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Running Head: LINKING SERIAL RAPE
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A Test of Case Linkage Principles with South African Serial Sex Offences.
Dr. Jessica Woodhams
Centre for Forensic and Criminological Psychology, University of Birmingham, UK.
Professor Gerard Labuschagne
Investigative Psychology Unit, South African Police Service, Pretoria, South Africa.
Department of Criminology, University of South Africa, Pretoria, South Africa.
This is the accepted version of the paper that was published in the Journal of Police and
Criminal Psychology in April 2012 for which the DOI is 10.1007/s11896-011-9091-1.
The original publication is available at www.springerlink.com.
Running Head: LINKING SERIAL RAPE
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Abstract
Case linkage involves identifying crime series on the basis of behavioral similarity and
distinctiveness. Research regarding the behavioral consistency of serial rapists has
accumulated; however, it has its limitations. One of these limitations is that convicted or
solved crime series are exclusively sampled whereas, in practice, case linkage is applied
to unsolved crimes. Further, concerns have been raised that previous studies might have
reported inflated estimates of case linkage effectiveness due to sampling series that were
first identified based on similar modus operandi (MO), thereby overestimating the
degree of consistency and distinctiveness that would exist in naturalistic settings. We
present the first study to overcome these limitations; we tested the assumptions of case
linkage with a sample containing 1) offenses that remain unsolved, and 2) crime series
that were first identified as possible series through DNA matches, rather than similar
MO. Twenty-two series consisting of 119 rapes from South Africa were used to create
a dataset of 7021 crime pairs. Comparisons of crime pairs that were linked using MO
vs. DNA revealed significant, but small differences in behavioral similarity with MO-
linked crimes being characterized by greater similarity. When combining these two
types of crimes together, linked pairs (those committed by the same serial offender)
were significantly more similar in MO behavior than unlinked pairs (those committed
by two different offenders) and could be differentiated from them. These findings
support the underlying assumptions of case linkage. Additional factors thought to
impact on linkage accuracy were also investigated.
Keywords: comparative case analysis, linkage analysis, behavioral linking, sexual
assault, sexual offense
Running Head: LINKING SERIAL RAPE
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1. INTRODUCTION
Case linkage is practiced by police agencies internationally and involves linking
crimes together to form a series on the basis of behavioral similarity and distinctiveness
(and in some cases, temporal or geographical proximity). It is sometimes referred to as
comparative case analysis or linkage analysis. Whilst case linkage can be applied to a
range of crime types, historically it has been used more often with serious offenses,
such as murder and stranger rape. Police units exist in different countries who conduct
case linkage on these more serious forms of crime, for example, the Serious Crime
Analysis Section in the United Kingdom and the Investigative Psychology Unit of the
South African Police Service. Case linkage can assist the Police in several ways
including the efficient deployment of limited police resources, increasing the amount of
evidence against an offender by combining that from different crime scenes and
different witnesses, and, after arrest, using evidence of behavioral similarity as similar
fact evidence in the prosecution of an offender (Labuschagne, 2010; Woodhams, Hollin
et al., 2007).
Case linkage can take a proactive form whereby databases of unsolved crimes
are searched to identify pairs (or groups) of crimes that share behavioral similarities,
and which might be temporally or geographically proximal. However, it is more
common for it to be conducted in a reactive manner, where the case linkage practitioner
is presented with one offense (often termed the index offense) and asked to identify
other crimes that were likely committed by the same offender (Woodhams, Bull et al.,
2007). Such scenarios might arise because of the severity of the index offense or
because a suspect has been identified for the index offense and the investigating officer
wishes to identify any other offenses that the suspect may have committed.
Running Head: LINKING SERIAL RAPE
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To be able to link crimes together on the basis of behavior requires two
assumptions about the behavior of serial offenders to be met. The first assumption, the
Offender Consistency Hypothesis (Canter, 1995), requires offenders to display a degree
of consistency in the way they commit their crimes across a series. The second
assumption is that offenders must show a degree of distinctiveness in the way they
commit their offenses so that their offenses can be differentiated from those of other
offenders (Bennell & Canter, 2002). These assumptions have been the subject of recent
empirical investigations with a range of crime types, including: burglary (Bennell &
Canter, 2002; Bennell & Jones, 2005; Goodwill & Alison, 2006; Green et al., 1976;
Markson et al., 2010; Yokota & Canter, 2004), robbery (Woodhams & Toye, 2007), sex
offenses (Bennell et al., 2009; Canter et al., 1991; Grubin et al., 2001; Knight et al.,
1998; Lundrigan et al., 2010; Santtila et al., 2005; Woodhams, Grant et al., 2007;
Yokota et al., 2007), homicide (Bateman & Salfati, 2007; Harbort & Mokros, 2001;
Salfati & Bateman, 2005; Santtila et al., 2008; Sorochinski & Salfati, 2010), arson
(Santtila et al., 2004) and car-theft (Tonkin et al., 2008).
1.1. Consistency and variability in sexual offending behavior
With regards to the first assumption of case linkage, behavioral consistency, it
has been suggested that sexual fantasy is one reason why we might observe consistency
in the offending behavior of serial rapists. This might be in a more general sense or
because of the presence of a paraphilia. Paraphilias are “repeated and intense sexual
urges, behaviour or fantasies in response to objects or situations that society deems
inappropriate” (Bennett, 2006, p. 262). They have been found to co-occur with sexual
aggression (Abel & Rouleau, 1990; Bradford et al., 1992, both as cited in Lussier et al.,
2007). Based on a large scale study of apprehended sex offenders, Gee and Belofastov
Running Head: LINKING SERIAL RAPE
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(2007) report that for the majority of sex offenders their offending behavior is fantasy-
driven.
Fantasy can influence a range of crime scene behaviors including victim
selection, the location of the offense, the method of approach, the methods used to
control the victim, sexual behaviors and the behaviors needed to complete the offense
without being apprehended (Gee & Belofastov, 2007). Paraphilias can affect the
“relationship” rapists have with their victim during the offense (Hazelwood & Warren,
2000). Such relationships include “master-slave” for sadistic offenders, and “boyfriend-
girlfriend” for an offender with a fantasy of a consenting sexual relationship.
