Change in Juvenile Offending Versatility Predicted by Individual, Familial, and Environmental Risks
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DOI: 10.11576/ijcv-4559
IJCV: Vol. 15/2021
Change in Juvenile Offending Versatility Predicted by
Individual, Familial, and Environmental Risks
Susanne Wallner
Institute of Psychology, Friedrich-Alexander University Erlangen-Nuremberg, Germany
susanne.wallner@fau.de
Hoben Thomas
Department of Psychology, Pennsylvania State University, USA
hxt@psu.edu
Mark Stemmler
Institute of Psychology, Friedrich-Alexander University Erlangen-Nuremberg, Germany
mark.stemmler@fau.de
Vol. 15/2021
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Suggested Citation: APA: Wallner, S., Thomas, H., Stemmler, M. (2021). Change in Juvenile Offending Ver-
satility Predicted by Individual, Familial, and Environmental Risks. International Jour-
nal of Conflict and Violence, 15, 1-16. doi:10.11576/ijcv-4559
Harvard: Wallner, Susanne, Thomas, Hoben, Stemmler, Mark. 2021. Change in Juvenile
Offending Versatility Predicted by Individual, Familial, and Environmental Risks. Inter-
national Journal of Conflict and Violence 15: 1-16. doi: 10.11576/ijcv-4559
This work is licensed under the Creative Commons Attribution—NoDerivatives License.
ISSN: 1864–1385IJCV: Vol. 15/2021
Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 1
vironmental Risks
Change in Juvenile Offending Versatility Predicted by
Individual, Familial, and Environmental Risks
Susanne Wallner
Institute of Psychology, Friedrich-Alexander University Erlangen-Nuremberg, Germany
Hoben Thomas
Department of Psychology, Pennsylvania State University, USA
Mark Stemmler
Institute of Psychology, Friedrich-Alexander University Erlangen-Nuremberg, Germany
Developmental and life-course criminology elucidate the developmental course and change of antisociality over
time, considering that longitudinal trajectories differ. Specific relations between risks and different antisociality
outcomes are emphasized. We assume that adolescents have different longitudinal trajectories considering the
change of offending over time and that risks contribute variably to offending pathways. The current study is
based on a German research project in which adolescents (N = 577) were interviewed in two German cities.
Based on self-reported crime data, we utilized the slope values of offending versatility (OV) over time as out -
come values in regression mixture models capturing the trends for participants over age and exhibiting two com -
ponents of offending adolescents. We explored the contribution of different risks to OV, defining specific risk
patterns: Acceptance of violence and peer delinquency have significant negative effects on the emergence of OV
within the group of adolescents with decreasing OV. Acceptance of violence has a significant negative effect, and
corporal punishment has a significant positive effect on the emergence of OV within the group of adolescents
with increasing or rather stable OV. The results underline the relevance of the violence-related risk factor cor-
poral punishment for the emergence of OV within the last-mentioned group.
