A LOG‐MULTIPLICATIVE ASSOCIATION MODEL FOR ALLOCATING HOMICIDES WITH UNKNOWN VICTIM‐OFFENDER RELATIONSHIPS*

• Date: 01 May 2002
• DOI: http://doi.org/10.1111/j.1745-9125.2002.tb00963.x
• Author: GLENN DEANE,MARK BEAULIEU,STEVEN F. MESSNER
• Published date: 01 May 2002

A LOG-MULTIPLICATIVE ASSGCIATION

MODEL FOR ALLOCATING HOMICIDES

RELATIONSHIPS*

WITH UNKNOWN VICTIM-OFFENDER

STEVEN

F.

MESSNER

GLENN DEANE

MARK

BEAULIEU

University at Albany, SUNY

This research note critically evaluates conventional methods for allo-

cating homicides with an unknown victidoffender relationship to

meaningful categories, and

it

proposes an alternative approach. We

argue that conventional methods are based

on

a problematic assump-

tion, namely, that the missing data mechanism is “ignorable.”

As

an

alternative to these methods, we propose an imputation algorithm

derived from a log-multiplicative model that does not require this

assumption. We apply this technique

to

estimate levels

of

homicides

disaggregated by victidoffender relationship using the Federal Bureau

of

Investigation’s Supplementary Homicide Report (SHR) data for

1996

and

1997,

and we compare the resulting estimates with those

obtained from the application

of

conventional procedures.

Our

results

yield a larger proportion

of

stranger homicides than are obtained from

the conventional methods.

KEY WORDS

Homicide, missing, imputation, log-multiplicative.

Researchers have long recognized the potential utility of disaggregating

the general category

of

“homicide” into more homogenous subtypes

(Wolfgang,

1958).

Over recent decades, much interest has focused on the

analysis of homicides disaggregated on the basis

of

the victim/offender

relationship (hereafter,

v/o

relationship). For example, a growing body

of

literature has examined intimate partner homicide and documented dis-

tinctive gender patterns: Women are much more likely than men are

to

kill

*

A previous version

of

this paper was presented at the annual meetings of the

American Society

of

Criminology. San Francisco. CA, November

2000.

Wc are grateful

to Wendy Regoeczi and thc anonymous referees for helpful comments on earlier drafts.

Support for this rcsearch was provided by the National Consortium on Violencc

Research (NCOVR). NCOVR

is

funded through grant

#

SBR 9513040 from the

National Science Foundation. Support was also provided by grants

to

the Center

for

Social and Demographic Analysis from NlCHD (PD30 HD32041) and NSF (SBR

9512290). Any findings, conclusions, or recommendations expressed herein are those

of

the authors and do not necessarily reflect the views

of

the funding agencies.

CRIMINOLOGY

VOLUME

40

NUMBER

2

2002

457

458

MESSNER

ET

AL.

and be killed by intimate patterns (Browne and Williams, 1993; Browne et

al., 1999). Similarly, researchers have found it useful to distinguish vio-

lence between strangers from other forms of violence for theoretical rea-

sons (Williams and Flewelling, 1988) and for the practical reason that most

people are especially fearful of stranger violence (Riedel, 1993, 1998).

A persistent and vexing issue in the study of homicide disaggregated

by

v/o relationship, however, is that of missing data. When the perpetrator is

unknown, v/o relationships cannot be determined. This proves to be the

case in a nontrivial number

of

cases.

To

illustrate, Riedel (1998:209)

reports that the percentage

of

recorded homicides in the Federal Bureau

of Investigation’s

(FBI’s)

Supplementary Homicide Reports (SHR) with

unknown v/o relationships ranged between 27% and almost 40% during

the 1977 to 1995 period.’ Variation across cities in the extent to which

information on offenders is recorded is also striking. In their study of 91

cities in 1990, Pampel and Williams

(2000:664)

identify three cities with no

missing data on perpetrators (Madison, Columbus, and Syracuse). Data

on v/o relationship for Washington, D.C., in contrast, are missing for 94%

of the homicides.

Despite widespread recognition

of

the seriousness

of

the missing data

problem in research on v/o relationships in homicide, criminologists have

done little work to develop techniques to deal with the problem. The most

important exceptions are the innovative adjustment procedures intro-

duced originally

by

Williams and Flewelling (1987) and elaborated more

recently by Pampel and Williams (2000). In addition, Regoeczi and Riedel

(1 999, 2000) have applied a maximum likelihood procedure (expectation

maximization) to impute missing values on v/o relationship with data for

Chicago and

Los

Angeles and provide detailed explanations and critiques

of

commonly used techniques for imputing missing values.

The purpose

of

this research note is to probe further into the logic of

conventional methods for imputing unknown v/o relationship homicides

and

to

propose an alternative approach. We focus on the methods popu-

larized by Williams and colleagues because their work has had the greatest

impact within the discipline. Our critique applies more generally, how-

ever, to all methods for imputing

v/o

relationship that assume an ignorable

1.

The SHR is likely to overestimate the proportion of homicides with

an

unknown v/o relationship relative to that found in the statistics of local

law

enforcement

agencies because the SHR are typically submitted at early stages

of

investigation.

before difficult cases are solved, and the reports are not updated subsequently. See

Langford et al. (1998). Maxfield (1989). and Riedel (1989). Nevertheless, any data

source that is not based

on

perfect clearance rates will have missing data

on

a

v/o

relationship.