Hazelwood and Warren (2000) explain that the behaviors used to control the victim will
be very relevant to the offender’s fantasy. If the offender has a fantasy of a consenting
relationship, they argue, he will not want to resort to physical violence to control the
victim, whereas physical violence will be important to the sadistic offender.
Based on their research, Gee and Belofastov (2007) propose that an offender’s
core sexual fantasy remains static over time but that the complexity of the fantasy can
develop, “hence, a sexual offender is more likely to deploy similar strategies and
resources across offences, in keeping with the origin of their core fantasy structure” (p.
64). As a sexual fantasy becomes more complex, completion of the sexual offense can
become more difficult (Gee & Belofastov, 2007). It can necessitate greater control of
the victim, which might be achieved through increased physical aggression (Hazelwood
& Warren, 2000). For example, with adolescent child abusers, Leclerc and Tremblay
(2007) found use of violence to be associated with the increasing intrusiveness of the
sexual behavior desired by the adolescent. These research findings suggest that both
stability and evolution will be evident within a rape series, and that rapists will vary in
Running Head: LINKING SERIAL RAPE
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the degree to which their offending behavior is driven by fantasy. Variation in
behavioral consistency between offenders as well as a degree of consistency across an
individual’s series should therefore be expected. It follows that case linkage will not be
an exact science.
1.2. Previous linkage research on serial sex offenders
Using a range of methods, eight studies have investigated the consistency and/or
distinctiveness of behavior exhibited by serial sex offenders across their series. Some
studies have quantified behavioral consistency in terms of how frequently offenders
exhibit the same behaviors (or clusters of behaviors) across crimes from their own series
(Grubin et al., 2001; Lundrigan et al., 2010). The observed co-occurrences are
compared to what would be expected by chance alone. Both Grubin et al. (2001) and
Lundrigan et al. (2010) found these frequencies to be significantly greater than chance.
Lundrigan et al. (2010) also demonstrated that the consistency in environmental
behaviors (characteristics of the crime sites selected) displayed within series was
significantly greater than that displayed across different series. In Grubin et al.’s (2001)
study, each offense in the dataset was compared to all others, in terms of MO, resulting
in a ranked list of offenses. Those offenses at the top of the ranked list were most
similar in behavior to the crime in question. Having conducted this procedure for all
crimes in the dataset, Grubin et al. were able to assess whether the crimes ranked within
the top 10% more often than chance represented offenses from the same series. They
found this occurred significantly more often than would be expected by chance alone.
Similarly, Yokota et al. (2007) were able to assign sex offenses to the correct
offender on the basis of similar MO at rates greater than what would be expected by
chance. Eighty-one serial sex offenders were selected from a database of 868 offenders
Running Head: LINKING SERIAL RAPE
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and one offense was chosen from the series of each of these offenders. Eighty-one trials
took place whereby each of the 81 offenses was compared to all others in the database
in terms of similarity in MO behavior. The 868 offenders within the database were rank
ordered depending on the similarity of their MO to the offense in question. Thirty per
cent of the time the correct offender was ranked number one out of 868. The rank at
which the correct offender was placed by the system ranged from 1-339.
Knight et al. (1998) assessed the consistency of offense behaviors across the five
most recent crimes of a sample of serial sex offenders. Offense behaviors were
arranged into domains and the within-series consistency assessed for the domains, as
well as the individual behaviors composing the domains, using a rating scale. Having a
firearm present, cutting/slashing clothing, an excessive response to victim resistance,
and the victim being bound were rated as high or very high in consistency. The
offender behaviors moderate in consistency were alcohol consumption during the crime,
taking drugs during the crime, the intentional infliction of pain, excessive profanity,
sexual dysfunction, sexual comments, the offender showing interest in the victim’s
enjoyment (e.g., pseudo-intimacy), being inquisitive, the offender being aroused by
causing harm, the offender humiliating the victim, sadistic infliction of pain, and the
sexual use of a foreign object during the incident. How well these variables
differentiated serial offenders was not, however, assessed.
Other researchers (Bennell et al., 2009; Canter et al., 1991; Mokros & Alison,
2002; Santtila et al., 2005; Woodhams, Grant et al., 2007) have used Jaccard’s
coefficient to measure similarity in MO behavior between pairs of sexual crimes.
Jaccard’s coefficient ranges from 0-1 and when used in this context larger values
represent greater similarity in MO behavior. The Jaccard’s coefficients obtained for
Running Head: LINKING SERIAL RAPE
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linked crime pairs (created by pairing two crimes committed by the same serial
offender) can be contrasted with the values obtained for unlinked crime pairs (typically
created by pairing two crimes committed by two different serial offenders). The
intention behind such analyses is to demonstrate that intra-individual variation in
behavior is less than inter-individual variation (Bennell & Canter, 2002). Linked crime
pairs should therefore be characterized by larger Jaccard’s coefficients than unlinked
crime pairs.
With a sample of 28 convicted adult serial sex offenders, Mokros and Alison
(2002) reported an average Jaccard’s coefficient of .41 for linked crime pairs compared
to .27 for unlinked crime pairs. Identical figures were reported by Bennell et al. (2009)
with a sample of 41 convicted adult serial rapists. With a small sample of seven serial
juvenile sex offenders, who had admitted their offenses and for which there was
corroborating evidence, Woodhams, Grant et al. (2007) reported average Jaccard’s
coefficients of .39 for linked pairs and .17 for unlinked pairs.
Some researchers have gone further than this and have tested whether behavioral
similarity (as measured using Jaccard’s coefficient) can be used to 1) accurately
differentiate linked from unlinked crime pairs, or 2) accurately assign crimes to the
correct series. With a sample of four solved rape series (constituting 12 offenses),
Canter et al. (1991) investigated how accurately crime pairs could be classified as
linked or unlinked. Using a coefficient of ≥.3 as a cut-off, 85% of the 66 crime pairs
were classified correctly.