Keywords: juvenile delinquency, developmental risks, longitudinal research, developmental criminology, regres-
sion mixture models
Acknowledgement: This paper includes results from the study “Chances and Risks in the Life Course” (CURL;
“The Emergence and Development of Deviant and Delinquent Behavior over the Life Course and its Significance
for Processes of Social Inequality”; for example, Reinecke et al. 2013; Reinecke, Stemmler, and Wittenberg 2016;
Wallner et al. 2019). The study (research project A2) was part of the Collaborative Research Center (SFB) 882
“From Heterogeneities to Inequalities”, which was established at Bielefeld University, Germany, in 2011 and
which was funded by the German Research Foundation (DFG) until 2016. The authors are grateful to Jost Rei -
necke, Maria Arnis, Nihad El-Kayed, Eva Link, Julia Meinert, Andreas Pöge, Debbie Schepers, Burcu Uysal,
Maren Weiss, and Jochen Wittenberg for their valuable work on the project. Additionally, the authors gratefully
acknowledge the cooperation of the schools and students participating in the CURL study
Developmental and life-course criminology considers course persistent vs. adolescence limited antisociality
the change of antisociality over time relating to the (Moffitt 1993, 2006) has been developed to integrate
developmental course (for example, see Farrington, Pi- sociological and psycho-biological theories and to ex-
quero, and Jennings 2013; Sampson and Laub 2016). plain the age-crime curve: “The taxonomy achieved its
Accordingly, Moffitt’s well-known taxonomy of life- original goal, to account for the age-crime curve. Its
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 2
vironmental Risks
dual theories of LCP [life-course persistent] and AL According to Jennings and Reingle (2012), trajectory
[adolescence limited] development met their original research should also focus on the identification of risk
goal of drawing from biological, psychological and so- and protective factors for differentiating developmen-
ciological theories to explain antisocial behaviour” tal trajectories, raising, for example, the following
(Moffitt 2018, 184). The age-crime curve represents question: “[D]o the same risk and protective factors
“one of the brute facts of criminology” (Hirschi and that distinguish non-offenders from life-course persis-
Gottfredson 1983, p. 552) displaying the relations be- tent offenders also distinguish adolescent-limited of-
tween crime and age and the change of delinquent fenders from life-course persistent offenders, or does
behavior over time (concerning the lifetime of individ- this same set of risk and protective factors have a dif-
uals). According to this, the prevalence of criminal be- ferential effect across trajectory groups?” (486). Over-
havior clearly increases from late childhood to adoles- all, empirical studies in developmental and life-course
cence and finally decreases in early adulthood (see criminology show the importance of numerous risk
Moffitt 1993; Farrington, Piquero, and Jennings 2013). factors – such as individual characteristics, familial
Incidentally, the peak occurs earlier in self-report of- characteristics, environmental characteristics – in the
fending data (including dark figures) than in regis- explanation of antisocial behavior in general (for ex-
tered data (official records/reported crime in official ample, see Corrado 2002, 2012; Craig et al. 2017; Far-
crime statistics; for example, see Boers and Reinecke rington, Ttofi, and Piquero 2016; Stemmler, Wallner,
2007; Loeber et al. 2015). The age-crime curve also and Link 2018; Thornberry et al. 2012; Wallner et al.
shows that many children and adolescents remain 2018). Related bio-psycho-social risk models corre-
trouble-free. Generally, the relations between age and spond with the life-course-persistent path proposed
crime in youth and early adulthood can be explained by Moffitt (see above). The bio-psycho-social risk
by co-occurring sociological, psychological, and bio- model of Lösel and Bender (2003) focuses on the rela-
logical changes (for example, see Sweeten, Piquero, tions between different risks, for example, poor child-
and Steinberg 2013). Longitudinal trajectories for anti- rearing and low self-control in childhood, deviant
social outcomes are quite different, especially in child- peers and beliefs in adolescence, and serious and vio-
hood and adolescence. Empirical criminological litera- lent criminality in early adulthood. Of course, other
ture reveals no consistent number of groups of antiso- risks are also considered and many other risk combi-
ciality. For example, according to Broidy et al. (2003), nations are possible. Concentrating on risk/needs
three to four different physical aggression trajectories management issues, Corrado (2002, 2012) summarizes
in childhood were most prevalent. Similarly, Jennings the risks for serious and violent antisocial behavior,
and Reingle (2012) found that studies examining vio- considering environmental, individual, family, inter-
lence, aggression, and delinquency trajectories mostly vention, and externalizing behavior contents and risk
reported three to four trajectory groups, where the domains, respectively (see also Stemmler, Wallner, and
number of groups generally ranged from two to seven. Link 2018; Wallner et al. 2018). Specifically, concerning
The number and shape of trajectory groups seem to different types or trajectories of delinquent behavior,
be quite variable (for example, depending on the sam- the relevance of risks varies, defining specific risk
ple composition, length of follow-up, and geographi- patterns (in other words, risks are different for differ-
cal location; ibid.). The studies, however, are in accor- ent developmental pathways): individual and family
dance with Moffitt’s taxonomy and comprise a risks (for example, concerning personality, child-rear-
chronic or life-course persistent group (chronics), a ing practices) play a particularly important role in life-
group of escalators or adolescent-limited offenders course persistent antisociality, whereas predictors of
(desistors), and a group without problem behavior adolescence limited antisociality (for example, prob-
(ibid.). The vast majority of empirical studies examin- lematic peer contacts, peer delinquency) are mainly
ing longitudinal data on antisocial trajectories apply related to the contemporary maturity gap in adoles-
General Growth Mixture Models (GGMM; for exam- cence (for example, Moffitt 1993; see also Odgers et al.
