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Running Head: LINKING SERIAL SEX OFFENCES
1
Linking serial sexual offences: Moving
towards an ecologically valid test of the
principles of crime linkage
Jessica Woodhams1*, Matthew Tonkin2, Amy Burrell3,
Hanne Imre4, Jan M. Winter 5,6, Eva K.M. Lam7, Gert Jan
ten Brinke8, Mark Webb9, Gerard Labuschagne10, Craig
Bennell11, Leah Ashmore-Hills12, Jasper van der Kemp13,
Sami Lipponen14, Tom Pakkanen15, Lee Rainbow9, C.
Gabrielle Salfati16 and Pekka Santtila17.
1University of Birmingham, UK
2University of Leicester, UK
3Coventry University, UK
4 Belgian Federal Police, Belgium
5Dutch National Police, the Netherlands
6Department of Clinical and Lifespan Psychology (KLEP),
Vrije Universiteit Brussel, Belgium
7The National Police of the Netherlands, the Netherlands
8Dutch National Police, the Netherlands
9National Crime Agency, UK
10 L&S Threat Management, South Africa
11Carleton University, Canada
12 Birmingham City University, UK
13 Vrije Universiteit Amsterdam, the Netherlands
14National Bureau of Investigation, Finland
15 Åbo Akademi University, Finland
16 John Jay College of Criminal Justice, New York
17New York University, Shanghai
This is the peer reviewed version of the following article: [FULL CITE], which has
been published in final form at [Link to final article using the DOI]. This article may
be used for non-commercial purposes in accordance with Wiley Terms and
Conditions for Use of Self-Archived Versions.
Running Head: LINKING SERIAL SEX OFFENCES
2
Linking Serial Sex Offences: Moving Towards an Ecologically Valid Test
of the Principles of Crime Linkage
LINKING SERIAL SEX OFFENCES
3
Abstract
Purpose: To conduct a test of the principles underpinning crime linkage
(behavioural consistency and distinctiveness) with a sample more closely
reflecting the volume and nature of sexual crimes with which practitioners work.
To assess whether solved series are characterised by greater behavioural
similarity than unsolved series. Method: A sample of 3,364 sexual crimes
(including 668 series) was collated from five countries. For the first time, the
sample included solved and unsolved but linked-by-DNA sexual offence series,
as well as solved one-off offences. All possible crime pairings in the dataset
were created and the degree of similarity in crime scene behaviour shared by
the crimes in each pair was quantified using Jaccard’s coefficient. The ability to
distinguish same-offender and different-offender pairs using similarity in crime
scene behaviour was assessed using Receiver Operating Characteristic
analysis. The relative amount of behavioural similarity and distinctiveness seen
in solved and unsolved crime pairs was assessed. Results: An Area Under the
Curve of .86 was found, which represents an excellent level of discrimination
accuracy. This decreased to .85 when using a dataset that contained one-off
offences, and both one-off offences and unsolved crime series. Discrimination
accuracy was significantly reduced with a sample composed solely of unsolved
but linked-by-DNA series (AUC = .79). Conclusions: Crime linkage is practised
by police forces globally and its use in legal proceedings requires demonstration
that its underlying principles are reliable. Support was found for its two
underpinning principles with a more ecologically valid sample.
Keywords: assumptions, comparative case analysis, linkage analysis,
case linkage, behavioural linking
LINKING SERIAL SEX OFFENCES
4
Linking Serial Sex Offences: Moving Towards an Ecologically Valid Test
of the Principles of Crime Linkage
Crime linkage
1
refers to a group of practices where the crime scene
behaviour displayed in multiple crimes is analysed for similarity and
distinctiveness to assess the likelihood of those crimes being committed by the
same offender. Where similar yet distinctive behaviour is observed, greater
confidence is attributed to the crimes being the work of the same perpetrator
(Woodhams, Bull, & Hollin, 2007). The underlying principles of crime linkage are
therefore that offenders will show a degree of consistency in their crime scene
behaviour over time (the Consistency Hypothesis; Canter, 1995), and that
offenders will show a degree of distinctiveness in their crime scene behaviour
(Bennell & Canter, 2002), allowing the crimes of one offender to be
distinguished from those of another offender committing a similar sort of crime
2
.
In many countries, police units exist that specialise in this behavioural
analysis for the most serious forms of crime (e.g., sexual offences and
homicides) (Bennell, Snook, Macdonald, House, & Taylor, 2012). This analysis
informs police investigations and can have several benefits such as identifying
1
Crime linkage is also referred to as linkage analysis (Hazelwood & Warren, 2004), case
linkage (Woodhams & Grant, 2006) and comparative case analysis (Bennell & Canter, 2002).
2
The assumption of consistency is operationalised in practice and research as an evaluation of
the similarity in crime scene behaviour between two or more crimes. Consistency is used in this
paper when referring to the behaviour displayed by the same individual over time/events, and
similarity is used when referring to linked/unlinked crime pairs and predicting linkage status
because, in practice, an analyst would not know for certain whether a set of crimes were by the
same person or not.
LINKING SERIAL SEX OFFENCES
5
crime series where physical trace evidence is lacking or is costly or time-
consuming to process, pooling evidence from multiple crime scenes, and
enhancing victim credibility (Davies, 1991; Grubin, Kelly, & Brunsdon, 2001;
Labuschagne, 2015). However, errors in linkage prediction can misdirect
investigative efforts and unnecessarily increase public fear of a serial offender
being active in the area (Grubin et al., 2001).