Using Jaccard’s coefficient as a measure of behavioral similarity, Santtila et al.
(2005) used multidimensional scaling to plot 43 offenses in a two-dimensional space
whereby offenses closer to one another in space were more behaviorally similar. For
Running Head: LINKING SERIAL RAPE
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each offense, its five closest neighbors were extracted and examined for series
membership. Another case from the same series was present within these five offenses
40% of the time. If the ten closest offenses were analyzed this figure rose to 60%.
1.3. Limitations of previous linkage research
Whilst these results are all promising in terms of supporting the underlying
assumptions of case linkage for serial sex offenses, they are characterized by a number
of limitations. One limitation is that the findings can be affected by the placement of
the decision threshold, or cut-off (Bennell et al., 2009). As Bennell and colleagues
explain, often studies have set specific decision thresholds when assessing linkages in
terms of choosing a specific cut-off for deciding when a crime pair should be considered
linked (Canter et al., 1991), or stipulating the number or percentage of ranked crimes to
be assessed for the presence of crimes from the same series (Grubin et al., 2001;
Santtila et al., 2005). Bennell et al. argue “Consequently, results that emerge from the
use of only one threshold are likely to provide an extremely distorted picture of one’s
ability to link crimes” (p. 298). To overcome this limitation, Bennell et al. propose
ROC analysis as the preferred form of analysis for case linkage research because it can
assess the probability of making correct and incorrect linkage decisions across the full
range of decision thresholds.
Linking crimes behaviorally can result in four different outcomes, two of which
are correct (hit, correct rejection) and two of which are incorrect (false alarm, miss)
i
(Bennell, 2005). ROC analysis plots the probability of a hit versus the probability of a
false alarm at each decision threshold (e.g., from 0 to 1 if using Jaccard’s coefficient)
rather than just one. From these values a curve is plotted (the ROC curve) with the
values for strict cut-offs (large Jaccard’s coefficients) located in the bottom left corner
Running Head: LINKING SERIAL RAPE
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of the plot and the values for lenient cut-offs in the top right corner of the plot.
Typically the curve would be a concave shape. If crimes that are linked can be
differentiated accurately from crimes that are not linked this would result in a high
overall level of discrimination accuracy and therefore a high ROC curve. Overall
discrimination accuracy is quantified in ROC analysis from the statistic called the Area
Under the Curve (AUC). A high ROC curve would correspond with a large AUC.
Interested readers are referred to Bennell (2005) and Bennell et al. (2009) for a more in-
depth discussion of the advantages of ROC analysis for the evaluation of case linkage
principles.
To demonstrate the utility of ROC analysis, Bennell et al. (2009) assessed how
accurately linked and unlinked serial rape pairs could be differentiated when using a
wide range of decision thresholds. If the assumptions of behavioral consistency and
distinctiveness are valid it should be possible to differentiate linked from unlinked
crime pairs with a good degree of accuracy. Bennell et al.’s analysis produced an AUC
of .75, which can be considered good according to published standards (Swets, 1988).
A second limitation of the existing research on case linkage relates to the types
of offenses that have been sampled. Studies of the case linkage principles, by their
nature, require researchers to be confident of the membership of offenses to a given
series. In the past, this has been achieved by sampling offenses which have been linked
together, and to a common offender, on the basis of a conviction. The difficulty with
this is that these offenses might have originally been linked together, solved and
prosecuted due to the offender’s behavioral consistency and distinctiveness. This
means they might be characterized by greater behavioral similarity than would be the
Running Head: LINKING SERIAL RAPE
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case in reality (i.e., in naturalistic police settings) where case linkage is attempted on
unsolved crimes (Bennell & Canter, 2002).
Researchers have therefore suggested that a way forward would be to sample
unsolved offenses that have been linked by DNA (Sorochinski & Salfati, 2010;
Woodhams, Bull et al., 2007). However, unsolved crimes that have been linked by
DNA still might have first been identified as a possible series due to similar MO. To
illustrate this point, in South Africa an investigating officer might identify a potential
rape series on the basis of similar MO and request that the samples taken from the
victims’ Sexual Assault Evidence Collection Kits be processed for DNA and compared
to each other as a priority. In this scenario, the crimes might remain unsolved and be
linked by DNA but the limitation of research conducted on such a sample would
remain; that the offenses were initially identified as a series due to behavioral
consistency and distinctiveness. Therefore, what is instead needed is a sample of series
where it is possible to confirm that they were first linked by DNA, not by MO.
A third limitation relates to how offenses are sampled from series in studies of
case linkage. It has been suggested in the existing case linkage literature that to include
series of different lengths within an analysis risks biasing results by giving greater
weight to the consistency (or inconsistency) of prolific offenders (Bennell & Canter,
2002). Researchers have therefore controlled for the representation of prolific offenders
in datasets by limiting the number of crimes selected from each series (e.g., Bennell et
al., 2009; Santtila et al., 2005). Typically, this decision is based on the size of the
smallest series in the dataset. This does not, however, reflect the reality of the linking
task in practice where databases of offenses that are searched will contain series of
different lengths. To the authors’ knowledge, a test of the effect of this sampling
Running Head: LINKING SERIAL RAPE
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strategy has not been conducted previously and therefore the impact of this sampling
method has yet to be established.
A final limitation is that research conducted thus far on linking serial sex
offenses has largely been limited to samples of series from the UK (Bennell et al., 2009;
Canter et al., 1991; Grubin et al., 2001; Mokros & Alison, 2002; Woodhams, Grant et
al., 2007) and other European countries (Santtila et al., 2005). The exceptions are
samples from Canada (Grubin et al., 2001), Japan (Yokota et al., 2007), the United
States (Knight et al., 1998) and New Zealand (Lundrigan et al., 2010). This is
problematic because cultural differences in the expression of crime scene behaviors
could impact the effectiveness of case linkage by affecting the second assumption of
case linkage; distinctiveness. For example, in one country, the use of a firearm in a
sexual assault might be relatively uncommon because of restrictions on firearm
ownership and the limited availability of illegal firearms. In contrast, in another country
the situation could be quite different. As an illustration, the number of rapes in which
weapons are used/displayed in South Africa is much higher (50%, Jewkes & Abrahams,
2002; 40%, Vetten & Haffejee, 2005) than in England and Wales (1-2%, Home Office,
2009). It is therefore important to determine whether evidence of good predictive
accuracy for linked versus unlinked crimes found with European data generalises to
other countries. This is particularly important in the case of South Africa where linkage
analysis does not just inform investigative decision-making but is admitted in legal
proceedings in support of similar fact evidence (Labuschagne, 2006, 2010).