ple, see Nagin 1999; Stemmler and Lösel 2015). 2008). Further, life-course persistent antisociality
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 3
vironmental Risks
seems to be associated with versatile and more seri- measure. Generally, antisociality captures deviant and
ous offending, whereas adolescence limited antisocial- delinquent behaviors (for example, Wittenberg and
ity is associated with less serious, more youth-typical Wallner 2016). However, studies suggest that diverse
offending (for example, see Moffitt 1993 and Odgers et antisocial trajectories are mostly defined by different
al. 2008; see also Elliott et al. 2017). Concerning antiso- risks; correspondingly, “[r]esearch has begun to
cial conduct problems, Odgers et al. (2008) approve demonstrate that there are a number of correlates of
the use of variety scores, which are “highly correlated offending … and other adverse outcomes … that can
with frequency scores … and [that] are commonly be considered alongside violence, aggression, and
used in population-based studies” (ibid., 676). Antiso- delinquency as manifesting a similar developmental
cial behavior in adolescence is often influenced by ad- process that can largely be explained by a shared sim-
verse peer contacts (for example, see Battin et al. 1998; ilarity in risk and protective factors” (Jennings and
Lösel and Bender 2003). A high rate of peer delin- Reingle 2012, 486). More recently, recapitulating previ-
quency (offending in groups) and a high rate of co-of- ous evidence, Gutman, Joshi, and Schoon (2019)
fending are typical characteristics of juvenile delin- stated that “different influences and processes may
quency (Wallner and Weiss 2019). Côté et al. (2006) explain diverse pathways of conduct problems” (ibid.,
examined the development of physical aggression in p. 181).
childhood and identified three different developmen- In the research presented here, we focus on the rela-
tal trajectories (low desisting, moderate desisting, tions between different risk variables and antisocial
high stable), and found that, for example, (1) specific outcomes in adolescence over time. Generally, refer-
risks distinguished between children with physical ag- ring to the research described above, the age-crime
gression trajectories and other children, and (2) hos- curve illustrates that the prevalence of crime increases
tile/ineffective parenting was predictively related to from late childhood to adolescence and decreases in
the high level group trajectory. Consistent with previ- early adulthood. In the current work, we focus on the
ous results, many studies defined specific factors pre- critical developmental stage of adolescence. As al-
dicting several distinct trajectories of different antiso- ready outlined, the associations between age and
cial outcomes (for example, see Corovic et al. 2017; crime in adolescence and early adulthood can com-
Gutman, Joshi, and Schoon 2019; Lacourse, Dupéré, monly be explained by co-occurring sociological, psy-
and Loeber 2008; Odgers et al. 2008; Seddig and Rei- chological, and biological changes (see above). The
necke 2017, see also Reinecke and Seddig 2011). For present work is primarily rooted in risk-factor re-
example, Lacourse, Dupéré, and Loeber (2008) defined search. Specifically referring to the empirical findings
specific factors predicting distinct trajectories of anti- outlined above, the following core hypotheses were
social outcomes (violence and theft) in a sample of derived. First, adolescents have different longitudinal
young men. Seddig and Reinecke (2017) explored self- trajectories considering the change in delinquent be-
reported delinquency trajectories, presented a solu- havior over time (in other words, adolescents’ trends
tion with seven classes, and explained membership in of offending versatility over age are varying in the
a special class of offenders utilizing patterns of spe- course of adolescence). Prior trajectory research com-
cific variables (for example, peer group, attitudes; see monly relied on GGMM (see above). In the present
also Reinecke and Seddig 2011). Corovic and col- study (on the basis of our longitudinal crime data),
leagues (2017) recapitulated various risk factors in however, we utilize the slope values of offending ver-
childhood and adolescence and adulthood adjustment satility (see methods section for a definition) as out-
outcomes differentiating between specific pathways come values in a mixture of regression routine (for ex-
of crime. However, these studies differ concerning the ample, see Benaglia et al. 2009) capturing the trends
outcome measure, specific sample characteristics (for for adolescents over time and, therefore, applying a
example, age), the number of antisocial pathways method which is not common in current (criminologi-
found and other issues. For example, different facets cal) trajectory research. Second, individual, familial,
of antisocial behavior are considered as the outcome and environmental risks in adolescence have distinct
