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Running head: STUDENTS, PROFESSIONALS, AND LOGISTIC REGRESSION
Linkage Analysis in Cases of Serial Burglary: Comparing the Performance of University
Students, Police Professionals, and a Logistic Regression Model
Craig Bennell and Sarah Bloomfield
Carleton University
Brent Snook
Memorial University of Newfoundland
Paul J. Taylor
Lancaster University
Carolyn Barnes
Carleton University
Linkage Analysis 2
Abstract
University students, police professionals, and a logistic regression model were provided with
information on 38 pairs of burglaries, 20% of which were committed by the same offender, in
order to examine their ability to accurately identify linked serial burglaries. For each offense pair,
the information included: (1) the offense locations as points on a map, (2) the distance (in km)
between the two offenses, (3) entry methods, (4) target characteristics, and (5) property stolen.
Half of the participants received training informing them that the likelihood of two offenses being
committed by the same offender increases as the distance between the offenses decreases. Results
showed that students outperformed police professionals, that training increased decision
accuracy, and that the logistic regression model achieved the highest rate of success. Potential
explanations for these results are presented, focusing primarily on the participants’ use of offense
information, and their implications are discussed.
Key words: Linkage analysis; comparative case analysis; serial burglary; criminal behavior;
decision-making
Linkage Analysis 3
Linkage Analysis in Cases of Serial Burglary: Comparing the Performance of University
Students, Police Professionals, and a Logistic Regression Model
Linkage analysis involves using crime scene information to decide if two (or more)
offenses were committed by the same offender (Bennell & Canter, 2002). Failure to link offenses
accurately can waste police resources, prolong criminal investigations, and prevent the
apprehension of the actual offender (Grubin, Kelly, & Brunsdon, 2001). Unfortunately, linkage
decisions are often made under conditions of considerable uncertainty because physical evidence
(e.g., DNA) is lacking or insufficient (Hazelwood & Warren, 2003). In the absence of physical
evidence, investigators will have to base their inferences on behavioral information (Bennell &
Canter, 2002; Bennell & Jones, 2005). Little is known, however, about the ability of investigators
to use crime scene behavior to make accurate linkage decisions (Woodhams, Hollin, & Bull,
2007).
Although studies have shown that it is possible to link offenses from offense behaviors
using statistical techniques (e.g., Bennell & Canter, 2002; Bennell & Jones, 2005; Goodwill &
Alison, 2006; Green, Booth, & Biderman, 1976; Grubin et al., 2001; Santtila, Fritzon, &
Tamelander, 2005; Santtila, Pakkanen, Zappala, Bosco, Valkama, & Mokros, 2008; Tonkins,
Grant, & Bond, 2008; Woodhams, Grant, & Price, 2007; Woodhams & Toye, 2007), only one
published study has examined how people perform on this task. Santtila, Korpela, and Häkkänen
(2004) examined the ability of 4 distinct groups of individuals to accurately link vehicle offenses.
They presented experienced vehicle offense investigators, experienced general investigators (i.e.,
investigators with no specialised training in vehicle crime investigation), novice general
investigators, and naïve participants with offense information relating to 30 offenses committed
by 10 known offenders (three offenses each). The participants were asked to review the offense
Linkage Analysis 4
information and determine which of the offenses they believed were linked. The results showed
that investigators, as a group, were significantly more accurate than naïve participants, but there
were no accuracy differences between the types of investigators (with each group correctly
identifying about half of the possible links). However, experienced vehicle offense investigators
focused their attention on a smaller sub-set of offense behaviors when making their linking
decisions compared to all other groups.
Santtila et al.’s (2004) study suggests that there are theoretical and practical reasons to
study how people perform linkage analysis. Theoretically, linkage analysis provides a reasonably
well-defined task that allows researchers to gather knowledge about human discrimination
processes across a range of varying conditions (e.g., levels of decision-maker expertise).
Practically, understanding how people perform linkage analysis will determine if there is a need
for training in this area (e.g., providing information about the most effective linking cues). If
people continue to perform poorly after receiving appropriate training, then there is a case for the
development and implementation of a decision aid.
The Performance of Decision-Makers on the Linking Task
Given the inherent ambiguity of offender behavior, and the sheer number of offense
behaviors that can occur in any given offense, it is unclear how well people will perform when
required to make linkage decisions. On the one hand, judgment and decision-making research has
demonstrated that people have a limited ability to process information (e.g., Miller, 1963; Neath,
1998) and that they often rely on heuristics to deal with the complexity of the real world
(Kahneman & Tversky, 1973). The majority of this research concludes that, because heuristic
processing does not match the performance of the rational choice model, people are prone to
exhibit a host of errors and biases, such as overconfidence, confirmation bias, insensitivity to
Linkage Analysis 5
sample size, illusory correlations, and so on (Dawes, Faust, & Meehl, 1989; Grove & Meehl,
1996; Kahneman & Tversky, 1973). This body of “heuristics and biases” research therefore
suggests that people (particularly novice decision-makers) will not be able to cope effectively
with the complexities inherent in linkage analysis, and will perform poorly on the task as a result
(see Payne, Bettman, & Johnson, 1993, for a discussion of how researchers have defined task
complexity by considering the number of decision alternatives, the amount of time to process
information, the number of attributes upon which a decision is based, etc.).
