Modeling Two Types of Peace

• Date: 01 June 2015
• Author: Will H. Moore,Bumba Mukherjee,Benjamin E. Bagozzi,Daniel W. Hill
• Published date: 01 June 2015
• DOI: 10.1177/0022002713520530
• Subject Matter: Research Note

Research Note

Modeling Two Types of

Peace: The Zero-inflated

Ordered Probit (ZiOP)

Model in Conflict Research

Benjamin E. Bagozzi

1

, Daniel W. Hill, Jr.

2

,

Will H. Moore

3

, and Bumba Mukherjee

4

Abstract

A growing body of applied research on political violence employs split-population

models to address problems of zero inflation in conflict event counts and related

binary dependent variables. Nevertheless, conflict researchers typically use standard

ordered probit models to study discrete ordered dependent variables characterized

by excessive zeros (e.g., levels of conflict). This study familiarizes conflict scholars

with a recently proposed split-population model—the zero-inflated ordered probit

(ZiOP) model—that explicitly addresses the econometric challenges that research-

ers face when using a ‘‘zero-inflated’’ ordered dependent variable. We show that the

ZiOP model provides more than an econometric fix: it provides substantively rich

information about the heterogeneous pool of ‘‘peace’’ observations that exist in

zero-inflated ordinal variables that measure violent conflict. We demonstrate the

usefulness of the model through Monte Carlo experiments and replications of pub-

lished work and also show that the substantive effects of covariates derived from the

ZiOP model can reveal nonmonotonic relationships between these covariates and

one’s conflict probabilities of interest.

1

Department of Political Science, University of Minnesota, Minneapolis, MN, USA

2

Department of International Affairs, University of Georgia, Athens, GA, USA

3

Department of Political Science, Florida State University, Tallahassee, FL, USA

4

Department of Political Science, Penn State University, University Park, PA, USA

Corresponding Author:

Benjamin E. Bagozzi, Department of Political Science, University of Minnesota, 1472 Social Sciences 267

19th Ave. S, Minneapolis, MN 55455, USA.

Email: bbagozzi@umn.edu

Journal of Conflict Resolution

2015, Vol. 59(4) 728-752

ªThe Author(s) 2014

Reprints and permission:

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DOI: 10.1177/0022002713520530

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Keywords

zero-inflation, civil wars, militarized interstate disputes, ordered probit

Applied conflict researchers are becoming increasingly aware of a class of statistical

models known as split-population, or zero-inflated,

1

models (e.g., Clark and Regan

2003; Moore and Shellman 2004; Svolik 2008; Xiang 2010).

2

These models address

the econometric challenges that arise when a dependent conflict variable is charac-

terized by an excess number of ‘‘peace’’ observations in its zero category (i.e., is

zero inflated). Thus far, conflict scholars have used split-population models to deal

with these problems of ‘‘zero inflation’’ primarily in the contexts of event counts

3

and binary dependent variables (Svolik 2008; Xiang 2010). Nevertheless, when

analyzing zero-inflated ordered dependent variables, scholars of political violence

typically use standard ordered probit (OP) or ordered logit (OL) models (Senese

1997, 1999; Huth 1998; Besley and Persson 2009; Wiegand 2011). As shown

subsequently, analysis of zero-inflated ordered dependent variables raises methodo-

logical challenges that cannot be adequately addressed by these conventional

techniques. This study, therefore, familiarizes conflict researchers with a split-

population model known as the zero-inflated ordered probit (ZiOP) model (Harris

and Zhao 2007), which explicitly addresses two main statistical issues prevalent

in many quantitative studies of ordered conflict variables.

The first statistical issue involves researchers’ coding of ordered dependent con-

flict variables. Specifically, scholars typically code ‘‘peace’’ observations in ordinal

dependent variables of conflict as ‘‘zero’’ and then evaluate the impact of explana-

tory variables on such ordinal dependent conflict variables which contain excess

zeros (i.e., are zero inflated). They also treat the excess zeros mentioned previously

as a homogeneous group even though it is empirically pla usible that theremay be two

differenttypes of zeros in the set of ‘‘inflated’’zero observationsin the orderedconflict

variable. For example, in the case of discrete ordered levels of interstate conflict,

peace-year zeros will be recorded by scholars for countries separated by vast geo-

graphic distances that simply do not interact with each other, as well as for years in

which ‘‘no conflict’’ (or the status quo) is observed for countries that have fought in

the past and have active ongoing p olitical disputes. Thus, it is likely that the two types

of zeros posited previouslymay relate to two distinctsources. This impliesthat treating

the zero observations as a homogeneous group in zero-inflated ordereddependent con-

flict variables is not statistically appropriate and may lead to biased estimates when

evaluating the impact of covariates on ordered conflict measures that contain excess

zeros.

The second issue is that scholars of political violence do not statistically account

for the observable and latent factors that generate the high proportion of zero

(i.e., peace) observations in ordinal dependent variables that have excess zeros

(Senese 1997, 1999; Huth 1998; Besley and Persson 2009; Wiegand 2011). This

Bagozzi et al. 729