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 4
vironmental Risks
influences on specific delinquent behavior (different ables the examination of participants’ development in
risks contribute variably to offending versatility path- childhood and adolescence. One important aim of the
ways defining specific risk patterns). Therefore, we current study is to investigate the relations among de-
predict different trajectories of offending versatility viant and delinquent behavior and various meaningful
(the different slope values of offending versatility; see precursors longitudinally. The project data is based on
methods section for a definition) based on different self-reports of male and female students who com-
risks for antisociality, contributing more specific and pleted several questionnaires. Participating students
detailed analyses on the prediction of divergent devel- were interviewed once a year as part of school-based
opmental trajectories and, thus, estimating the rela- and postal surveys (Weiss and Wallner 2019).
tions between different predictor effects and various
offending versatility trajectories (see results section). 1.2 Sample
Specifically, we assume that the developmental risks – Participants were surveyed in the German cities of
acceptance of violence, impulsivity, peer delinquency, Nuremberg and Dortmund with three annual follow-
and corporal punishment – are differently associated up assessments since 2012, providing a large sample.
with distinct pathways of offending versatility. This The Nuremberg sample comprises only students from
research therefore focuses on violence-related risks lower-track schools, whereas the Dortmund sample is
(corporal punishment, acceptance of violence; see composed of a broader range of school types. Impor-
methods section for justification). It should also be tantly, we use the longitudinal sample (three-wave
noted that several violent offenses are considered for panel) of male and female students of the older cohort
the outcome offending versatility (see also methods (9th to 11th grade); the sample comprises only stu-
section for further details). Again, in a nutshell, this dents participating in our study at the first, second,
work differs from prior work in trajectory research in and third assessment points (t1, t2, t3; N = 577 adoles-
that it explores the application of a longitudinal cents: n = 350 female and n = 227 male). The mean age
method for identifying different developmental path- of the ninth-graders was about 15 years at t1. At t1,
ways that is unusual in this context and applies this 41.9 percent (n = 242) of the students attended a
method to validate these pathways, using juvenile lower-track school. Overall, 53.6 percent (n = 309) of
risks relating to diverse developmental domains, the sample have a migration background (t1). In the
hence, far exceeding the information provided by current work, we apply to the broad definition of “mi-
mere description. gration background“ used by the Federal Statistical
Office (Destatis, Germany; Statistisches Bundesamt
1 Methods 2012): Accordingly, those persons have a migration
1.1 Research Project background who immigrated to Germany after 1949
In line with the research project “Chances and Risks as well as all persons born in Germany without Ger-
in the Life Course” (CURL; research project A2 “The man citizenship and all persons born in Germany with
Emergence and Development of Deviant and Delin- German citizenship with at least one parent who is an
quent Behavior over the Life Course and its Signifi- immigrant or born in Germany without a German
cance for Processes of Social Inequality”; e.g., Rei- passport. Generally, the definitions of migration back-
necke et al., 2013; Reinecke, Stemmler, and Wittenberg ground differ. In any case, regarding the heterogeneity
2016; Wallner et al. 2019) the development of deviant of the present sample, limitations regarding the inter-
and delinquent behavior is studied. This project is pretability of the results have to be considered (see
part of the Collaborative Research Center (“Sonder- discussion section). For further details of the sample
forschungsbereich”, SFB) “From Heterogeneities to In- see Weiss and Wallner (2019). The mean t1 offending
equalities” (SFB 882), which was established at Biele- versatility score of the remaining three-wave panel (M
feld University, Germany, in 2011 and was funded by = 1.09, SD = 2.21) was only marginally lower than the
the German Research Foundation (DFG) until 2016. mean t1 offending versatility score for the whole sam-
The study uses a cohort-sequential design that en- ple (M = 1.27, SD = 2.38, N = 1417), providing some in-
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vironmental Risks
formation on dropout issues. See Weiss and Link cording to Arnis (2015), Cronbach’s alpha was satis-
(2019) for further information on panel mortality in factory (α = .75; 9th grade).