On the other hand, a number of more recent studies have shown that simple heuristics
can, under certain conditions, lead to accurate decisions (Gigerenzer et al., 1999; Gigerenzer &
Goldstein, 1996; Todd & Gigerenzer, 2001). In particular, these studies have demonstrated that
heuristics can be successful when the structural properties of a heuristic match the structure of
discriminating information within the decision environment (i.e., ecologically rational heuristics;
Martignon & Hoffrage, 1999). For example, if a police officer uses an “error minimization”
heuristic to predict the location of an at-large serial offender’s home based on where his offenses
were committed (e.g., by choosing a point located in the middle of his offenses), the likely result
is an accurate prediction because this heuristic matches the empirical regularity that the majority
of serial offenders reside within their area of criminal activity (Bennell, Snook, Taylor, Corey, &
Keyton, 2007; Snook, Canter, & Bennell, 2002; Snook, Taylor, & Bennell, 2004; Taylor, Snook,
Bennell, 2009). This body of “bounded rationality” research therefore suggests that people will
perform well on the linking task if they use heuristics that match the structure of the decision
environment.
Taken together, these studies highlight the importance of studying the cognitive strategies
that people use when making linking decisions and determining whether those strategies match
Linkage Analysis 6
what we know about the information that is useful for making these decisions. Recently, Bennell
and his colleagues (Bennell, 2002; Bennell & Canter, 2002; Bennell & Jones, 2005) have
demonstrated that the distance between burglary locations (i.e., inter-crime distance) is the single
most reliable indicator of whether or not burglaries are committed by the same offender, with
shorter distances indicating a greater likelihood that the offenses are linked (see Tonkin et al.,
2008, and Woodhams & Toye, 2007, for similar findings with other crime types). They also
showed that three commonly used linking cues (entry method, target characteristics, and property
stolen) were ineffective for linkage analysis when applied to cases of burglary. Thus, we might
reasonably predict that people are more likely to make accurate linking decisions if they know
that burglars typically commit their crimes close together in space. In contrast, they are more
likely to make bad decisions if they assume, for example, that the same burglar always enters
their targets in the same way.
The kinds of information that people attend to in this decision-making task, and what role
police experience plays in the selection of relevant linking cues and subsequent linking
performance, remains unclear. Santtila et al.’s (2004) results suggest that investigative experience
(although not necessarily experience related to the exact type of crime under consideration) plays
an important role, allowing people to draw on previously acquired schemas to select, process, and
implement relatively effective linking strategies, at least compared to naïve participants. This
accords well with research in other domains, which suggests that experience improves decision-
making (e.g., Corcoran, 2007; Lamond & Farnell, 1998). However, as highlighted by Santtila et
al., there is also a body of research suggesting that experience may not play a central role in
successful decision-making (e.g., Dawes, 1989; Garb, 1989).
Training Decision-Makers to Consider Relevant Information
Linkage Analysis 7
It is important to train people to make better decisions if they rely on irrelevant
information. In many domains, novices are taught to improve their decisions by focusing on
relevant information (e.g., Jacoby, Morin, Johar, Gurhan, Kuss, & Mazursky, 2001). Research
suggests that it is also possible to train experts to consider relevant information, and thus increase
their decision accuracy, especially in complex decision tasks (e.g., Gaeth & Shanteau, 1984). In
the forensic domain, for example, research suggests that many professional lie detectors rely on
inappropriate verbal and non-verbal cues when attempting to detect deception, potentially
explaining why these individuals perform so poorly (often no better than chance) on lie detection
tasks (Vrij, 2000, 2008). However, providing training on how to use relevant cues can apparently
reduce the effect of irrelevant information on lie detection accuracy. For example, when Porter,
Woodworth, and Birt (2000) provided training to Canadian parole officers, their decision
accuracy increased significantly.1 Importantly, Porter et al. also showed that the training had a
relatively long-term effect on an individual’s ability to accurately detect lies (i.e., performance
was maintained over a 5-week period).
In contrast to this research, other research has found that training may not result in
substantial improvements to decision-making performance. In some instances, cognitive overload
caused by the training may be partly to blame (Clark, Nguyen, & Sweller, 2005). In other cases,
“expert” trainees may exhibit resistance to training, preferring to rely on their past experiences
(which can be biased) rather than the empirical evidence. This resistance can be attributed, at
least in part, to the type of cognitive conceit discussed by Myers (2002), whereby people think
1 In addition to providing the parole officers with information about empirically-based verbal and non-verbal cues to
deception, the training provided by Porter et al. (2000) also included feedback about the accuracy of judgements. It is
difficult to separate out the impact of providing parole officers with information about relevant cues and this
feedback. Having said this, Porter et al. speculate that the positive effect of feedback on lie detection performance
may be attributed to the fact that such feedback allows “participants gradually to detect (consciously or
unconsciously) valid cues to deception and modify their decision-making accordingly” (p. 655).
