Issues Associated With the Formulation of a Small Area Model for Estimation of State-Level Crime Victimization Rates

• Published date: 01 February 2025
• DOI: http://doi.org/10.1177/10439862241289784
• Author: Emily Berg
• Date: 01 February 2025

Article

Journal of Contemporary Criminal Justice

2025, Vol.41(1) 30–50

ÓThe Author(s) 2024

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DOI: 10.1177/10439862241289784

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Issues Associated With the

Formulation of a Small Area

Model for Estimation of

State-Level Crime

Victimization Rates

Emily Berg

1

Abstract

Subnational estimation is an important and challenging problem in thecontext of the

National Crime Victimization Survey (NCVS). Directestimates for subnational

domains are often unreliable due to small sample sizes. Model-based procedures have

potential to improve upon direct estimators. However, model-based estimation pre-

sents several new challenges. One must identify suitable covariates, and an appropri-

ate model form must be specified. This article discusses issues associated with the

formulation of a small area model for production of state-level estimates of crime

victimization rates. An analysis of direct estimates and covariates motivates the

development of a Bayesian multivariate model. A model in the original scale is com-

pared to a model in the log scale. Efficiency gains from the model relative to the

direct estimators are examined. One challenge is that direct estimates can equal

zero. Two ways of handling zero direct estimates are discussed.

Keywords

Bayesian, lognormal, small area estimation

Introduction

The Bureau of Justice Statistics (BJS) has traditionally published direct estimates

based on the National Crime Victimization Survey (NCVS). A direct estimate is a

weighted sum of sampled units, where the weights reflect sample selection

1

Iowa State University, Ames, USA

Corresponding Author:

Emily Berg, Department of Statistics,Iowa State University, 2438 Osborn Drive, Ames, IA 50011, USA.

Email: emilyb@iastate.edu

probabilities and nonresponse adjustments. Direct estimates are often considered reli-

able at the national scale, and BJS routinely publishes direct, national-level estimates

in its annual bulletin Criminal Victimization (Thompson and Tapp, 2023).

Subnational estimation is an important topic for the NCVS. Data users require sub-

national data for research and policy purposes. A challenge in producing subnational

estimates is that sample sizes in subnational domains are often small. These small

sample sizes can cause direct estimates to be unreliable,as indicated by unacceptably

high coefficients of variation.

In response to the demand for subnational data and the challenges associated with

producing such estimates, the NCVS underwent a redesign in 2016 (Kena & Morgan,

2023). This enabled publication of direct estimates for 22 large states in Criminal

Victimization in the 22 Largest U.S. States, 2017–2019 (Kena & Morgan, 2023).

However, estimates for the remaining 28 states and the District of Columbia (DC)

were not published and are still desired. Despite the redesign, state-level estimation

remains a challenging problem.

One way to address the challenges associated with subnational estimation is to

transition from direct estimation to model-based estimation. The National Academies

of Sciences recommended that BJS ‘‘investigate the use of modeling . . . toconstruct

and disseminate subnational estimates of major crime types’’ (National Research

Council, 2008). Model-based estimates can be more efficient than direct estimates.

One way in which model-based estimators improve upon direct estimators is by

incorporating population-level auxiliary information. If the auxiliary information is

sufficiently correlated with the survey response variables, then incorporating this

information can improve the estimators.Model-based procedures also use stronger

assumptions than direct estimators. If the model assumptions are satisfied, then the

model-based estimators are more precise than direct estimators.

BJS has invested considerable resources in model-based estimation. Specifically, a

multivariate dynamic model (MDM) was developed (Fay, 2021; Fay et al., 2013; Fay

& Li, 2011). The multivariate component ofthis model means that multiple types of

crime are modeled in a unified fashion. The dynamic component integrates data from

a lengthy time series. The MDM was used to produce estimates at state levels.

Due to the difficulty of obtaining subnational estimates, BJS expressed interest in

exploring alternatives to the MDM. In this direction, we pursue alternative modeling

strategies. Our primary innovation is to develop a Bayesian lognormal model. We

develop this model in the direction of obtainingstate-level estimates of crime victi-

mization rates. This document describes the process of developing the multivariate

lognormal model. One of the challenges that emerges is that direct estimates of zero

can pose difficulties. Therefore, this document also explores alternative strategies for

handling direct estimates of zero.

This Bayesian lognormal model differs from the MDM in four main ways. First,

the MDM operates in a frequentist paradigm, while we use Bayesian inference proce-

dures. In the frequentist paradigm, model parameters are regarded as fixed unknown

quantities, whereas prior distributions are assigned to model parameters in the

Berg 31