the longitudinal study. Acceptance of violence. We also assessed acceptance
of violence using a scale from the CrimoC study
1.3 Measures (Boers and Reinecke 2007, see also Boers and Rei-
The data basis of the present study is derived from necke 2019 for further details on the CrimoC study;
the three-wave panel of the older cohort. First, several see Dünkel and Geng 2003). According to Dünkel and
risk variables (i.e., individual, familial, and environ- Geng (2003), self-reported violent behavior is substan-
mental risks; independent variables, predictors, t1), tially positively related to acceptance of violence in
were used, also including violence-related risks. To adolescence. The measure comprises nine items in a
justify the selection of risk variables, we refer to risk- five-point rating format ranging from does not apply
factor research described above, particularly to our at all through does definitely apply (for example,
own previous work on these topics (for example, “When another person attacks me physically, then I
Stemmler, Wallner, and Link 2018; Wallner et al. 2018; fight back”). High scale values represent high levels of
Wallner and Stemmler 2019). The selection applied acceptance of violence. Further information is pro-
were relevance concerning serious and violent antiso- vided by Meinert, Kaiser, and Guzy (2014). The corre-
cial behavior (for example, see Corrado 2002, 2012), sponding alpha coefficient was satisfactory at α = .76
age-appropriateness, broad content (to include differ- (9th grade; Arnis 2015).
ent risk domains, ibid.), and availability within our re- Corporal punishment. To operationalize parenting
search project. Second, delinquency (offending versa- practices including parenting deficits we utilized a
tility; dark figures, outcome measure, t1 – t3; see sec- scale from the modified version of the Alabama Par-
tion “Offending versatility” below for justification), enting Questionnaire (APQ; see Essau, Sasagawa, and
was utilized, also comprising several violent offences. Frick 2006; Shelton, Frick, and Wootton 1996). In our
Further information on relevant measures, items, and research project we utilized a modified self-report ver-
scales can be obtained from Arnis (2015) and Meinert, sion for children and adolescents (see Meinert, Kaiser,
Kaiser, and Guzy (2014). Overall, we also utilized sev- and Guzy 2014) which is based on a German parent
eral (partly modified) items and scales from the version of Lösel et al. (2003). We used four items from
CrimoC study (Boers and Reinecke 2007, see also the subscale Corporal Punishment. The items are an-
Boers and Reinecke 2019). Additional information on swered in a five-point rating format ranging from
that study, particularly information related to trajec- never through always. One example: “My parents hit
tory research, can be obtained from, for example, Rei- me.” High scale values indicate high levels of corporal
necke and Seddig (2011) and Seddig and Reinecke punishment by parents. The alpha coefficient was ex-
(2017). cellent (α = .89; 9th grade; Arnis 2015).
Impulsivity. Self-ratings concerning low self-control Peer delinquency. We assessed peer delinquency (i.e.,
were derived from the German version of the Gras- precisely, the deviant and delinquent behavior of
mick Scale (Grasmick et al. 1993; German version: Ei- peers) following the CrimoC study (for example,
fler and Seipel 2001). At t1, the scale consisted of ten Boers and Reinecke 2007, see also Boers and Reinecke
items. Overall, items from the five-point subscales 2019 for more information on the CrimoC study) and
Risk Behavior, Impulsivity, Temper, and Simple Tasks PADS+ (Peterborough Adolescent and Young Adult
were utilized ranging from strongly disagree through Development Study; for example, Wikström et al.