Linkage Analysis 8
they know more than they actually do. For example, Memon, Holley, Milne, Kohnken, and Bull
(1994) examined whether training police officers on the cognitive interview, a technique known
to increase the amount of correct information elicited from witnesses, would improve their
interviewing performance. Although similarly trained students improve their performance (Milne
& Bull, 1999), the police officers in Memon et al.’s study did not. The lack of improvement by
the police officers was partially due to their reluctance to give up their old interviewing methods
(cf. Dando, Wlicock, & Milne, 2008, 2009).
Developing Statistical Models to Aid Decision-Making
If training in an area is ineffective, it may be necessary to develop and implement
decision aids (Dawes & Hastie, 2001; Swets, Dawes, & Monahan, 2000). The development of
decision aids can also serve as a normative benchmark against which human performance can be
measured. Researchers have developed statistical models in many domains where cognitive
limitations have been shown to result in decision errors (Swets et al., 2000), including domains
that are relevant to criminal justice professionals (e.g., Jones & Bennell, 2007; Rice & Harris,
1995; Yun, 2007). The primary question with respect to these decision aids is whether or not they
provide any advantages over human judgments. Historically, statistical models have been
considered the preferred method for a range of consequential decisions where the primary goal is
to maximize decision accuracy. Meehl (1954), for example, reviewed a wide array of empirical
research that compared the accuracy of human judges to statistical models and concluded that
statistical models are superior to clinical judgments (see Grove & Meehl, 1996, for a more recent
review that reaches a similar conclusion). This also appears to be the case in many criminal
justice contexts (e.g., Hanson & Bussiere, 1998; Szucko & Kleinmuntz, 1981; Walters, White, &
Greene, 1984).
Linkage Analysis 9
However, some previous research has also highlighted the possibility that statistical
models may not always outperform human decision-makers. Indeed, research has shown that
individuals drawing on appropriate cognitive heuristics can sometimes make decisions that are as
accurate as decisions based on statistical models (Bennell et al., 2007; Leli & Filskov, 1984;
Martignon & Schmitt, 1999). Paulsen (2006), for example, compared the ability of students and a
range of statistical and computational models to predict where serial offenders live on the basis of
their crime site locations. He found that students who used appropriate (i.e., ecologically rational)
heuristics performed as well as simple statistical models and more complex computationally-
based procedures designed for the purpose of making geographic profiling predictions.
The Current Study
In the current study, we compare university students, police professionals, and a logistic
regression model on their ability to accurately link serial burglaries. Based on a review of the
literature, we expected that individuals who possess police experience would achieve
significantly higher levels of decision accuracy on the linking task compared to individuals with
no police experience given that police professionals are more likely to have knowledge of
relevant linking cues. We also expected that, regardless of their level of police experience,
providing human judges with information about relevant linking cues would significantly
increase their decision accuracy on the linking task. However, we expected that the level of
decision accuracy achieved by human judges would be significantly lower than that achieved by
a statistical model designed for the purpose of linking serial burglaries, even after the judges
receive training.
Linkage Analysis 10
Method
Participants
Participants (N = 71) were 40 undergraduate students who took part in the study for
course credit at Carleton University and 31 police professionals who were recruited primarily
through postings on police-related newsgroups.2 In this study, a police professional was defined
as anyone having experience in crime analysis, police work, or a related field (e.g., police
psychology). Approximately half of the participants in each group (n = 20 students and n = 14
professionals) were given training on how to conduct the linking task (discussed in more detail
below), while the remaining participants in each group (n = 20 students and n = 17 professionals)
were not trained.
The mean age of the student group was 21.1 years (SD = 3.2), and there were no
significant age differences between the trained (M = 20.7 years, SD = 3.9) and untrained (M =
20.6 years, SD = 2.3) groups. With regards to gender, the student sample contained a total of 18
men and 22 women, and there were no significant gender differences between the trained (men =
9, women = 11) and untrained (men = 9, women = 11) groups. According to the demographic
information provided by each student, none of them had any prior experience in crime analysis,
police work, or linkage analysis.
Twenty-nine police professionals provided demographic information. Of these 29
participants, there were 14 crime analysts, 9 police officers, and 6 other professionals (e.g., police
psychologists). Fifteen participants were recruited from the United States, 8 from the United
Kingdom, and 6 from Canada. The mean age of the professional group was 38.1 years (SD =
2 It is difficult to provide an accurate response rate for the professional group given that it is impossible to know how
many professionals were reached through our various recruitment postings. However, we can report that 51 packages
were sent to police professionals who indicated an interest in taking part in the study. Given that 31 professionals
sent back completed packages, the return rate was 60.8%.