1.4. Research regarding factors that affect consistency
As well as investigating the degree of behavioral consistency and distinctiveness
shown by serial sex offenders and whether this is sufficient for their offenses to be
Running Head: LINKING SERIAL RAPE
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linked, research has been conducted with a range of crime types to determine if there are
factors that can affect the behavioral consistency displayed by serial offenders. This
research has been informed by theories from personality psychology which propose that
factors such as expertise and time-elapsed between events affect the degree of
consistency observed in non-criminal human behavior (see Woodhams, Hollin et al.,
2007 for a review).With non-criminal behavior, experience of an activity is related to
greater behavioral consistency (Hettema & Van Bakel, 1997) and it is proposed that this
is because the more frequently a behavioral strategy is triggered in response to a
situation the more likely it will be activated again in the future (Greene, 1989). For non-
criminal behavior greater consistency is also observed across events that are closer
together in time (Pervin, 2002). This is because over a shorter time period a person’s
personality system, which is purported to consist of mental representations that when
activated result in behavior (Mischel, 1999), will have had little time to develop or
change. Woodhams, Hollin et al. (2007) suggested that we might therefore see greater
behavioral similarity between linked crime pairs that are temporally proximal compared
to pairs that are temporally distal, and we might expect to see an increase in behavioral
consistency as serial offenders gain expertise in their offending behavior.
Three studies have now directly assessed whether there is a relationship between
the time elapsed between linked crime pairs and behavioral similarity. These have been
conducted with serial burglaries (Markson et al., 2010), car-thefts (Tonkin et al., 2008),
and juvenile stranger sex offenses (Woodhams et al., 2008). No evidence for such a
relationship has been found.
Tonkin et al. (2008) assessed the effect of expertise on behavioral consistency
by comparing the Jaccard’s coefficient for the first and last pair in the series committed
Running Head: LINKING SERIAL RAPE
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by their 20 most prolific car thieves. If expertise increased behavioral consistency, the
last pair in the series would be expected to be characterized by greater similarity than
the first pair in the series. No significant difference was found.
1.5. The Current Study
The current study aimed to extend the existing research on case linkage, and
address various limitations, by:
1. Testing the assumptions of case linkage using ROC analysis, with a South African
sample of serial rapes, predicting that;
a) Linked crime pairs would be characterized by greater behavioral similarity
(larger Jaccard’s coefficients) than unlinked crime pairs.
b) Linked crime pairs could be accurately distinguished from unlinked crime pairs
on the basis of similarity in MO behavior.
2. Including in the sample rape series that remain unsolved rather than relying solely
on samples of solved or convicted rape series.
3. Determining, where possible, the basis on which each series in the sample was first
identified as a potential series, allowing for a comparison of the behavioral
similarity of crime pairs from series first identified by DNA compared to those first
identified from MO. It was tentatively predicted that;
a) Pairs of crimes from DNA-identified series would be characterised by less
behavioral similarity than those from MO-identified series.
4. Conducting an explicit test of the effect of sampling all offenses from a series versus
a constant number of offenses from a series.
5. Investigating the effect on behavioral similarity of time elapsed between offenses
from the same series. It was predicted that;
Running Head: LINKING SERIAL RAPE
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a) There would be a negative relationship between time elapsed in days
between a pair of offenses and their level of behavioral similarity.
6. Investigating the effect on behavioral similarity of a serial rapists’ experience in
terms of the known rapes he has committed. It was predicted that;
a) Pairs of crimes occurring later in a series would be characterised by greater
behavioral similarity.
2. METHOD
2.1. Data
One hundred and nineteen cases of serial sexual assault were identified by the
Investigative Psychology Unit (IPU) of the South African Police Service, for which a
police file existed, which contained, as a minimum, a copy of the victim’s account of
the sexual assault. Where the victim’s account was in Afrikaans, it was translated into
English by the second author who is fluent in both languages. The vast majority of the
offenses were defined as a rape (97%, n = 115), according to the Criminal Law (Sexual
Offenses and Related Matters) Amendment Act (2007), with three cases being classified
as attempted rapes and one being an indecent assault. These cases were committed by
22 male serial rapists. A serial offender was defined as an offender who had offended
against two or more victims on different occasions
ii
. An offender who on one occasion
had assaulted two or more victims at the same time was not considered to be a serial
offender.
The number of crimes in a series ranged from two to 65 with the mode being
three. For 74% (n = 88) of the cases, an offender had been convicted, 14% of the
offenses (n = 17) were solved and the remaining 11% (n = 14) were unsolved. For nine
series, the files confirmed that they were first linked by DNA. For a further nine series,
Running Head: LINKING SERIAL RAPE
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they had initially been linked due to similar MO. For two series, how they were first
linked had not been recorded. For the remaining two series some of the offenses were
linked by DNA first and the others by similar MO, however it was not clear which
offenses were first linked by DNA and which by MO. Of the 119 victims, 93% (n =
111) were female and 25% (n = 25) were aged less than 18 years. Ninety-two per cent
of victims (n = 109) were strangers to the offender.