Crime linkage analysis can also inform legal decision making and has
been admitted as similar fact evidence for robbery, burglary, homicide,
kidnapping and rape prosecutions in State v. Mogale (2012), State v. Nyauza
(2007), State v. Steyn (2012), State v. Sukude (2006) and State v. van Rooyen
(2007) in South Africa, in R v. R.B. (2003) and R. v. Burlingham (1993) in
Canada (Labuschagne, 2015), and in Pennell v. State (1991), State v. Russell
(1994), People v. Prince (2007) and State v. Yates (2007) in the United States
(Pakkanen, Santtila, & Bosco, 2015). However, such evidence has also been
ruled inadmissible in some cases due to concerns about the reliability of its
underlying principles and the methods used (Her Majesty’s Advocate v. Young,
2013; State of New Jersey v. Fortin, 2000). Regarding the latter, when making
their assessments, these courts have been guided by legal standards for the
admissibility of scientific expert evidence including the Daubert criteria (Daubert
v. Merrell Dow Pharmaceuticals Inc., 1993) and the Federal Rules of Evidence
(i.e., Rule 702; 2011). These standards require that the testimony is the product
of reliable principles and methods and that there needs to be a known or
potential error rate for the practice. In HMA v. Young (2013), for example, a voir
dire admissibility hearing was held to consider the empirical support for crime
LINKING SERIAL SEX OFFENCES
6
linkage analysis and its principles; crime linkage analysis evidence was
ultimately ruled inadmissible.
Crime linkage can, therefore, have a potentially significant impact on
police investigations and legal outcomes (whether prosecutions or appeals). As
such, it is important that research seek to test the viability of crime linkage and
to test this in the most realistic way possible.
Paradigms for assessing the principles of crime linkage
The basic tenet of studies of the crime linkage principles is to assess the
accuracy with which quantitative measures of similarity in crime scene
behaviour (i.e., similarity coefficients) can be used to predict whether two or
more crimes are linked
3
. The similarity coefficients are usually calculated from
binary codings of offender crime scene behaviour (e.g., Did the offender kiss
the victim? – Yes/No?). These codings can be pre-existing, having been
completed by trained police staff as part of their routine practice (see Method),
or the coding is completed by researchers based on police files documenting
each offence. These data are then subject to statistical analysis.
There are two common analytical approaches used: the first rank orders
crimes, offenders or series in order of similarity in behaviour to the “query” crime
and assesses the accuracy of prediction though comparison to actual series
membership and compares this level of accuracy to what would be expected by
chance alone (e.g., Santtila, Junkkila, & Sandnabba, 2005). The second
approach (e.g., Bennell & Canter, 2002) assesses the degree of behavioural
3
Other quantitative metrics can also be used in linkage predictions (e.g., the inter-crime
distance).
LINKING SERIAL SEX OFFENCES
7
similarity shared by a given pair in the dataset and determines, based on
whether this is high or low, if the pair was likely committed by the same offender
(linked), or whether the two crimes in the pair are by two different offenders
(unlinked), respectively. Both of these approaches simultaneously assess the
two principles of crime linkage – behavioural consistency and distinctiveness.
Receiver Operating Characteristic (ROC) analysis is the preferred
measure of predictive accuracy in forensic psychology (Harris & Rice, 1995)
and is commonly used to quantify the accuracy with which behavioural similarity
can be used to predict series membership or linkage status (linked/unlinked)
(see Bennell, Mugford, Ellingwood, & Woodhams, 2014, and Winter et al.,
2013). It has four possible outcomes: a hit (where a pair is predicted to have
been committed by the same offender and was), a false alarm (where a pair is
predicted to have been committed by the same offender but was not), a correct
rejection (where the two crimes in a pair are predicted to have been committed
by two different offenders and they were) and a miss (where the two crimes in a
pair are predicted to have been committed by two different offenders and were
committed by the same offender). Predicting which series a given crime belongs
to (same series/different series) can be conceptualised in the same way (e.g., a
hit would be where a crime is correctly predicted to be a member of a series)
(Winter et al., 2013). A ROC analysis plots the proportion of hits against the
proportion of false alarms at every possible decision threshold (in this case at
each predicted probability value) from the most stringent threshold to the most
lenient. This produces a ROC curve and the Area Under the Curve (AUC)
represents the predictive accuracy of the decision task. The AUC ranges from 0
LINKING SERIAL SEX OFFENCES
8
to 1, with 0.5 representing chance level accuracy and values closer to 1.0
representing high levels of predictive accuracy.
To assess the predictive or diagnostic accuracy of a method or tool, the
outcome being predicted needs to be known (or become known) for the cases
to which the method/tool is applied. In the context of crime linkage research this
equates to using a sample where the series membership of crimes is known; for
example, offender 1 is known to be responsible for crimes 1, 2 and 3 in the
dataset. A robust test of the crime linkage principles necessitates confidence in
such attributions and studies have typically used offender conviction and/or
scene-to-scene DNA hits as confirmation of series membership. It follows that
the conditions under which the principles are tested will never represent the
exact conditions under which police analysts conduct crime linkage: police
analysts search for crime series within datasets of series and one-off offences,
where series membership is known in some cases but not in others, and where
their predictions of series membership may not be confirmed due to a lack of
feedback or to investigative efforts not yielding an outcome (Davies, Alrajeh, &
Woodhams, 2018). However, the ecological validity of studies designed to test
the crime linkage principles can be improved by designing studies that more
closely resemble the data searched by analysts.