Linkage Analysis 11
13.1), and there was a significant age difference between the trained (M = 45.5 years, SD = 12. 8)
and untrained (M = 32.7 years, SD = 10.1) groups, t(27) = 3.06, p < .01. The professional sample
consisted of 13 men and 16 women, and there was a significant gender difference between the
trained (men = 10, women = 4) and untrained (men = 3, women = 12) groups, X2 = 8.57, df = 28,
p < .01. There was no significant difference between the trained (M = 2.3 years, SD = 5.4) and
untrained (M = 3.5 years, SD = 3.6) groups in terms of their crime analysis experience, nor was
there a significant difference between the trained (M = 8.2 years, SD = 4.3) and untrained (M =
9.3 years, SD = 4.6) groups with respect to their police experience. Finally, there was no
significant difference between the trained (M = 2.2 years, SD = 5.2) and untrained (M = 1.7 years,
SD = 3.1) groups with respect to previous linkage analysis experience.
Materials
All participants were required to complete an experimental booklet, which consisted of an
informed consent form and a package containing 38 pairs of commercial burglaries. Each
burglary was committed in a large urban city in the UK between January 1999 and January 2000,
and was randomly extracted from a larger database of burglaries collected from the area as part of
a previous research project (Bennell & Canter, 2002). Approximately 20% of these burglary pairs
(8 out of 38) represented linked pairs, which is consistent with the estimated proportion of linked
pairs that is encountered when working with large numbers of commercial burglaries in the area
where these burglaries were committed. Two versions of this package were constructed, with the
38 pairs of burglaries presented in a different random order in each package to control for order
effects (no order effect was found and, therefore, order of presentation is not considered in
subsequent analyses).
Linkage Analysis 12
For each of the offense pairs, information relating to the following behaviors was
provided: (1) a map (size = 17.8 cm x 24.1 cm) consisting of all 76 offense locations, with the
relevant offense pair highlighted, (2) the straight-line distance (km) between the offense pair, (3)
how the offender entered the buildings, (4) the characteristics of the buildings that were targeted
in each offense, and (5) the property that was stolen from the buildings. The information was
provided in such a way that all information for a particular offense pair could be viewed at the
same time. This information was extracted from a burglary database maintained by the police
force where these offenses had occurred as part of a previous study (Bennell & Canter, 2002).
The goal of that study was to develop a logistic regression model for identifying relevant linking
cues (discussed in more detail below).
Procedure
Human performance. Students were tested in a research laboratory, in groups comprised
of one, two, or three participants. The students were asked to work individually through the
experimental booklet at their own pace and were unsupervised throughout the duration of the
study to reduce any potential demand characteristics. Completion of all tasks in the booklet took
approximately 45-minutes. Police professionals received the experimental booklet in the mail and
returned it to the first author upon completion.3
Before participants examined the 38 offense pairs contained in the booklet, they were
each provided with an information sheet. This sheet informed all participants that 20% of the
offense pairs that they would be examining were linked offense pairs. Providing base rate
3 The fact that a different procedure was used to collect data from the students and professionals could have
introduced a number of confounding variables, most of which we believe would favor the police professionals’
performances on the linking task. For example, the professionals could have taken more time to complete their
packages than the students, and they could have relied more on external sources for assistance (e.g., crime analysis
packages). The results of this study, however, do not support this view. As will be discussed below, the students
generally outperformed the professionals with respect to linking accuracy.
Linkage Analysis 13
information to participants is not uncommon in studies like the current one (e.g., Santtila et al.,
2004; Swets, Getty, Pickett, D’Orsi, Seltzer, & McNeil, 1991). This sort of information is also
sometimes available in naturalistic settings, although the exact base rate typically varies across
jurisdictions.4 In addition, participants in the trained group were provided with instructions on
how to decide whether or not offense pairs were linked (untrained participants received no
additional information). Specifically, these instructions indicated that: “When determining
whether commercial burglars have been committed by the same offender, previous research has
indicated that the closer two offenses are to one another geographically, the more likely it is that
the same offender committed them”. These instructions were based on past research, which has
shown that the most reliable indicator of whether or not burglaries are linked is inter-crime
distance (Bennell, 2002; Bennell & Canter, 2002; Bennell & Jones, 2005).
For each offense pair, participants were asked to indicate, on a 10-point scale (1 = “not at
all confident that the offenses are linked”, 10 = “extremely confident that the offenses are
linked”), how confident they were that the same offender committed the pair of offenses. They
were also asked to indicate, for each offense pair, the extent to which they based their decision on
each of the provided cues, again on a 10-point scale (1 = “not at all” to 10 = “very much”).5 After
completing the package of 38 offense pairs, the participants were asked to fill out a demographic
questionnaire and to provide comments about the study if they wished. The participants were
then debriefed, with the police professionals sent a debriefing form after completing the study.
4 None of the participants in this study were from the jurisdiction where the burglary data originated and,
consequently, these participants would not be aware of the base rate unless told about it explicitly.
5 The potential for problems when using self-report measures to determine cue reliance should be noted. There is a
relatively large literature, which suggests that people may not have access to their mental processes and, even if they
do, they may not be able to articulate anything about those processes (e.g., Nisbett & Wilson, 1977). Thus, the results
related to our reliance scores should be treated with an appropriate level of caution.
Linkage Analysis 14
Logistic regression model. To examine the relative accuracy of a statistical model, the
logistic regression model developed by Bennell and Canter (2002) was applied to each of the 38
offense pairs (no alterations were made to the original regression model). The offense pairs used
in the current study were not part of the sample of offenses that was used to construct Bennell
and Canter’s regression model, but rather they comprised the validation sample. Thus, the results
of the regression model used in the current study will not be artificially inflated, as they would
have been if offenses from the original construction sample had been used.
