAE Models for States and Counties

❯ Models used the PIAAC survey results in conjunction with data 

from the 2013-2017 Census Bureau’s American Community Survey (ACS)

❯ Included the following covariates: education attainment, poverty, 

race/ethnicity, health insurance, and service occupations 

❯ Model structures

• Proportions -- Area-level bivariate Hierarchical Bayes linear three-fold 

models

• Averages – Area-level univariate Hierarchical Bayes linear three-fold 

models

❯ Models were fit at the county level, and predictions aggregated to state level

❯ Models were subjected to rigorous diagnostic checks 

❯ 4,500 posterior samples were generated

❯ Credible intervals are provided to indicate how confident the user can be in 

the estimates

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Set 2: PIAAC SAE Model for States and Groups

❯ 10 Groups were created

• 6 age groups:16-24, 25-34, 35-44, 45-54, 55-64, and 65-74

• 4 education groups: less than high school, high school diploma or GED, 

some college (no degree or attained associate’s degree), and bachelor’s 

degree or higher

❯ Models, like Set 1, used the PIAAC survey results in conjunction with ACS data 

❯ Included a subset of the following covariates: education attainment, poverty, 

race/ethnicity, health insurance, and service occupations 

❯ Model structure for proportions and averages involved an area-level univariate 

Hierarchical Bayes linear models

❯ Models were fit at the state level

❯ Predictions were benchmarked to state-level model-based estimates

❯ Evaluated the model predictions

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Set 3: PIAAC SAE Model for Counties and Groups

❯ An allocation deterministic model approach used the following:

Set 3 County group pseudo posterior sample 

= Set 2 state group posterior sample * Set 1 county posterior sample / Set 

1 state posterior sample

❯ Computation assumes ratios of county-to-state model-based posterior 

samples are constant across groups

❯ Aggregations of county by age/education group estimates agree closely, but 

not exactly, to the state by age/education group model-based estimates

❯ Credible intervals are provided to assess the precision of estimates (as in 

Sets 1 and 2)

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Demonstration

Skills Map: nces.ed.gov/surveys/piaac/skillsmap

U.S. State and County Estimates: 

nces.ed.gov/surveys/piaac/state-county-estimates.asp

PIAAC Website: nces.ed.gov/surveys/piaac/

Photos are for illustrative purposes only. All persons depicted, unless otherwise stated, are models. 8
Skills Map Landing Page

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PIAAC SAE Products

❯ Skills Map -- https://nces.ed.gov/surveys/piaac/skillsmap/

• User guide – accessed via button in Skills Map

❯ Other state and county materials --

https://nces.ed.gov/surveys/piaac/skillsmap/

• FAQs

• Brochure

• Methodology reports – one for each of the three sets of estimates 

-Set 1 estimates – Krenzke, et al (2020)

-Set 2 estimates – Li, et al (2022)

-Set 3 estimates – Erciulescu, et al (2022)

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Acknowledgements

❯ Westat statistical team: Tom Krenzke, Leyla Mohadjer, Jianzhu Li, Weijia 

Ren, Robert Fay, Andreea Erciulescu, Lin Li, Wendy Van de Kerckhove

❯ Consultant: J.N.K. Rao

❯ International Expert Panel: William Bell, Partha Lahiri, Danny 

Pfeffermann, Dan Sherman, and Avi Singh

❯ Interaction Design Team: Angelica Paul, Alexander Schneider, Justin 

Kemmerer, Meganne Abbott, Varun Karne

❯ Westat PIAAC Project Director: Jacquie Hogan

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