A critical reflection on studies of the crime linkage principles
More than a decade of research testing the crime linkage principles
exists and the general conclusion from this body of research is that the
principles are empirically supported to an extent (Bennell et al., 2014): some
serial offenders show sufficient behavioural consistency and distinctiveness for
their crimes to be linked; however, some offenders and some series are
LINKING SERIAL SEX OFFENCES
9
characterised by inconsistent and/or indistinct behaviour (Slater, Woodhams, &
Hamilton-Giachristis, 2015). However, most of these research studies have
sampled series confirmed by conviction. Only sampling series confirmed by
conviction does not reflect the data searched by analysts and may artificially
inflate the accuracy with which linked crime pairs can be distinguished from
unlinked crime pairs, or with which crimes can be attributed to the correct
series. This is because convicted series might have been solved and convicted,
in part, due to the distinctive and consistent behaviour of the offender (Bennell
& Canter, 2002). Improving ecological validity by extending the sampling frame
to include unsolved crime series that are linked by DNA allows researchers to
establish ground truth without biasing the sample in this way (Woodhams et al.,
2007). To date, a handful of studies have adopted this design, but these remain
the minority (Pakkanen et al., 2015). Only one study exists with sexual offences:
Woodhams and Labuschagne (2012a) included in their sample of 599 linked
crime pairs, 19 linked pairs that were unsolved but linked by DNA (representing
3% of the linked pairs). Linked crime pairs could be distinguished from unlinked
crime pairs with an AUC of .88, therefore providing empirical support for the
crime linkage principles. A larger AUC was found than had been reported in
previous studies (e.g., 0.75, Bennell, Jones, & Melnyk, 2009).
Two further studies of the crime linkage principles with sexual offences
have improved the ecological validity of their samples by extending their
sampling frame to include one-off sexual offences alongside serial offences.
Winter et al. (2013) sampled 90 serial sex offences and 129 one-off offences
and found AUCs ranging from.80-.89. Slater et al. (2015) found an AUC of .86
LINKING SERIAL SEX OFFENCES
10
with a sample of 144 convicted serial offences and 50 convicted one-off
offences.
Despite these improvements in methodological design, the sample sizes
of these studies remain small. Indeed, this criticism applies to most studies of
the crime linkage principles with sexual offences. Sample sizes range from 43
to 244 offences (Bennell et al., 2009; Santtila et al., 2005; Slater et al., 2015;
Winter et al., 2013; Woodhams & Labuschagne, 2012a)
4
. This can be
contrasted with the volume of sexual crimes searched by police analysts in
countries that use the Violent Crime Linkage Analysis System (ViCLAS) (e.g.,
approximately 8,000 cases are on the ViCLAS database in Belgium and 30,000
in the UK; [Blinded]).
The current study was therefore designed to test the principles of crime
linkage using a research design with improved ecological validity, by, for the
first time, utilising a much larger sample of crimes, and sampling convicted and
unsolved but linked-by-DNA series, as well as convicted one-off offences. Our
research questions were:
1) Are crimes committed by the same offender (“linked” crime pairs)
characterised by greater behavioural similarity than crimes committed
by different offenders (“unlinked” crime pairs), which would imply both
greater behavioural consistency and greater distinctiveness?
2) At what level of accuracy could linked crime pairs be differentiated
from unlinked crime pairs as assessed by ROC analysis?
4
Yokota, Fujita, Watanabe, Yoshimoto, and Wachi (2007) are the exception having sampled
1252 offences by 868 offenders.
LINKING SERIAL SEX OFFENCES
11
3) Would the inclusion of unsolved series and one-off crimes in the
sample reduce the ability to distinguish linked from unlinked crime
pairs?
Method
Data
The study utilised police crime data relating to 3,364 sexual offences committed
by 3,018 offenders (mean number of crimes per series = 3.25, range = 2 – 32
crimes). These data were provided by police units from five countries that
specialise in crime linkage with sexual offences: 1) the Serious Crime Analysis
Section (SCAS, UK, n = 2,579 offences); 2) the Investigative Psychology
Section of the South African Police Service (n = 245 offences); 3) the National
Bureau of Investigation, Finnish National Police (n = 123 offences); 4) the
Central Unit-Team ViCLAS, Dutch National Police (n = 173 offences); and 5)
the Zeden-Analyse-Moeurs unit, Belgian Federal Police (n = 244 offences).
Within these data, there were solved serial crimes (n = 2,081) and solved
apparent one-off crimes (n = 1,191) that had resulted in a conviction, and
unsolved serial crimes that were linked by DNA (n = 92)
5
. A breakdown of the
data from each country is included in Table 1.
5
In this study, unsolved crime series consisted of crimes that had been linked via DNA. Thus,
while they remain unsolved, we can be confident that the same offender was responsible.
Apparent one-off crimes consisted of crimes committed by an offender who only had one
recorded conviction for sexual offending at the time of data collection. This does not preclude
the possibility that the offenders have committed other sexual offences for which they have not
been convicted, but this limitation is unavoidable. No cases in our analyses were offences
LINKING SERIAL SEX OFFENCES
12
Three datasets (UK, Belgium and the Netherlands) were collated from
data already stored on the ViCLAS (see Collins, Johnson, Choy, Davidson, &
MacKay, 1998). ViCLAS stores records of serious crimes including the crime
scene behaviour engaged in by the offender in a standardised manner. It is
used to support the process of crime linkage in Belgium, the Czech Republic,
France, Germany, Ireland, the Netherlands, New Zealand, Switzerland and the
United Kingdom (Wilson & Bruer, n.d.). In Belgium, the Netherlands and the UK,
police investigators submit the case papers for each offence to be included on
the database to the analytical units. The types of cases submitted to the three
analytical units include stranger sexual offences and sexual homicides. In the
UK, the data were extracted directly from ViCLAS by an analyst from the SCAS.
In Belgium and the Netherlands, crime analysts employed in the ViCLAS units
manually extracted the data from ViCLAS and other relevant systems (e.g.,
crime records to identify solved and unsolved cases). In both countries, all data
retrieved from ViCLAS were reviewed by the analysts against the original paper
files to ensure the coding was in accordance with the coding dictionary and
quality control was assessed using the current quality assurance manual. These
datasets were encrypted and sent to the third author.