The model used in this research, which is discussed more thoroughly by Bennell and
Canter (2002), was based solely on inter-crime distances, and took the form:
where p is the probability of an offense pair being linked. The probabilities that resulted when
this model was applied to each of the offense pairs in the experimental booklet are the equivalent
of participant ratings. To establish differences in decision accuracy across the statistical model
and our participants, these probabilities were compared to participant ratings using the procedure
outlined below.
Measuring Decision-Making Accuracy
Decision accuracy was measured using receiver operating characteristic (ROC) analysis.
ROC analysis is a procedure that has been adopted in a variety of medical and industrial settings
to evaluate the accuracy of diagnostic decisions (Swets, 1996). Regardless of whether ROC
analysis is used to examine decisions made by people or statistical models, the general procedure
for conducting the analysis is the same. Hit probabilities (pH) and false alarm probabilities (pFA)
are calculated for various decision thresholds set along a rating scale, such as the 10-point scale
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log p
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( =−2.82 −0.88(inter - crime distance)
Linkage Analysis 15
used by our participants. These values are then plotted on a graph, with pH on the vertical axis
and pFA on the horizontal axis. The result of plotting these values and connecting the various
points is a concave-downward curve known as a ROC curve.
Each point along a ROC curve represents the pH/pFA ratio that occurs when using a
specific decision threshold. The height of a ROC curve represents the overall level of
discrimination accuracy achieved by the decision-maker (i.e., higher ROC curves are
characterized by greater pH/pFA ratios) (Swets, 1996). Height in this case is measured by
calculating the proportion of the graph’s area falling under the ROC curve, which is referred to as
the area under the curve (AUC).6 Values for the AUC typically range from .50 to 1.00, where .50
corresponds to a ROC curve falling along the positive diagonal, indicating chance accuracy, and
1.00 corresponds to a ROC curve falling along the left and upper axes of the graph, indicating
perfect accuracy. According to criteria proposed by Swets (1988), AUCs between .50 and .70
indicate low accuracy, AUCs between .70 and .90 indicate moderate accuracy, and AUCs
between .90 and 1.00 indicate high accuracy. The advantage of the AUC over other measures of
accuracy (e.g., percentage correct) is that it is not biased by where the decision threshold is
placed (Swets, 1996). This is because the AUC corresponds to the position of the entire ROC
curve rather than any single ROC point (Swets et al., 2000).
The ROC analysis sub-routine in SPSS (v. 17) was used to conduct all ROC analyses.
This program allows users to calculate a variety of standard ROC measures, including the AUC,
the standard error associated with the AUC, and 95% confidence intervals (CI95) around the AUC.
In this study, ROC curves were derived from pooling the results from participants within each
6 Given that some readers may be more familiar with d’ than the AUC, these values will also be provided. As with
the AUC, a higher d’ value indicates greater linking accuracy.
Linkage Analysis 16
group and running the analysis across pooled ROC curves to determine if one group exhibited
significantly greater accuracy than the other groups (Swets & Pickett, 1982).
Results
Decision-Making Accuracy
As can be seen in Figure 1, the AUCs for the ROC curves associated with untrained and
trained students are .70 (SE = .03; CI95 = .65 to .76; d’ = .75) and .79 (SE = .02; CI95 = .74 to .84;
d’ = 1.15), respectively. The AUCs for the ROC curves associated with untrained and trained
professionals are .64 (SE = .03; CI95 = .59 to .70; d’ = .51) and .71 (SE = .03; CI95 = .66 to .76; d’
= .79), respectively. The ROC curve for the logistic regression model represents an AUC of .87
(SE = .02; CI95 = .82 to .91; d’ = 1.60). All AUCs in Figure 1 are significantly above chance (all
p´s < .001).
[Insert Figure 1 about here]
To understand the influence of expertise and training on decision accuracy, a 2 (Expertise:
student and professional) x 2 (Training: untrained and trained) ANOVA was conducted with
linking accuracy scores (i.e., AUCs) as the dependent variable. As was expected, we found a
significant main effect for Expertise, F(1, 67) = 9.09, p < .01,
η
2 = .12, but in contrast to what we
hypothesized, students (M = .76, SD = .14) outperformed professionals (M = .67, SD = .13).7 In
line with our expectations, a significant main effect was also found for Training, F(1, 67) = 9.71,
7 In an attempt to understand why the professionals did not perform as well as the students, in either the untrained or
trained condition, the accuracy scores of the various sub-groups comprising the professional group were scrutinized
with respect to their background (policing, crime analysis, or other) and location (United States, United Kingdom, or
Canada). While the small number of judges in each sub-group prevented us from conducting formal significance
tests, the accuracy scores for the professionals appear to be low due largely to the relatively poor performance of
Linkage Analysis 17
p < .01,
η
2 = .13, with those who received training (M = .77, SD = .13) outperforming those who
did not (M = .67, SD = .13). The two-way interaction between Expertise and Training was not
significant, indicating that training had the desired effect of increasing linking accuracy
regardless of the degree to which the judges possessed police experience.