2.2. Procedure
Prior to reading the police files, published checklists of rapist behavior (Bennell
et al., 2009, 2010; Canter & Heritage, 1990; Canter et al., 2003; Mokros & Alison,
2002; Porter & Alison, 2004; Salfati & Taylor, 2007; Santtila et al., 2005; Woodhams,
2008) and a checklist which had been developed previously on a sample of South
African rapes (De Wet, 2008) were consulted. These different checklists were
amalgamated to form an overall checklist of rapist crime scene behaviors (see Appendix
1). Using the contents of the police file, the first author coded each crime in the dataset
against the checklist in a binary fashion with a 1 being recorded where a behavior
reportedly occurred and a 0 being recorded where it did not (or where this was
unknown). For two offenses from two different series the offender had assaulted more
than one victim during the same event. In these cases one victim was chosen at random
from the offense and only the behaviors in which the offender engaged with this victim
were coded. The inter-rater reliability of this coding was assessed with 10% of the
sample, which was chosen at random and dual coded. The kappa statistic was 0.70
which indicates a ‘good’ and ‘substantial’ level of reliability (Cicchetti, 1994; Landis &
Koch, 1997), and the percentage agreement was 91.47%. How a crime series was first
identified was extracted from the police file where this had been recorded.
Running Head: LINKING SERIAL RAPE
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Once each offense had been coded for the offender’s crime scene behavior, pairs
of crimes were created. A method commonly adopted for assessing the assumptions of
case linkage (Bennell & Canter, 2002; Bennell & Jones, 2005; Bennell et al., 2009;
Markson et al., 2010; Tonkin et al., 2008; Woodhams & Toye, 2007) was used in this
study. This method was originally proposed by Bennell (2002). This involves creating
a subset of linked crime pairs and a subset of unlinked crime pairs and generating a
measure of behavioral similarity for each pair (quantified using Jaccard’s coefficient).
This was conducted using a program called B-Link which was devised by Dr. Craig
Bennell in 1999.
To assess whether the inclusion of all offenses from each series in the analysis
would affect the results, in terms of not controlling for the behavior of prolific
offenders, two different sets of crime pairings were needed. Initially, a dataset of pairs
were created using all offenses from all series and generating all possible pairs. This
resulted in 599 linked crime pairs and 6422 unlinked crime pairs (N = 7021). To create
the alternative dataset, two offenses were randomly selected from each of the 22 series.
Two offenses were selected since this was the smallest length of a series. All possible
pairings were generated resulting in a new dataset of 22 linked crime pairs and 924
unlinked crime pairs (N = 946).
The binary coding of the offender’s behavior for each offense were the input
data for calculating Jaccard’s coefficients between pairs of crimes. As noted above,
Jaccard’s coefficient is often used in linkage research as a measure of behavioral
similarity. This is because it has the advantage of discounting joint non-occurrences of
a behavior in the calculation of similarity. As explained by Bennell and Canter (2002),
this is advantageous due to the quality of information within police files, which was not
Running Head: LINKING SERIAL RAPE
18
collected for the purposes of research. Whilst an offender might have displayed a
behavior during an offense its eventual recording in the police file can depend on a
number of factors (and thus, non-occurrences of behavior in the dataset may not actually
indicate that a behavior did not occur). These include the victim’s memory, their
willingness or ability to report the details of the offense, the interviewer’s skill and, in
the case of a victim statement, how closely what is written in the statement reflects what
the victim reported in interview (Alison et al., 2001). As noted by Bennell and Jones
(2005), such errors will add noise to the data reducing the likelihood of finding
relationships rather than increasing this possibility.
Having calculated the similarity in MO behavior for each crime pair (quantified
by one Jaccard’s coefficient for each pair), various analytical steps were taken. Tests of
differences were calculated to compare the behavioral similarity of different types of
linked crime pairs (DNA linked vs. MO linked), as well as the linked and the unlinked
crime pairs. Following these tests, a standard logistic regression analysis was conducted
to examine the extent to which the measures of behavioral similarity could be used to
accurately discriminate between linked and unlinked crime pairs.
When conducting logistic regression analysis it is important to validate the
results to ensure that they generalise beyond the data used to develop the regression
model (Tabachnick & Fidell, 1996, as cited in Santtila et al., 2005). To carry out the
cross validation, we used the leave-one-out method from the syntax reported in
Herrmann (1998). Leave-one-out cross-validation involves taking each case out of the
dataset one at a time. When a given case has been extracted, a logistic regression model
is developed using the remaining dataset (representing the development data), which is
then applied to the extracted case only (representing the validation data) to produce a
Running Head: LINKING SERIAL RAPE
19
predicted probability. This case is then returned to the dataset and the procedure
repeated with the next case in the dataset until cases have been exhausted. The
predicted probabilities produced from the syntax formed the input data for the ROC
analysis. All analyses were conducted with PASW 18.
3. RESULTS
3.1. Pairs identified from DNA matches versus similar MO
Prior to assessing the two underlying assumptions of case linkage, the subset of
linked crime pairs, which was composed of series first identified by DNA or series first
identified on the basis of similar MO, was assessed to determine if these two types of
linked pairs differed in behavioral similarity. Eighteen series were compared, nine
which had been first linked by DNA and nine which had been first linked on the basis of
similar MO. A Kolmogorov-Smirnov test had confirmed that the distribution of
Jaccard’s coefficients was not significantly different from a normal distribution
therefore an independent-samples t-test was conducted.
The crime pairs from the series which had been identified from MO had larger
Jaccard’s coefficients (M = .51, SD = .11) compared to the pairs constituting series that
had been linked first by DNA (M = .47, SD = .10). However, this difference was only
just significant (t (171) = 1.98, p = .049, d = .38) and represented a small effect size
(Cohen, 1988). For this reason, in subsequent analyses the linked crime pairs were
analyzed together rather than being split into sub-types.
3.2. Analyses using all crimes in the series
The distribution of Jaccard’s coefficients for the linked and the unlinked crime
pairs were plotted on a histogram to examine the degree of overlap for the two
distributions (see Fig. 1). While the two distributions overlap, the linked crime pairs
Running Head: LINKING SERIAL RAPE
20
tend to have larger Jaccard’s coefficients (M = .52, SD = .10, Range = .20 - .85) in
general than the unlinked crime pairs (M = .34, SD = .10, Range = .01 - .73),
representing greater similarity in MO behavior.