The data from Finland were already coded due to its use in previous
research studies (Häkkänen, Lindlöf, & Santtila, 2004; Santtila et al., 2005). The
South African data were collected by the third author in situ at the Investigative
“taken into consideration” (TICs). In England and Wales, during sentencing procedures, an
offender can admit to other offences to “wipe the slate clean” and ask that the Court take these
into consideration (Sentencing Council, 2012).
LINKING SERIAL SEX OFFENCES
13
Psychology Section of the South African Police Service (SAPS) over a three-
month period. Information was extracted directly from hard copy case files.
The crime linkage practitioners from the UK, Belgium and the
Netherlands assessed the comparability of a large set of variables across the
different countries resulting in a common coding dictionary of 166 variables that
could be considered comparable. For each crime in the dataset, information
pertaining to these 166
6
binary behavioural variables was, therefore, collated.
These variables represent the type and quality of information stored regarding
crimes on ViCLAS. Our data sharing agreements preclude the disclosure of the
exact variables, however, they encompassed behaviours designed to gain and
maintain control over the victim (e.g., how the victim was approached, whether
a weapon was used and how, the instrumental use of violence), behaviours
associated with exiting the crime scene or evading capture (e.g., wearing
gloves, a mask or a disguise, giving a false name, taking forensic precautions),
sexual behaviours (e.g., whether the victim was penetrated and how, whether
the offender ejaculated, if and how clothing was removed), target selection
variables (e.g., the time and day of the offence, the age and gender of the
victim, whether the victim was physically or mentally impaired) and behaviours
thought to reflect the offence ‘style’ of the offender and that “are not directly
necessary for the success of the attack” (Grubin et al., 2001, p. 26) (e.g., the
6
For Finland, information on 42 rather than 166 behavioural variables was present. The data for
Finland were historic and therefore the case files couldn’t be revisited to code additional
variables. Instead, a 0 was entered for these additional variables for each Finnish case. This
was not considered problematic due to the use of Jaccard’s coefficient which does not include
joint non-occurrences in its calculation of the similarity between a pair.
LINKING SERIAL SEX OFFENCES
14
offender complimenting the victim, showing concern or revealing personal
information).
To assess the reliability with which these 166 variables could be coded,
the first five series from South Africa (n = 20 cases) were dual coded by the first
and third author for inter-rater reliability analysis (representing 11,700 discrete
codes). Both are experienced coders of crime scene behaviours. Kappa and/or
percentage agreement was calculated for 161 of the 166 variables. The
remaining five variables related to objective characteristics of a crime
scene/crime (day of the week and time of the day split into four categories).
Seventy variables were coded as present by at least one of the coders
therefore it was possible to calculate a Kappa statistic for these. Kappa values
for these variables ranged from .74 - 1.00 with 52 of the 70 variables achieving
a Kappa value of 1.00. The remaining 96 variables, all achieved 100%
percentage non-occurrence agreement. It is just as important to demonstrate
the reliable coding of non-occurrence since joint non-occurrence is considered
by analysts in the linking of crimes (Davies et al., 2018) and is used in the
calculation of some similarity coefficients (although not Jaccard’s coefficient).
While the researchers coded the data in South Africa, the variables had
already been coded for the other countries, preventing further tests of coding
reliability, however it still stands that the coding of these variables was
demonstrated to be reliable on South African case files. For the UK, Belgium
and the Netherlands, a rigorous data coding and quality assurance process is
used: Data are entered onto ViCLAS by trained analysts who work with such
data on a daily basis. The training of analysts is a lengthy process, typically
lasting several months (but it can last as long as a year, or longer if necessary),
LINKING SERIAL SEX OFFENCES
15
and involving close supervision by an experienced analyst. In each country,
data entry onto ViCLAS is closely supervised by senior analysts and guided by
a detailed quality control guide/coding manual, which explains the meaning of
individual ViCLAS variables and gives examples of how these variables should
and should not be coded. Consequently, all analysts entering data onto the
ViCLAS system are following the same coding rules. Furthermore, before
analysis begins on any case, the case is reviewed to ensure that the information
entered on the ViCLAS system matches the original police files. Any
inconsistencies are fed back to the analyst who entered the data onto the
system and amended within the ViCLAS database itself.
Finally, inter-rater reliability (IRR) had already been assessed for the
Finnish data. As is published in the respective papers, a mean K of .77 was
found for Santtila et al. (2005). All variables also yielded a K > 0.61 for
Häkkänen et al. (2004) with two exceptions and one of these variables featured
in our datasets – that of revealing personal information. While this did not reach
an acceptable level of inter-rater agreement for Häkkänen et al. (2004), it was
coded reliably in our assessment of IRR with the South African data (K=.83).
Once all five datasets had been received, they were reformatted into
one row per offence
7
and manually joined together by the third and eleventh
author.
Analytic strategy
7
The binary coding was at the offence, rather than the offender, level (for offences committed
by groups) therefore no attempts were made to attribute specific behaviours to individual
offenders.
LINKING SERIAL SEX OFFENCES
16
Our analysis followed a method designed by Professor Craig Bennell in
2002 (Bennell, 2002) which has been used in many empirical tests of the crime
linkage principles since (see Bennell et al., 2014, for a review). Using a
specially designed piece of software, B-LINK (Bennell, 2002), four separate
datasets of linked and unlinked crime pairs were created (see Table 2)
8
. Using
the binary coded behavioural data for each crime (the 166 variables), B-LINK
calculates the Jaccard’s coefficient for every pair in the dataset thereby
providing a quantitative measure of how similar the two crimes are in terms of
offender crime scene behaviour.