To compare the performance of the human judges to the statistical model, a one-sample t-
test was conducted (α = .05). As expected, the accuracy of the human judges (M = .72, SD = .14)
was significantly lower than the statistical model (M = .87), t(70) = 8.96, p < .001, d = 1.07. This
was also found to be the case for each of the four separate groups of human judges when their
accuracy scores were compared to the statistical model (all t’s > 3.02).
Reliance on Behavioral Cues
In order to gain a better understanding of the accuracy results, the reliance ratings
provided by the human judges were examined. Figure 2 shows the average reliance scores for
each piece of information for the untrained and trained students and professionals.
[Insert Figure 2 about here]
To understand the influence of expertise and training on the reliance scores, a 5 (Cue:
map, distance, target, entry, and property) x 2 (Expertise: student and professional) x 2 (Training:
untrained and trained) mixed ANOVA was conducted with reliance scores as the dependent
variable. We found no significant main effects of Expertise or Training, but a significant main
effect of Cue was found, F (4, 268) = 25.78, p < .001,
η
2 = .28. This main effect was subsumed
by a significant two-way interaction between Expertise and Cue, F (4, 268) = 4.16, p < .01,
η
2 =
police officers, particularly in the trained condition. No obvious differences in accuracy scores were found across
Linkage Analysis 18
.06, and between Training and Cue, F (4, 268) = 6.63, p < .001,
η
2 = .09. There was no two-way
interaction between Expertise and Training, and no three-way interaction between Expertise,
Training, and Cue.
Use of behavioral cues. To assess whether the participants placed significantly more
emphasis on one behavioral cue than another, we performed a series of paired-samples t-tests
(Bonferonni corrected α = .005). These tests indicated that participants relied on inter-crime
distance significantly more than all other pieces of information (all t’s > 3.02). Our participants
also relied on the map information significantly more than all other pieces of information (all t’s
> 4.37), with the exception of inter-crime distance. All other comparisons were not significant.
Expertise and behavioral cues. A series of independent-samples t-tests were then used to
compare reliance ratings across students and professionals for each of the five behavioral cues
(Bonferonni corrected α = .01). There was a significant difference in the use of maps, with the
students (M = 5.9, SD = 1.4) relying on them more than the professionals (M = 5.0, SD = 1.6),
t(69) = 2.52, p < .01, d = .61. There was also a strong, albeit non-significant trend found indicating
that students placed more weight on inter-crime distance (M = 6.2, SD = 1.2) compared to the
professionals (M = 5.5, SD = 1.4), t(69) = 2.44, p < .05, d = .59. All other comparisons were not
significant.
Training and behavioral cues. A series of independent-samples t-tests were also used to
compare reliance ratings across untrained and trained participants for each of the five behavioral
cues (Bonferonni corrected α = .01). No significant differences were found. However, there were
strong trends found indicating that the trained individuals placed more weight on the maps (M =
5.9, SD = 1.2) compared to untrained individuals (M = 5.2, SD = 1.7), t(69) = 2.12, p < .05, d =
professionals from different countries, in either the untrained or trained condition.
Linkage Analysis 19
.51, as well as more weight on inter-crime distances (M = 6.2, SD = 1.2) compared to untrained
individuals (M = 5.6, SD = 1.4), t(69) = 2.12, p < .05, d = .51. All other comparisons were not
significant.
Discussion
This study examined the ability of university students, police professionals, and a logistic
regression model to infer from behavioral information whether or not the same offender
committed two burglaries. Overall, the results showed that: (1) students outperformed
professionals with respect to decision accuracy, (2) providing information to participants about
relevant linking cues resulted in higher levels of decision accuracy, and (3) the logistic regression
model significantly outperformed all participants. These findings have implications for our
understanding of how people perform linkage analysis and whether or not there is a need for
training and/or decision aids to assist with this task.
The Role of Police Experience
The finding that both untrained students (AUC = .70) and professionals (AUC = .64)
performed significantly above chance levels on the current linking task was surprising. None of
the students that took part in this study reported any experience with policing, crime analysis, or
linkage analysis, and previous research has demonstrated that police professionals perform
relatively poorly on the linking task (Santtila et al., 2004). Therefore, it would not have been
unreasonable to assume that participants in this study would have performed at around chance
levels under conditions where they were provided with no training.
Given their above chance performance, it is tempting to conclude that the untrained
participants were aware of the fact that an offender’s spatial behavior could be used for linking
purposes. However, while the reliance scores provided by these participants indicate that they
Linkage Analysis 20
focused some of their attention on the relative location of the burglaries and the distances
between them, they focused significantly more attention on the other less relevant cues (e.g.,
property stolen). While this strategy is not ideal, it does ensure moderate levels of accuracy since
effective linking cues are focused on in addition to the irrelevant cues.