strongly agree (see Meinert, Kaiser, and Guzy 2014). 2012). According to the PADS+ scale Peer Crime In-
One example: “When I am really angry, other people volvement and specific CrimoC delinquency items, our
better stay away from me”. High scale values indicate measure incorporates different deviant (drug use) and
low levels of self-control and high levels of impulsiv- delinquent acts (for example, theft, break-in), respec-
ity. In the context of the present work, we use the tively, committed by peers (see Meinert, Kaiser, and
short label “impulsivity” for this aggregate scale. Ac- Guzy 2014). Participating students were asked how
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often friends committed particular acts, for example, criminal behavior – in contrast to, for example, the
“Does it often happen that some of your friends press frequency of crime (for example, see Boman, Mowen,
somebody for money?”. Seven items capture the fre- and Higgins 2019) or crime specialization (for exam-
quencies in a five-point rating format ranging from ple, see Lussier et al. 2017; Tzoumakis et al. 2012).
never through very often. High scale values represent Crime frequencies are widely utilized. However,
high levels of peer delinquency. The alpha coefficient Bendixen, Endresen, and Olweus (2003, 135) suggest
was quite acceptable (i.e., α = .85; 9th grade; Arnis that “using a scale including the (raw) frequencies of
2015). antisocial acts committed instead of a variety scale
Offending versatility. Delinquency items were based would result in reduced internal consistency, lower
on a modified version of the Self-Report on Delinquent stability over time, smaller group differences and
(and Deviant) Behavior (“Delinquenzbelastungsskala”, weaker associations with conceptually related vari-
DBS; Lösel 1975; available in Weiss, Runkel, and Lösel ables. Similarly, in regression analyses the (raw) fre-
2012; for example, theft) and on the Delinquency Scale quency scale contributed little to the explained vari-
(“Delinquenzskala”; CrimoC; for example, Boers and ance in conceptually related variables over and be-
Reinecke 2007; for example, scratching; see also Boers yond that contributed by the variety scale”. Therefore,
and Reinecke 2019 for further details on the CrimoC we utilized a variety index which captures the diver-
study). The adolescents’ self-reports on criminal be- sity of offending at each assessment (t1 – t3) and – in
havior include dark figures referring to unrecorded some aspects – reveals the intensity of offending over
crime and providing other information than registered time. Thus, offending versatility represents the num-
data. As mentioned above (see introduction), the peak ber of different delinquent acts committed by an indi-
occurs earlier in self-report data on offending (includ- vidual in the last year at each of the three time points;
ing dark figures) than in registered data (for example, therefore, high scale values indicate high levels of of-
see Boers and Reinecke 2007; Loeber et al. 2015). We fending versatility.
applied the epidemiological definitions of prevalence
and incidence: “Basically, prevalence (or prevalence 1.4 Strategy of Analyses: Capturing Trends in
rate) refers to the number of diseases or spells of dis- Longitudinally Assessed Offending Versatility
ease existing at a particular point in time or within a Responses
specified time period related to the total number of Slope values of offending versatility over time. Initially,
persons exposed to risk (a population or a defined self-reported crime data are considered utilizing the
group of people). Incidence (or incidence rate) on the slope values of offending versatility over time. The of-
other hand measures the rate of appearance of new fending versatility response is a count of the number
cases in the group or population, i.e., the number of of adolescent-reported offenses during the past year
diseases/spells of disease beginning within a specified (see methods section). It is easily interpreted, and less
period of time related to the total number of persons likely influenced by memory or guessing. These re-
exposed to risk during that period” (Olweus 1989, sponses take integer values from zero to fifteen in the
187). In the current work, delinquent acts refer to van- first assessment and zero to nine in the third. Figure 1
dalism, property crime, violent crime, and drug deal- displays the roughly L-shaped histograms of the of-
ing (Wallner and Weiss 2019; Wittenberg and Wallner fending versatility measures at each of the three as-
2016). Nineteen different criminal acts were consid- sessment points.