**Insert Fig. 1 approx here**
The distributions of the linked and the unlinked crime pairs did not depart
significantly from a normal distribution. Thus, a paired t-test was conducted to
determine if the difference between linked and unlinked crime pairs was significant.
This requires an equal number of pairs in each subset, therefore 599 unlinked crime
pairs were chosen randomly from the larger set of 6422 unlinked crime pairs. The
linked crime pairs were significantly more similar in MO than the unlinked crime pairs
(t (598) = 29.95, p < .001, d = 1.80), with a very large effect size (Cohen, 1988).
ROC analysis was conducted to assess the predictive accuracy of similarity in
MO behavior using the predicted probabilities produced by the leave-one-out logistic
regression analysis. The resulting AUC was .88 (SE = .01, 95% CI = .86-.89),
representing a significant (p<.001) and excellent level of predictive accuracy (Hosmer
& Lemeshow, 2000). The ROC curve can be seen in Fig. 2.
**Insert Fig. 2 approx here**
Youden’s index was calculated to identify the decision-threshold (for deciding
when a pair should be considered linked) at which the proportion of hits would be
maximised whilst the proportion of false alarms would be minimised (Bennell, 2005).
This threshold corresponded with a Jaccard’s coefficient of .425.
3.3. Analyses using two crimes per series
The same analyses as reported in the previous subsection were repeated with the
smaller subset of crimes where just two offenses per serial offender had been sampled.
Running Head: LINKING SERIAL RAPE
21
The distributions for behavioral similarity can be seen in Fig. 3. As was the case when
all crimes per series were sampled, the linked crime pairs continued to be characterized
by greater behavioral similarity and larger Jaccard’s coefficients in general (M = .47, SD
= .12, Range = .23 - .74) than the unlinked crime pairs (M = .34, SD = .11, Range = .10
- .71). The linked crime pairs in this subsample were, however, characterized by less
behavioral similarity than the linked pairs in the previous analysis, as can be seen from
the mean Jaccard’s coefficient, which decreased from .52 to .47. Overall, the linked
crime pairs appeared to be characterized by greater similarity in MO behavior than the
unlinked crime pairs.
**Insert Fig. 3 approx here**
The distributions of the linked and the unlinked crime pairs in this sub-sample
were not significantly different from a normal distribution, therefore a paired t-test was
conducted using 22 randomly selected unlinked crime pairs from the subset of 924
unlinked crime pairs. This test confirmed that the linked crime pairs were significantly
more similar in MO behavior than the unlinked crime pairs (t (21) = 4.96, p < .001, d =
1.43), with a large effect size (Cohen, 1988). The effect size was, however, smaller in
magnitude than in the previous analysis.
A leave-one-out cross-validation analysis was again conducted and an AUC
computed using the predicted probabilities for the 946 pairs (22 linked crime pairs and
924 unlinked crime pairs). The ROC curve can be seen in Fig. 4. The AUC was .77
(p<.001, SE = .05, 95% CI = .67-.87) which is smaller than that from the previous
analysis, suggesting a reduction in predictive accuracy when the influence of prolific
offenders is controlled for. However, this AUC still represents a significant and
adequate level of predictive accuracy (Hosmer & Lemeshow, 2000).
Running Head: LINKING SERIAL RAPE
22
**Insert Fig. 4 approx here**
Youden’s index was again calculated to identify the decision-threshold at which
the proportion of hits would be maximised whilst the proportion of false alarms would
be minimised (Bennell, 2005). This threshold represented a Jaccard’s coefficient of
0.35.
3.4. The effect of time elapsed on behavioral consistency
The number of days elapsed between the dates of offenses constituting each
linked pair (n = 599) was calculated. This was correlated with the behavioral similarity
of each pair using a Spearman’s correlation analysis (due to the skewed distribution of
the time elapsed variable). For those series consisting of five or more offenses,
individual correlations were also conducted to assess whether, for each offender, there
was a relationship between time elapsed and behavioral similarity. The results of all of
these analyses can be seen in Table 1. They suggest little support for a relationship
between behavioral consistency and time elapsed between offense pairs.
**Insert Table 1 approx here**
3.5. The effect of experience on behavioral consistency
To investigate the effect of experience on behavioral consistency, those series
containing five or more offenses were selected (n = 9) and from these the first known
offense pair and the last known offense pair were extracted. The similarity in MO for
the first and last pair in each series can be seen in Table 2. An increase in similarity in
MO from first pair to last pair can be seen in seven of the nine series, indicating greater
behavioral consistency for offenses later in the series, although for some the increase in
Jaccard’s coefficient is small.
**Insert Table 2 approx here**
Running Head: LINKING SERIAL RAPE
23
4. DISCUSSION
4.1. Assessments of methodological variation
The data collected for the purpose of this research study provided an opportunity
to test a number of methodological issues, as well as the fundamental principles of case
linkage. In the past, valid concerns have been raised regarding whether findings
generated from convicted samples of serial offenders would generalize to unsolved
series. Specifically, concerns were raised as to whether the levels of behavioral
consistency and distinctiveness found with convicted crime series would generalize to
unsolved crime series or if these would be characterized by lower levels of consistency
and distinctiveness (Bennell & Canter, 2002). This study took a first step in
investigating this concern by comparing the behavioral similarity of linked crime pairs
which were first identified as part of a series based on MO to those identified from
DNA matches. The crime pairs taken from series first identified by MO were more
behaviorally similar than those that were first identified on the basis of DNA evidence,
however, this difference was only just significant with a small effect size. Having said
this, before concerns about the ability to generalize from convicted crime series to
unsolved crime series can be completely allayed these findings would need to be
replicated and larger samples of first-linked-by-MO and first-linked-by-DNA series
collected to allow for comparative ROC analysis.
We were also able to assess the effect of controlling for the behavioral
expression of prolific serial offenders in the analyses by varying whether we sampled all
crimes in each series or randomly chose a constant number of crimes from each series.
These two methods represent those that have been used in existing studies. When
sampling all offenses from each series, our analysis yielded an AUC of .88 whereas this
Running Head: LINKING SERIAL RAPE
24
decreased to .77 when sampling a constant number of offenses from each series.