The finding that untrained students generally outperformed the untrained professionals
was also somewhat surprising, especially in light of Santtila et al.’s (2004) results, which showed
that police investigators significantly outperformed naïve participants in a linking task involving
vehicle crimes. Of course, it could simply be the case that experience is unrelated to success on
the linking task and that our results are correct. This has certainly been found to be the case in
other domains (e.g., Dawes, 1989; Garb, 1989). However, there are also potential problems with
our study that provide alternative explanations for why these differences between the two studies
emerged. These problems may have negatively impacted participant performance, especially in
the case of our police professionals.
First, unlike the data provided to investigators in Santtila et al.’s (2004) study, the
participants in the current study were provided with data from an area that was potentially very
different from where most of them resided and/or worked.8 While this issue is unlikely to
seriously impact student performance (because students know little of how burglars behave), it
could impact the performance of police professionals who may be using locally-derived
analytical knowledge that does not match the criminal patterns found within the study’s data. For
example, while a police officer serving in a rural Canadian town may know that inter-crime
distances in his jurisdiction tend to be about 8 km, this will not serve him well when applying
8 Note that Santtila et al. (2004) also used data from a location that was different from the location where their
participants resided and/or worked, but both locations were major cities in Finland (P. Santtila, personal
communication, March 11, 2009). It is likely that these cities are much more similar than the various locations relied
Linkage Analysis 21
that knowledge to crimes committed in a densely populated urban centre in the UK where the
average inter-crime distance is 2 km (as it is with the data set being used in this study). A number
of the police professionals in the current study noted that knowledge of the area in which the
offenses were committed would have increased their performance and it will be important to
examine this issue in the future.
Second, providing participants (especially the police professionals) with additional
information about the crime pairs could have increased their performance. The absence of
temporal information (i.e., when the crimes were committed) was a particular concern, with over
50% of the professionals, but none of the students, indicated that having access to temporal
information would have allowed them to make more accurate decisions. For example, one
professional commented, “To me, a crucial omission in your variables is the date and time of
each burglary. These details would be vital in determining a particular burglar’s mobility - could
he rob two places 5 km apart on the same day?” Unfortunately, temporal information was not
available for the current study and often is not in cases of burglary due to the fact that burglaries
often occur when homes are unoccupied (Ratcliffe, 2002). However, when it is available,
temporal information can be useful for making linking decisions, as indicated by the fact that the
use of timing was highly related to increased accuracy in the study by Santtila et al. (2004). Thus,
the need to evaluate the importance of temporal information in linkage analysis is a valid concern
and something that future research should address.
The Role of Training
While all participants focused on irrelevant cues when making linking decisions, the
current study did find that training had an effect on linking accuracy, with both trained students
on in the current study, which consisted of towns and cities from three different countries, with different population
densities, road networks, land use patterns, etc.
Linkage Analysis 22
and trained professionals outperforming untrained students and untrained professionals,
respectively. Again, the reliance scores indicate that this general increase in performance was a
result of trained participants incorporating, although not to a significant degree, the instructions
on how to best go about deciding whether or not two offenses are linked. In this way, the results
are similar to those reported by other researchers (e.g., Gaeth & Shanteau, 1984; Porter et al.,
2000).
While training improved performance for all groups of participants, it had a particularly
strong influence on the students. This finding is, in large part, a result of the trained students
placing more reliance on relevant cues than their counterparts (especially police officers). For
example, the students placed more emphasis on both the maps and distance information
compared to the professionals once they had received training. Comments from the police
professionals indicate that this may have happened because these individuals often believed their
experience and knowledge should be given more weight than the training. For example, a number
of the trained professionals stated that they disagreed that it was fruitful to use inter-crime
distance to link offenses. One participant stated that, “…priority was given to targets followed by
the MO for entry…in my experience criminals committing multiple offenses usually follow this
sequence”. Another remarked, “I discounted distance in the main as burglars are very mobile and
I concentrated on MO and what was stolen to detect possible correlations”. Empirical research
suggests that these assumptions are incorrect for the majority of serial burglary cases (Snook,
2004; Wiles & Costello, 2000), and they are certainly incorrect for the burglaries in the current
data set (Bennell & Canter, 2002). Students in our study did not indicate such resistance,
presumably because they lack prior experience with this type of task and do not have
preconceived ideas about cues that are (supposedly) effective for making linking decisions.
Linkage Analysis 23
The Value of a Statistical Model
With an accuracy score of .87, the logistic regression model developed by Bennell and
Canter (2002) significantly outperformed all groups of human judges, even after training. This
suggests that it might be useful for the police to adopt a simple statistical approach for linkage
analysis. This result, and conclusion, is consistent with the majority of research that has
compared statistical and clinical approaches to decision-making (e.g., Meehl, 1954; Grove &
Meehl, 1996). There are many possible explanations for the superiority of the regression model in
this study (Dawes et al., 1989). Perhaps the most logical one is that the model only contains the
significant spatial predictor, while the participants were free to use any linking cue (and the
participants clearly did not rely solely on the spatial information).