ered (for example, scratching, bicycle theft, robbery). One central question is how to model these offend-
Partially, several delinquent acts refer to the same ing versatility responses in a way that reflects
crime type, so that some categories are overrepre- changes in offending versatility response trajectory
sented. The considered delinquency items varied con- over the three assessment time points within some re-
cerning severity. We employed the versatility of crime gression model. An answer is not obvious, partly be-
(i.e., [offending] versatility) in the past twelve months cause repeated measurements data models often re-
focusing on the range, heterogeneity, and diversity of quire full specification of the joint distribution of re-
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 7
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Figure 1: Histograms of offending versatility responses
Frequency
Frequency
Frequency
Versatility Time 1 Versatility Time 2 Versatility Time 3
Notes: Ordinates have been truncated; heights at zero are 354, 458, 484; vectors of mean and variance are (1.09,
4.36), (.48, 1.97), (.26, .67), times one to three respectively; n = 571; Versatility: offending versatility.
sponses and typically under distribution normality. treated as continuous outcomes. A positive slope, yi >
These empirical facts preclude the plausible use of a 0, indicates increasing offending versatility over the
very large class of possible models including those three years; a negative slope, yi < 0, indicates a de-
based on normal or multivariate normality. creasing offending versatility, and yi = 0 indicates no
The approach selected is the following: Define a lin- change.
ear slope response for each i by linearly regressing The distribution of the yi slopes, the response vari-
each i’s three offending versatility integer scores able, reveals large individual differences. Among the
against the time points designated as 1, 2, 3. For indi- 577 individuals, half (287) reported zero offenses at all
vidual i, a slope yi indicates i’s offending versatility three times. Because of their consistency, these is are
trajectory over the three offending versatility re- viewed as special and treated as such in the analyses
sponses. These slope values take on 19 discrete values below. An i is an element in the set τ: i ∈ τ if and only
from -7 to 2.5, a sufficient number to hopefully be if its offending versatility scores are (0; 0; 0), or “triple
considered continuous outcomes. Still, they will be zeros” (with τ denoting triple or three; read ∈ as “in”
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 8
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and ∉ as “not in”; τ is a set with elements individuals i lowing, we refer to the corresponding Regression Mix-
with triple zeros, in other words, zero offending versa- ture Model.
tility responses at all three assessment points). These i There are i = 1, 2,…, n individuals, each with re-
∈ τ are regarded as following a zero variance mass sponse yi arranged in a column vector y1,…, yn of n in-
point distribution (see below). dependent observations. Recall, yi is i’s slope. The as-
There were 28 additional is with estimated slopes of sociated covariates for each i are x1,…, xn. Each xi has
zero but not in τ. 174 individuals displayed negative p predictors in a row vector p + 1 long, xi = (1, xi,1,
estimated slopes; only 26 had positive estimated …,xi,p) with the first entry coded one for the intercept.
slopes, signaling an increase in offenses over time. The The design matrix X has n rows and p + 1 columns.
remaining 62 = 577 – 287 – 28 – 174 – 26 individuals Thus, there are n pairs of the form (yi, xi) with each i
had missing offending versatility values, denoted NA assumed to belong to only one of m = 3 three regres-
for “not available” (R Core Team 2017). R software was sion mixture components. The first component j = 0
used for all analyses (see below). Of the 62 individuals denotes those i ∈ τ, while i ∉ τ were admissible for ei-
with offending versatility NA values, six had NA val- ther of components j = 1, 2 in the normal mixture of
ues on two times. For all but one i, these NAs oc- regressions to be defined explicitly momentarily (see
curred on the second or third time. Of 56 is with NA below). To anticipate, using BIC (Schwarz 1978) the
on one time, most had identical offending versatility data support no more than two normal components.
values on the other two times or a smaller value on Following Schwarz, the model with the largest BIC is
the second time than on the first. This finding sug- taken as the best model.
gested that it would be reasonable to impute for those βj is a column vector of coefficients associated with
is with a single missing NA their smallest observed components j = 1, 2. βj = (βj0, βj1, …, βjp), so there are p
values. Most of the imputed values were zero. Follow- + 1 values of β for each βj, j = 1, 2.