The approach of contrasting the behavioural similarity of linked and
unlinked crime pairs, whether using tests of difference or ROC analysis,
simultaneously tests both the assumption of behavioural consistency and the
assumption of behavioural distinctiveness. If offenders are consistent in their
crime scene behaviour, the level of behavioural similarity for linked pairs is
relatively high. If offenders commit their crimes in a distinctive manner, the
pairing of two crimes by two different, distinctive individuals means unlinked
crimes pairs share few behaviours and thus the level of behavioural similarity is
low. Therefore, to distinguish linked from unlinked crime pairs based on relative
8
Only unlinked crimes were paired that occurred within the same country since initial analyses
indicated that a significantly larger AUC was obtained when contrasting linked crime pairs with
unlinked crime pairs that included two crimes from different countries (AUC = .91) than when
contrasting them to unlinked pairs composed of crimes only from the same country (AUC =.86)
(D = .005, p<.001).
LINKING SERIAL SEX OFFENCES
17
behavioural similarity with a high degree of accuracy requires both assumptions
to be valid.
Three stages of analysis were conducted separately on the four
datasets. This allowed us to examine if behavioural similarity, distinctiveness
and discrimination accuracy varied as a function of whether apparent one-off
crimes and/or unsolved serial crimes were included in the sample under
analysis: (1) Mann-Whitney U tests assessed whether the Jaccard’s coefficients
for the linked crime pairs were significantly larger than those for the unlinked
crime pairs. Significance tests were accompanied by effect size calculations; (2)
Binary logistic regression using a leave-one-out classification method
9
(LOOCV;
Woodhams & Labuschagne, 2012a) with linkage status (linked or unlinked) as
the outcome variable and Jaccard’s coefficient as the predictor variable was
used to produce predicted probabilities that were entered into; (3) ROC
analyses. As outlined above, ROC curves give an indication of discrimination
accuracy via the AUC. The AUC is an effect size (Harris & Rice, 1995) and is
therefore independent of sample size (Sullivan & Feinn, 2012).
The findings produced using these four datasets were then compared. A
key comparison was between dataset 1 (which contained solved, unsolved,
serial and apparent one-off crimes) and dataset 4 (which contained just solved,
serial crimes). Dataset 1 more closely represents the data that might be used in
9
A LOOCV logistic regression includes a cross-validation step and involves removing a given
case from the dataset and developing a logistic regression model on the remaining cases. The
model is then applied to the extracted case to yield a predicted probability value. This process is
then repeated for each case in the dataset. Cross-validation such as this ensures that models
constructed will generalise to new data.
LINKING SERIAL SEX OFFENCES
18
practice when analysts are linking crimes, whereas dataset 4 is comparable to
the data used in most previous studies of the crime linkage principles, which is
characterised by the limitations outlined above.
While the proportion of linked crime pairs formed from series that were
unsolved but linked-by-DNA was much higher in this study (12%) compared to
in Slater et al. (2015; 3%), it was possible that their removal in datasets 3 and 4
might have little impact due to the size of the samples or be obscured by the
inclusion of the one-off crimes. Consequently, meaningful differences between
solved and unsolved crime series might be obscured. An additional analytic
approach was, therefore, developed whereby a subset of linked and unlinked
crime pairs were generated from the unsolved but linked-by-DNA crime series
and the three stages of analysis repeated. This allowed for comparison in
findings between crime pairs generated from two solved serial offences (n =
4,006 linked pairs and n = 1,267,648 unlinked pairs) and from two unsolved
serial offences (n = 563 linked pairs and n = 1,467 unlinked pairs). This was an
alternative way of examining whether the principles of consistency and
distinctiveness were supported when including unsolved crime data in samples.
It is also important to note that, although a large AUC value indicates
support for the principles underpinning crime linkage, it can still be associated
with a considerable number of decision-making errors, particularly when there is
an imbalance in the ratio of “positive” (linked) to “negative” (unlinked) cases,
which is certainly the case with these data (see Longadge, Dongre, & Malik,
LINKING SERIAL SEX OFFENCES
19
2013, for a review of the so-called “class imbalance problem”)
10
. This issue is
not unique to crime linkage and applies in other classification domains (e.g., risk
prediction, diagnosis of rare diseases). Therefore, a final step in the analysis
was to illustrate the number and type of errors made when adopting a particular
decision threshold (i.e., a specific level of similarity used to determine when two
crimes are similar and distinctive enough to warrant being linked). Based on
discussions with crime linkage practitioners, we selected the false alarm rate of
15% for these illustrations since, in practice, it is preferable to minimise the
number of false alarms
11
. With the false alarm rate fixed at 15%, the proportions
of hits, correct rejections and misses were calculated using the full dataset (i.e.,
solved series, unsolved series and one-off offences).
The ROC analysis was also repeated for each country individually using
the full dataset for each country. The compositions of these samples can be
seen in Table 1.
Results
Mann-Whitney U tests for international sample
The behavioural similarity of the linked crime pairs was significantly
larger than that of the unlinked crime pairs (p < .001) across all four datasets
10
It is important to note that the class imbalance problem arises from the methodology of
creating all possible (linked and unlinked) pairs, therefore it will impact on any statistical
technique used alongside this method.
11
The impact of choosing different decision thresholds is an entire research question in itself
and certainly something that should be subject to empirical study and cost-benefit analysis,
however this is beyond the scope of the current article.
LINKING SERIAL SEX OFFENCES
20
(see Table 3), thereby demonstrating comparable support for the principles of
crime linkage across datasets. The effect size r was approximated using the
formula from Pallant (2007) resulting in effect sizes ranging from .04 to .07.