In addition, it is clear from the results that participants were either not able to, or decided
not to, incorporate the base rate information into their decision process. Recall that the initial
instructions provided to all participants included a statement that approximately 20% of the
offense pairs were linked. However, it was not unusual for participants to indicate that as many as
50% of the offense pairs were linked. This occurred even for participants in the trained
conditions, despite the fact that, after training, they had access to a very effective linking strategy
(i.e., they could have separated the 20% of offense pairs with the shortest inter-crime distance
from the rest of the pairs and declare these to be the linked offenses).
Limitations of the Current Study
Despite the potential importance of the current findings there are at least three limitations
within the current study that need to be considered when interpreting the results (beyond those
that have already been highlighted and the obvious problem of sample size).
Linkage Analysis 24
First, there are potential confounds in the current study between the training received by
the police professionals and other demographic variables. Specifically, the trained group of
professionals was significantly older than the untrained group and was comprised of significantly
more men and less women. While there is no obvious reason we can think of to suspect that age
or gender would be related to performance on the linking task, it is difficult to know without
further study what influence these variables had in the current study and how they impacted the
training that was provided. Importantly, other demographic variables, which are arguably more
important (e.g., previous crime analysis and linking experience), did not differ across the trained
and untrained professional groups.
Second, it is unclear what effect the provision of base rate information (i.e., that 20% of
the crime pairs were linked) had on the performance of the participants in the current study. It is
seems unlikely that this information favored one group over any other. However, this information
could have had: (1) a performance enhancing impact on all of the groups, allowing them to
perform better than they would have without this information, or (2) no impact at all (see Tversky
& Kahneman, 1982, for a discussion of base rate neglect). While providing such information is
not uncommon in research of this type (e.g., Santtila et al., 2004; Swets et al., 1991), base rate
information will not always be known in real-world situations where linkage analysis is
conducted. Therefore, it will be important in the future to examine how this information impacts
linking performance. It will also be important to examine the impact of providing base rate
information in different ways (e.g., as a frequency instead of a percentage) given that the format
of presentation is potentially important (e.g., Cosmides & Tooby, 1996; Gigerenzer & Hoffrage,
1995).
Linkage Analysis 25
Third, one must consider the relatively impoverished nature of the training that was
provided to participants in the current study and how this might have influenced their
performance. Indeed, by modifying the training, the performance of participants could be
enhanced, perhaps to a point where they could make linking decisions that are as accurate as the
statistical model. We are currently examining four revisions to the training to determine whether
performance can be further improved: (1) offering the training through a more authoritative
source (e.g., an experienced police officer), (2) explicitly informing participants that they should
ignore irrelevant cues (e.g., property stolen) while focusing on relevant cues, (3) providing
participants with a specific decision threshold to use when considering inter-crime distances (e.g.,
“link the offense pair if the distance between the two offense locations is less than 2 km”), and
(4) presenting feedback following each linking decision to inform participants whether their
decision was correct or not.
Conclusion
The results of this study may have implications for the future of linkage analysis.
Although this procedure is vital to the success of serial crime investigation, it would seem that
the methods currently used by police professionals are open to improvement. Specifically, this
study demonstrated a worthwhile improvement in linking accuracy following brief training in the
use of relevant linking cues. However, the results also support previous research from other
domains in that humans appear unable to perform as well as a statistical model developed
specifically for the purpose of linkage analysis, at least under the current testing conditions. This
suggests that it might be useful for the police to adopt a statistical approach for linkage analysis.
Linkage Analysis 26
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Linkage Analysis 33
Author Note
Craig Bennell and Sarah Bloomfield, Department of Psychology, Carleton University,
Ottawa, ON, Canada; Brent Snook, Department of Psychology, Memorial University of
Newfoundland, St. John’s, NL, Canada; Paul J. Taylor, Department of Psychology, Lancaster
University, Lancaster, UK; Carolyn Barnes, Department of Psychology, Carleton University,
Ottawa, ON, Canada.
We would like to thank Dr. Jeffrey Pfeifer for his assistance in recruiting participants for
this project and all the individuals who participated in the study. Support for the research reported
in this paper was provided to the third author by the Natural Sciences and Engineering Research
Council of Canada.
Please address correspondence to Craig Bennell, 1125 Colonel By Drive, Department of
Psychology, Carleton University, Ottawa, ON, Canada, K1S 5B6; Telephone: (613) 520-2600
ext. 1769; Fax: (613) 520-3667; Email: cbennell@connect.carleton.ca.
Linkage Analysis 34
Figure Captions
Figure 1. ROC graph of accuracy scores for students, professionals, and the logistic regression
model.
Figure 2. Student and professional reliance ratings as a function of training and the five different
linking cues.
Linkage Analysis 35
Figure 1
Logistic regression (AUC = .87, d’ = 1.60)
Trained students (AUC = .79; d’ = 1.15)
Trained professionals (AUC = .71; d’ = .79)
Untrained students (AUC = .70; d’ = .75)
Untrained professionals (AUC = .64; d’ = .51)
Linkage Analysis 36
Figure 2
4.5
5
5.5
6
6.5
7
7.5
Map Distance Entry Target Property
Linking Cue
Reliance Score (/10)
Trained students
Unt raine d s t uden t s
Trained profes sionals
Unt raine d profes sionals