Similarly, the decision-threshold for predicting that a pair of crimes is linked, as
calculated using Youden’s index (Bennell, 2005), varied when using these different
sampling methods. When sampling all offenses from all series, the threshold
represented a larger Jaccard’s coefficient than when sampling a constant number of
offenses from each series. This variation suggests that findings from published studies
which have utilized different methods for sampling crime pairs from series might not be
comparable. In reality the number of offenses from crimes series would not be constant
in databases of offenses used by the police for case linkage and thus adopting the more
stringent test in case linkage research (whereby a constant number of offenses per series
is sampled) does not necessarily reflect the reality of the linking task. Indeed, studies
that sample a constant number of offenses from each series could be underestimating
the accuracy with which crimes can be behaviorally linked in reality. In future studies,
researchers could therefore present both sets of output, where sample sizes allow.
4.2. Behavioral consistency and distinctiveness in serial rape
Tests of difference demonstrated that the linked crime pairs in our sample were
significantly more similar in MO behavior than the unlinked crime pairs with large
effect sizes. The Jaccard’s coefficients obtained for our linked and unlinked crime pairs
in all analyses were larger than those found in existing studies of adult serial rapists
(Bennell et al., 2009; Mokros & Alison, 2002), but not very different. As has been the
case with existing studies (Bennell et al., 2009; Mokros & Alison, 2002; Woodhams,
Grant et al., 2007), on average, the Jaccard’s coefficients for the linked crime pairs did
not approach 1.0, providing further evidence that serial rapists are not perfectly
consistent in their MO behavior. The Jaccard’s coefficients from the linked and the
Running Head: LINKING SERIAL RAPE
25
unlinked crime pairs were shown to overlap to quite a degree and it is clear from the
descriptive statistics that some serial offenders are recorded as showing more
consistency in their behavior across their crimes than others. This replicates what has
been found with previous studies (Bennell et al., 2009; Woodhams, Grant et al., 2007).
It also reflects what would be expected based on the literature regarding the role of
sexual fantasy in serial sex offending (Gee & Belofastov, 2007; Hazelwood & Warren,
2000), and situational variation due to victim behavior, third-party disturbance or
changes in offender mood (Davies, 1992; Hazelwood & Warren, 2004; Labuschagne,
2010). This suggests that in practice whilst we might be able to identify the series of
some rapists based on similarity in MO behavior, there are others for whom this would
be very difficult, if not impossible. This may be because the offenders are not
sufficiently consistent or distinctive in their MO, or it is possible that the ways in which
they express behavioral consistency are not discernable to the victim or are not routinely
recorded in police files.
Within the literature on risk assessment, it has been recognised that for some
offenders it will not be possible to classify them as being at high- or low-risk of violent
recidivism using actuarial methods (Monahan et al., 2001) because “based on current
knowledge, the aggregate degree of risk presented by these intermediate cases cannot be
statistically distinguished from the base rate of the sample as a whole” (p. 92).
Similarly, for case linkage we might be able to confidently classify some crime pairs as
linked (due to their large Jaccard’s coefficients) and others as unlinked (due to their
small Jaccard’s coefficients). However, as suggested by the overlapping distributions
reported here and by other authors (Bennell et al., 2009; Woodhams, Grant et al., 2007),
there are also likely to be some crime pairs which we will not be able to confidently
Running Head: LINKING SERIAL RAPE
26
classify as linked or unlinked. Analyses that allow for the investigation of such a
scenario are underway (Bennell et al., 2011).
Despite recognising some of the difficulties in classifying offenses as belonging
to the same series or not, the ROC analyses produced figures indicative of adequate to
excellent levels of predictive accuracy. The AUC of .77 obtained in the current study
when sampling a constant number of offenses from each rape series was very similar to
that obtained by Bennell et al. (2009), which was .75, under similar sampling
conditions. That adequate levels of predictive accuracy were reached under the more
stringent conditions is promising and suggests that the findings from UK and European
samples generalize to South Africa. Such findings are important when one considers
that linkage analysis is used to inform police investigations as well as legal proceedings
in South Africa (Labuschagne, 2006, 2010).
4.3. Examination of temporal proximity and expertise
Since 2007, a handful of studies have investigated the relationship between
behavioral consistency and expertise and time elapsed between offenses. When
sampling all linked pairs, there was no discernable relationship between behavioral
consistency and time elapsed, which replicates findings with serial juvenile sex
offenders (Woodhams, et al., 2008), car thieves (Tonkin et al., 2008), and burglars
(Markson et al., 2010). However, as noted above, offenders vary in the degree of
consistency they show across their series, therefore, analyses were repeated using the
series containing five or more offenses to determine if such a relationship would hold
for some offenders but not others. For most offenders there was a weak or moderate
negative relationship between consistency and the amount of time (in days) elapsed
between offenses within crime pairs, whereas for two offenders there was a weak
Running Head: LINKING SERIAL RAPE
27
positive relationship or none at all. For no offenders was there a strong negative
relationship, as predicted.
There are several reasons why this might be: first, in light of the under-reporting
of rape to the authorities in South Africa, as in other countries (Statistics South Africa,
2000), there are likely to be gaps in series with offenses missing from the sequence.
Second, as indicated by the distribution of Jaccard’s coefficients for linked crime pairs,
the serial offenders in this sample are not perfectly consistent in their behavior. As
noted above, this can be for several reasons, not least of all victim behavior and its
potential for inhibiting the expression of desired behaviors by the offender (Davies,
1992; Labuschagne, 2010).
Regarding the effect on behavioral consistency of offenders accruing experience
in offending, the number of prolific offenders in the current sample precluded the use of
inferential statistics; however, comparison of the Jaccard’s coefficient for the first crime
pair and the last crime pair in the series suggested some indication of increasing
consistency with increasing experience for seven offenders. Needless to say, this is a
potential relationship that would benefit from further investigation, however it is likely
the relationship is complex in nature. As recently explained by Sorochinski and Salfati
(2010), and as referred to above, there are several reasons why we might see behavioral
change from offense-to-offense even when an offender has gained experience of
offending, such as changes in violence due to frustration at being unable to achieve a
fantasy.