ROC analysis for international sample
For the sake of brevity, only the ROC analyses are presented here, but a
summary of the binary logistic regressions using LOOCV can be obtained from
the first author upon request. Table 4 displays the AUC values and Figure 1 the
ROC curves. All AUCs represent an excellent level of predictive accuracy
(Hosmer & Lemeshow, 2000). Furthermore, the AUCs were similar across all
four datasets. The inclusion of one-off offences in the sample, reduced
discrimination accuracy (as measured by the AUC) significantly, D = 1.99; p <
.05, although the change in the AUC was small (from .86 to .85). The change in
discrimination accuracy (AUC of .86 to .85) when both unsolved and one-off
offences were added to the sample (dataset 1) compared to when they were
absent (dataset 4) approached significance, D = 1.93, p = .05.
Separate analyses for solved vs. unsolved serial crime pairs for
international sample
When sampling only solved series, the AUC was .86 (p < .001, SE =
.003, 95% CI = .86 - .87, as per Table 4) whereas when sampling only unsolved
series, the AUC was .79 (p < .001, SE = .011, 95% CI = .77 - .81) representing
an adequate level of discrimination accuracy (Hosmer & Lemeshow, 2000). The
difference between these two values was statistically significant (D = 5.47, p <
.000001).
The number and types of correct/incorrect decisions at a 15% false alarm
rate threshold for international sample
LINKING SERIAL SEX OFFENCES
21
Table 5 summarises the proportion of hits, misses and correct rejections
when the threshold of a 15% false alarm rate was applied.
ROC analysis for each country separately
A ROC analysis was also run for each country’s data separately. The
results can be seen in Table 6.
Discussion
There is a growing trend of international courts viewing crime linkage
analysis as a form of behavioural science and thus qualifying for assessment
against legal standards governing the admission of scientific evidence
(Pakkanen et al., 2015). This, alongside its use to inform police decision-
making, makes the reliability of its underlying principles an important subject for
empirical research.
We tested the reliability of its underlying principles simultaneously using
ROC analysis to assess the accuracy with which linked crime pairs could be
distinguished from unlinked crime pairs based on quantitative measures of
behavioural similarity. The AUCs obtained (.79 - .86) are similar in size to those
seen in past, smaller scale studies (e.g., Slater et al., 2015; Winter et al., 2013;
Woodhams & Labuschagne, 2012a) and represent an adequate (.79) to
excellent (.80 and above) level of discrimination accuracy. Even the AUC
obtained when sampling only from unsolved but linked-by-DNA series (.79) was
larger than AUCs reported in previous studies (e.g., Bennell et al., 2009).
These previous studies demonstrated little impact of including either one-
off crimes, or unsolved but linked-by-DNA series, on the AUC values obtained.
However, their small samples sizes and the fact that none of these studies
LINKING SERIAL SEX OFFENCES
22
included confirmed series alongside one-off and unsolved crime series, meant
less confidence could be placed in their findings. Through the cooperation of
police and academics from five countries, a much larger sample was collated
allowing for a more rigorous and ecologically valid test of the crime linkage
principles. Our findings mirror those of previous studies; the inclusion of one-off
crimes and unsolved crime series had little impact on the AUCs when using the
full sample.
These findings are of global significance bearing in mind the use of crime
linkage to inform police decision-making around the world regarding the most
serious types of crimes (Bennell et al., 2014; Wilson & Bruer, n.d.). Our results
also provide the sorts of research findings regarding the principles of crime
linkage which have been sought by the courts in the past, and which will likely
be sought in the future, when deciding on the admissibility of crime linkage
analysis as a form of expert evidence.
There are, however, important caveats to these generally positive
findings. Our final phase of analysis considered the scale and type of decision
errors that would be made if a decision threshold was utilised that capped the
false alarm rate at 15%. This illustrated that, despite our logistic regression
models achieving high AUCs, a considerable number of errors in linkage
predictions can occur when using these statistical models. For example, due to
the relative base rates of linked versus unlinked pairs in our dataset, a 15%
false alarm rate corresponds with more than 500,000 false alarm predictions
being made. The number of misses is much smaller at just over 1,000. Such
errors arise because within the dataset there are linked crime pairs which are
characterised by inconsistency and indistinctiveness, and unlinked crime pairs
LINKING SERIAL SEX OFFENCES
23
which are highly similar with respect to crime scene behaviour (see the Min and
Max values in Table 3). Therefore, the principles of crime linkage do not hold for
all cases.
Bearing in mind the police resources that might be put into further
analytical and investigative work with this number of false alarms, it is likely that
a more stringent false alarm rate would be needed in practice (this would, of
course, result in a reduced hit rate)
12
. While the paper does not provide a
definitive answer as to the error rate associated with crime linkage in practice, it
still aids the courts and researchers/practitioners by allowing them to appreciate
the volume of errors that can occur even when specific linking strategies are
associated with high AUCs. An important next step would be to establish the
base rates of linked and unlinked pairs in databases such as ViCLAS to
estimate the extent of the class imbalance problem in practice
13
. This,
combined with a full cost-benefit analysis that considers the human and
financial savings/costs associated with the four decision outcomes of the
linkage task, would help inform future decisions regarding the most appropriate
decision threshold to use.
12
However, it should be noted that such large figures would only apply if you are comparing all
crimes in a given database at the same time. In practice, certain filters to reduce the number of
cases retrieved would be applied in addition (e.g., offender ethnicity, time, place, geography).
For example, a case linked by DNA but where the specific DNA profile is not in the national
database, will lead to the decision to exclude all cases with a known offender as a first filter
(Davies et al., 2018).
13
The volume of unsolved crimes in such databases would make it impossible to know the real
base rates of linked and unlinked pairs.
