www.rti.org RTI International is a trade name of Research Triangle Institute. RTI and the RTI logo are U.S. registered trademarks of Research Triangle Institute.

A Practical Framework for Arealevel Small Area Estimation

Stephanie Zimmer
All about process

o Audience is statisticians who are not familiar with small-area-estimation 

(SAE)

o Make SAE approachable and break process into components

o Develop a framework for area-level SAE

o Use concrete examples

• National Crime Victimization Survey (NCVS)

• Ohio Medicaid Assessment Survey (OMAS)
Step 1: Understand the requirements

o What are the outcomes?

o What is the small area of interest (domain)? Geographic level, 

demographic group, etc.

o What is the time period?

o What software can be used? Does it need to be off the shelf? Does it 

need to be open?

o Anything else?
Step 1: Example

Requirement OMAS NCVS

Outcome Health insurance rates for 

adults 19+

Victimization rates and 

prevalence rates for 12 

crime types – personal and 

household

Domain Ohio counties State, large counties, large 

CBSAs

Time period 2017 2009-2015 (3-year 

estimates for each year)

Software requirement Off the shelf Software must be available 

in the Census RDC

Other State estimates must sum 

to national estimates
Step 2: Understand the survey data and sampling design

o Is the design longitudinal, cross-sectional, and/or panel?

o What type of variance estimation is used for direct estimates?

o Are the domain identifiers, sampling variables and all outcomes available 

on the file?

o Summarize the number of observations per domain and be sure to include 

domains that may have 0 observations

o Calculate direct survey estimates and standard errors in the domains 

where possible for later comparison
Step 2: Example - NCVS

o Longitudinal and panel design

o Taylor’s series and replicate weights available

o Geographic identifiers only available on restricted use file

o Direct estimates and standard errors were calculated in a subset of states
Step 3: Identify and obtain potential auxiliary data

o Common auxiliary data sources include:

• Administrative records

• Data from large area surveys such as the American Community Survey or 

censuses

• Commercial data

o Requirements of auxiliary data

• Include every domain of interest with matching definitions

• No missing values

o Obtaining data may take a lot of time including data use agreements

o Use simple regression or decision trees to reduce set of potential 

variables
Step 3: Auxiliary data example – OMAS potential variables

o ACS 5-year, 2012-2016

• Adult population (N)

• Hispanic (p)

• Am. Indian/Alaskan Native (p)

• Aged 65+ (p)

• Non-citizen (p)

• Housing unit ownership (p)

• Adults with less than high school (p)

• Male (p)

o County business patterns

• Adults employed by non-retail firms 

(p)

o SAIPE

• Income (median)

• Poverty, all ages (p)

• SNAP receipients (N)

o BEA

• Per capita income

o BLS

• Unemployment rate (avg)

o 2010 Census

• Rural housing units (p)
Step 3: Auxiliary data example – OMAS selected variables

Selection process

o Used linear model with 

stepwise selection of 

variables 

o AIC used for criteria

Selection results

o BEA

• Per capita income

o SAIPE

• Poverty, all ages (p)

o ACS 5-year, 2012-2016

• Housing unit ownership (p)

• Adults with less than high school (p)
Step 4: Choose model and assumptions

o Consider the data (longitudinal or cross-sectional)

o Consider the outcome (mean, proportion, other)

o Consider the software limitations and availablity
Step 4: Example - OMAS

o Modified Fay-Herriot hierarchical Bayes model

o Sampling model:

• Relates the survey direct estimate with the true proportion

• Includes sampling error component

o Link between parameter of interest and auxiliary variables

• Linear model using logit transformation

• Includes random error component
Step 5: Estimation

o Write the code

o Have thorough code review

o Perform model diagnostics

o Check convergence in Bayesian estimation
Step 5: Example - OMAS

o R package R2OpenBUGS used to estimate parameters which calls 

OpenBUGS from R

o Convergence examined visually with trace plots and with the GelmanRubin potential scale reduction factor
Step 6: Evaluation and validation

o Compare the direct estimates, SAE estimates, and other similar estimates

o Compare precision between direct and SAE estimates
Step 6: NCVS Example: Victimization rate - Direct vs SAE
Step 6: NCVS Example: SE - Direct vs SAE 
Step 6: NCVS Example: UCR (Admin data) vs NCVS
Summary

o This paper is geared towards a statistician beginning work in SAE or a 

non-statistician just wanting to understand the process

o It includes references to seminal works with more details – these are still 

important

o We want to make this more accessible and open to all
Resources

o Small Area Estimation for the National Crime Victimization Survey: A 

Guide for Data Processing and Estimation Procedures, 2021

o A Practical Guide to Small Area Estimation, Illustrated Using the Ohio 

Medicaid Assessment Survey
Thank you

Contact: Stephanie Zimmer| email: sazimmer@rti.org

Dan Liao

Rachel Harter