4.4. Limitations
With regards to the limitations of the current study, the sample size (N = 22
series), whilst similar to other linkage studies (N = 23 series, Salfati & Bateman, 2005;
Running Head: LINKING SERIAL RAPE
28
N = 16 series, Santtila et al., 2005; N = 23 series, Santtila et al., 2008; N = 19 series,
Sorochinski & Salfati, 2010), is still small and thus the findings will need replication.
Further, when conducting case linkage in reality, practitioners must try to identify crime
series from large collections of crimes that were committed by both serial and non-serial
offenders. On this occasion, the researchers were not able to collect a sample of
apparent one-off rapes to include in the analyses to more closely resemble the reality of
case linkage; however, future research will address this limitation.
The decision was taken to investigate the discrimination accuracy of all MO
behaviors combined rather than considering the relative performance of different types
of MO behaviors, as has been done in previous studies of rape (e.g., Grubin et al.’s
(2001) analysis of control, escape, sex and style behaviors). This decision was taken
because studies utilising ROC analyses have reported superior performance when
testing the predictive accuracy of all MO behaviors combined compared to individual
behavioral domains (Bennell et al., 2009). This said, there remains the possibility that
some combination of individual MO behaviors (not necessarily reflecting pre-defined
domains) might be more effective for linking crimes than MO behaviors overall. This is
an important avenue for future efforts.
4.5. Conclusion
It is tentatively concluded that initial evidence has been found supporting the
underlying assumptions of case linkage with serial rapes from South Africa. This adds
to a growing body of linkage research which, despite methodological shortcomings, is
finding serial offenders to be sufficiently consistent and distinctive in their MO
behavior for series to be differentiated.
Running Head: LINKING SERIAL RAPE
29
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Running Head: LINKING SERIAL RAPE
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Running Head: LINKING SERIAL RAPE
38
Appendix 1: Checklist of offender behaviors.
Hours of light
Weekday
Lone Victim
On Foot
Car
Bicycle
Stalked
Hides
Surprise
Con-engages
Con-employ
Con-offers help
Con-authority
Con-needs help
Con-bribe
Urinates
Extended con
Property stolen
Identifies victim
Engaging manner
Inquisitive
Impersonal
Direct threat
Indirect threat
Demeans
Verbal aggression
Lie to upset
Confrontation
Compliments
Self-disclosure
Implies knowing
Positive presentation
Sexual comments
Remorse
Mitigates responsibility
React-not deterred
Reassures
React-accommodates
Consideration
Sexual participation
Undressed victim
Penile vaginal penetration
Penile anal penetration
Digital vaginal penetration
Masturbate offender
Multiple rape
Fellatio
Kissed
Physical intimacy
Erection
Ejaculation
Erectile dysfunction
Self masturbation
Pornography
Breast
Requires victim look
Simulates intercourse
Sandwich rape
Instrumental violence
Gratuitous violence
Witness-violence
Binding
Gagging
Ripped clothes
Strangling
Slapping
Punching
Kicking/Stamping
Bludgeoning
Hair-pulling
Cutting
Shooting
Biting
Whipping
Pelting
Liquid-face
Public approach
Private approach
Public assault
Private assault
Vehicle assault
Contained
Forced entrance
Intrudes
Weapon seen
Weapon-to scene
Weapon-from scene
Knife
Firearm
Rock
Bottle
Handbag
Slingshot
Wire
Ornament
Stick
Blindfold
Disguise
Prevent look
Condom
Clean
Precautionary question
Lie - protect identity
Don’t report
False report
Stay
Pursues
Extends time
Returns victim
Further contact
Releases victim
Calm departure
Rapid departure
Gives gift
Running Head: LINKING SERIAL RAPE
39
Table 1: Correlations for temporal proximity and behavioral similarity overall, and for
each series of five or more offenses.
Series Number
All
5
9
10
11
15
16
17
20
22
r
-.02
-.10
-.17
.24
-.30
-.18
.29
-.25
-.26
-.46
p
n.s.
n.s.
<.01
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
n
599
21
406
36
21
15
15
15
10
10
Running Head: LINKING SERIAL RAPE
40
Table 2: The Jaccard’s coefficient for the first and last offense pair in the eight series
which had a length equal to or greater than 5 offenses (n = 9).
Series Number
5
9
10
11
15
16
17
20
22
First Offense Pair
.38
.34
.48
.61
.44
.69
.50
.52
.20
Last Offense Pair
.56
.48
.65
.52
.48
.52
.61
.57
.55
Running Head: LINKING SERIAL RAPE
41
Fig. 1: The distribution of Jaccard’s coefficients for unlinked crime pairs (left) and
linked crime pairs (right) (N = 7021 pairs).
Running Head: LINKING SERIAL RAPE
42
Fig. 2: The ROC graph for differentiating linked and unlinked crime pairs using MO
behaviors (N = 7021 pairs).
Running Head: LINKING SERIAL RAPE
43
Fig. 3: The distribution of Jaccard’s coefficients for unlinked crime pairs (left) and
linked crime pairs (right) when sampling only two crimes from each of the 22 series (N
= 946)
Running Head: LINKING SERIAL RAPE
44
Fig. 4: The ROC graph for differentiating linked and unlinked crime pairs using MO
behaviors (N = 946 pairs).
i
A hit is where crimes are predicted to be linked and they do belong to the same series in reality, a correct
rejection is where crimes are predicted to be unlinked and they are the work of different offenders in
reality, a false alarm is where crimes are predicted to be linked and in reality they are the work of two
different offenders, and a miss is where crimes are predicted to be unlinked whereas they do belong to the
same series in reality.
ii
The definition adopted in this study corresponds with international research programmes on various
forms of serial offending (Beauregard et al., 2007; Grubin et al., 2001; Park et al., 2008; Santtila et al.,
2005; Tonkin et al., 2008) and the Federal Bureau of Investigation’s (2008) definition for serial murder.