LINKING SERIAL SEX OFFENCES
24
In addition, we found a significant difference in AUC when contrasting
linked and unlinked pairs using a sample generated from solved series vs.
unsolved but linked-by-DNA series. This finding is similar to that reported by
Woodhams and Labuschagne (2012a) with a much smaller sample. They
observed that linked crime pairs first identified as a series on the basis of DNA
were characterised by less behavioural similarity (a smaller Jaccard’s
coefficient) than those first identified on the basis of similar modus operandi.
The actual composition of crime types in databases used for crime
linkage, such as ViCLAS, is not currently known (e.g., ratios of serial, one-off,
solved and unsolved). However, our findings highlight the importance of such
studies since the trends seen in our data of decreasing discrimination accuracy
with the addition of one-off offences and with unsolved but linked-by-DNA series
could be more pronounced if databases contain many more offences of these
types. One study has assessed how varying proportions might affect the
discrimination accuracy yielded from statistical analyses; Haginoya (2016)
found no effect of varying the ratio of one-off offences to series on the ability to
link crimes, however this analysis was limited to the linking features of
geographical and temporal proximity. The optimum approach would be to
conduct a study on the entire police database in each country. Where this is not
possible, it is important in the future to (a) conduct a study where the proportion
of serial to one-off offences is systematically varied to determine how this
impacts on discrimination accuracy using offender crime scene behaviours and
to replicate Haginoya; and (b) to determine what the ratio is on existing
databases so that researchers can evaluate how much the proportions in their
datasets reflect reality. This ratio would only be an estimate as it cannot be
LINKING SERIAL SEX OFFENCES
25
known for definite that a crime is truly a one-off offence or part of an undetected
series. However, an estimate with these limitations in mind would still help
inform the sampling frames of future studies where a full database cannot be
used for analysis.
Related to this point, our study is a test of the principles of crime linkage
and is not a test of the practice of crime linkage. This does not invalidate our
findings because we set out to answer legal questions facing international
courts surrounding the admissibility of crime linkage evidence and to inform an
evidence-based policing approach to crime linkage (Rainbow, 2015). However,
the accuracy of practitioner decision-making with and without the aid of
statistical models to support their decision-making is a topic in need of study.
Finally, it is also important to recognise that the sample of crimes utilised
in this study was dominated by UK crimes as the UK analytical unit, SCAS,
contributed the largest number of cases. It was not possible to repeat all
statistical manipulations conducted with the multi-country dataset with the
dataset from each country individually because the numbers of solved vs.
unsolved series, or series vs. one-off offences, were insufficient. However, one
overall ROC analysis was conducted on the full dataset available per country
using the steps described above. The AUCs per country (.76 to .85) were all
within the range observed for previous studies of the crime linkage principles
with serial sexual offences (i.e., .75 to .89; Bennell et al., 2009; Slater et al.,
2014; Winter et al., 2013; Woodhams & Labuschagne, 2012a) for all countries
LINKING SERIAL SEX OFFENCES
26
with the exception of Finland
14
. The variation in discrimination accuracy across
the countries is interesting but it is difficult to draw any firm conclusions from
this. It is possible that they result from differences in the relative compositions of
the samples (e.g., solved vs. unsolved or serial vs. one-off). There may be
optimal sets of modus operandi behaviours per country and identification of
these may improve discrimination accuracy. Authors have previously
commented that behaviours may vary in their relative distinctiveness from
country to country (Woodhams & Labuschagne, 2012b). Alternatively, the
differences observed may be due to the series sampled from each country and
with a different set of series the findings might vary. This underscores the
importance of future research studies aiming for a large, realistic sample of
crimes when investigating crime linkage within a country. As noted above,
ideally, where they exist and where permission is given, studies should utilise
the entire dataset of crimes on databases that assist with crime linkage in that
country (e.g., ViCLAS).
Conclusion
The paper reported a test of the reliability of the principles underlying
crime linkage with the largest and most ecologically valid sample of sexual
offences to date, made possible by international police-academic cooperation. A
sample of several thousand crimes, which included convicted series, unsolved
14
The AUC of .85 obtained with the multi-country sample with dataset 1 was unchanged with
the removal of the Finland subset of cases from the overall sample. The smaller AUC for
Finland may reflect the reduction in behavioural information available for linkage predictions
with 42 vs. 166 behaviours.
LINKING SERIAL SEX OFFENCES
27
but linked by DNA series, and convicted one-off sexual offences, was collated
and subject to LOOCV logistic regression and ROC analysis. Support for the
reliability of the underlying principles of crime linkage analysis was found.
However, our calculations indicate that despite the large AUC values achieved
by the regression models, there is still the potential for a large number of
decision-making errors to be made due to the low base rate of same-offender
crime pairs in the samples.
LINKING SERIAL SEX OFFENCES
28
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LINKING SERIAL SEX OFFENCES
33
Table 1. Characteristics of the Offences contained within the Sample per Country
Country
Number of
Series/Cases
Number of Offenders
Timeframe
Length of
Series
Number of
Victims, Gender
and Age (in
Years) Where
Known
Gender and
Age (in Years)
of Offenders
Where Known
South Africa
35 series
245 serial cases
Serial = 36c
1998-2012
2-32
N = 356
M = 45, F = 285
Age range = 0-68
M = 85
Age range =
17-55
Finland
16 series
43 serial cases
80 one offs
Serial = 17a
One-off = 85a
1983-2001
2-8
N= 124a
F = 43b
Age range = 15-62
M = 16b
Age range =
16-49b
United Kingdom
534 series
1,579 serial
cases
1,000 one offs
Serial = 1,612
One-off = 1,000
1966-2013
2-20
N = 2643
M = 149, F = 2486
Age range = 1-94
M = 1549, F =
6
Age range =
12-77
The
Netherlands
38 series
123 serial cases
50 one offs
Serial = 39a
One-off = 52a
1989-2014
2-10
N = 178
M = 5, F = 172
Age range = 4-96
M = 89, F = 0
Age range =
13-55
Belgium
45 series
183 serial cases
61 one offs
47a serial offenders
80 one off offenders
1985-2014
2-12
N = 259
M = 11, F = 247
Age range = 3-84
M = 124, F = 1
Age range =
15-69
Notes: M = Male, F = Female. Age range for offenders includes the offender’s age at each offence, where known, and therefore is based on the number of
crimes rather than the number of offenders.
aThe data provided indicated where there were multiple offenders (or victims) per incident but not the actual number. These will therefore be the minimum
number of offenders (or victims) in the subsample.
bThe data for the one-off offences were not available therefore the figures here are solely for the serial sample.
cThis is the figure for the offenders confirmed to be serial offenders (i.e., convicted or DNA-linked to two or more offences). There were additional, unverified
suspects in some offences who had not been identified. This will therefore be the minimum number of offenders in the sample.
LINKING SERIAL SEX OFFENCES
34
Table 2. The Composition of the Four Datasets Subject to Analysis
Dataset
Number
1
2
3
4
Types of crime
included
Solved serial
crimes,
unsolved
serial crimes,
and solved
apparent one-
off crimes
Solved and
unsolved
serial crimes
only
(apparent
one-off
offences
removed)
Solved serial
crimes and
solved
apparent one-
off crimes
(unsolved
serial crimes
removed)
Solved serial
crimes only
(unsolved
serial and
apparent one-
off crimes
removed)
Number of
crimes
3,364
2,173
3,272
2,081
Number of
linked/unlinked
pairs
4,569 linked
crime pairs
and
3,401,679
unlinked pairs
4,569 linked
pairs and
1,296,211
unlinked pairs
4,006 linked
pairs and
3,363,884
unlinked pairs
4,006 linked
pairs and
1,267,648
unlinked pairs
LINKING SERIAL SEX OFFENCES
35
Table 3. Statistical Comparisons of Linked and Unlinked Crime Pairs in terms of
Behavioural Similarity
Dataset
Linked Crime
Pairs
Median
Jaccard
(Min. – Max.)
Unlinked
Crime Pairs
Median
Jaccard
(Min. – Max.)
Test Statistics
All Data Included
.44
(.00 – 1.00)
.24
(.00 – 1.00)
Z = 82.36, p
<.001, r = .04
Apparent One-Off Crimes
Removed
.44
(.00 – 1.00)
.23
(.00 – 1.00)
Z = 85.14, p
<.001, r = .07
Unsolved Crimes Removed
.44
(.00 – 1.00)
.24
(.00 – 1.00)
Z = 76.66, p
<.001, r = .04
Both Apparent One-Off and
Unsolved Crimes Removed
.44
(.00 – 1.00)
.23
(.00 – 1.00)
Z = 79.51, p
<.001, r = .07
LINKING SERIAL SEX OFFENCES
36
Table 4. Receiver Operating Characteristic Analysis Testing Discrimination Accuracy
across the Four Datasets
Dataset
Area Under
the Curve (SE)
95% Confidence
Interval
All Data Included
.85 (.003)*
.84 - .86
Apparent One-Off Crimes Removed (Series only)
.86 (.003)*
.86 - .87
Unsolved Crimes Removed (Solved only)
.85 (.003)*
.84 - .85
Both Apparent One-Off and Unsolved Crimes
Removed (Solved Series Only)
.86 (.003)*
.86 - .87
*p <.001
LINKING SERIAL SEX OFFENCES
37
Table 5. Number of Hits, Misses, Correct Rejections and False Alarms Using a Decision Threshold of 15% False Alarms
Predicted Linked
Predicted Unlinked
Linked in Reality
71% Hit Rate
(3,247 linked crime pairs were correctly identified)
29% Miss Rate
(1,322 linked crime pairs were incorrectly classified
as unlinked)
Unlinked in Reality
15% False Alarm Rate
(532,170 unlinked crime pairs were incorrectly
classified as linked)
85% Correct Rejection Rate
(2,869,509 unlinked crime pairs were correctly
identified)
LINKING SERIAL SEX OFFENCES
38
Table 6. Receiver Operating Characteristic Analysis Testing Discrimination Accuracy
across the Five Different Countries
Country
Area Under the
Curve (SE)
95% Confidence
Interval
UK1
.83 (.005)*
.82 - .84
Belgium2
.85 (.012)*
.82 - .87
Finland3
.56 (.039)
.49 - .64
Netherlands4
.76 (.019)*
.73 - .80
South Africa5
.79 (.007)*
.78 - .80
1 serial, one-off, solved and unsolved crimes (Linked pairs n = 2,537, Unlinked pairs n = 3,321,794)
2 serial, one-off, solved and unsolved crimes (Linked pairs n = 400, Unlinked pairs n = 29,246)
3 serial, one-off, solved and unsolved crimes (Linked pairs n = 55, Unlinked pairs n = 7,448)
4 serial, one-off, solved and unsolved crimes (Linked pairs n = 189, Unlinked pairs n = 14,689)
5 serial, solved and unsolved crimes (Linked pairs n = 1,388, Unlinked pairs n = 28,502)
*p<.001
LINKING SERIAL SEX OFFENCES
39
(1)
(2)
(3)
(4)
Figure 1: The ROC curves which correspond with the AUCs in Table 4 for (1) All
Data Included; (2) Apparent One-Off Crimes Removed; (3) Unsolved Crimes
Removed; and (4) Both Apparent One-Off and Unsolved Crimes Removed.