ing imputation, contained 307 individuals or 54 per- Let N (·|µ,σ²) denote a conditionally normal density
cent of the usable sample (.54 = 307/571) with 38 zero function with mean µ and variance σ². (Let N (µ,σ²)
slopes i ∉ τ and a total of 264 i ∉ τ. In summary, fol- denote a normal density unconditionally.) The regres-
lowing imputation 571 = 307 + 264 individuals had us- sion mixture model is:
able slope response values. Consequently, just six of (1)
577 individuals were excluded from all subsequent
I(i) = 1 if i ∉ τ, and zero otherwise. σj² are variances
analyses. Of course, some additional individuals were
of components j = 1,2; λj ≥ 0,
excluded if they had NA values on a predictive covari-
ate because NA responses are inadmissible in the mix-
ture of regressions in the R package mixtools (Be- Thus, like conventional regression, model (1) is condi-
naglia et al. 2009), the source of all mixture routines tioned on the observed predictors.
employed below. 1, if i
f ( yi | x i ) (2)
So far our initial empirical results addressed the 0, otherwise
common gap in research relating to the availability of f (yi | xi) is a zero variance mass point at zero with
different methods in the identification of specific de- height one. Note that f (yi | xi) does not depend on xi.
velopmental pathways (see introduction). The follow- The proportion of the observations following f (yi | xi)
ing analyses employ the slope values of offending ver- is λ0. Those i ∈ τ and consequently their yis receive no
satility to explain distinct juvenile pathways over further analysis. It is worth noting that handling the
time. zeros in (2) is similar to a zero-inflated Poisson in pa-
The Regression Mixture Model. Next, we use the rameterization, a model often used in studies with
slope values of offending versatility (see above) as many observed zero values such as Tzoumakis et al.
outcome values in a mixture of regression routine en- (2012); in both, zeros are viewed as components of
compassing the trends over time. Therefore, in the fol- mixture distributions.
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 9
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Intuitively, consider only those i ∉ τ, and consider varying. The corresponding slope model described
fitting an ordinary multiple regression equation, as in above models the growth trajectory of slopes assess-
conventional settings, except that it is hypothesized ing three occasions over a time span of two years. In
that there is more than one regression equation ap- addition to the component of non-offending adoles-
propriate for the data. The task is to decide with cents, two components of offending adolescents were
which regression, j = 1, 2, for i ∉ τ the pair (yi, xi) is a defined. Perhaps there are appropriate alternative ap-
partner. The solution “matches-up” the observations proaches to the data modeling perspective employed
with their most probable regression equations via an here. Growth mixture models might seem an obvious
iterative EM algorithm. Matching is achieved using a candidate, however, these models make strong as-
Bayes Rule classifier. Rather than least squares, as in sumptions, including distributional multivariate nor-
conventional regression, the approach is maximum mality, assumptions often ignored. Consequently, the
likelihood under normality. If further details are re- results can be misleading (Bauer and Curran 2003).
quired, there are general discussions of finite mixtures Even univariate normality fails dramatically here as
and mixtures of regressions available in many sources the discrete Figure 1 distributions reveal. The ap-
(for example, Benaglia et al. 2009; McLachlan and Peel proach taken here is less susceptible to such concerns.
2000).
The approach in the current setting is not quite 2 Results: Contribution of Risks to Offending
standard however, as there is one large component Versatility
modeling those i ∈ τ that must be considered. The Finally, the contribution of different developmental
zero variance mass point distribution f (yi | xi), is quite risks to offending versatility trajectories is examined,
non-normal in distribution. Consequently, this com- displaying the predictive importance of these risks for
ponent is treated in an ancillary fashion. Thus, only distinct components of offending versatility. The con-
those i ∉ τ pairs (yi, xi) are analyzed under the mix- tribution of longitudinally assessed individual, famil-
tools call regmixEM. The λ1 and λ2 component weights ial, and environmental juvenile risks to explain differ-
are then adjusted at the end, so that the three λ esti- ent pathways is brought into focus – going beyond
mates sum to one. the mere description of pathways. For brevity, we con-
The distribution of point mass component at zero sider the analysis under model (1).
f (yi | xi) seems easily defended. The assumed condi- Let p = 4, with predictor variables acceptance of vio-
tional normality of components j = 1 and j = 2 in (1) is lence, impulsivity, peer delinquency, and corporal
more difficult to defend rigorously, but it is hoped a punishment, with values taken at the first time point
mixture of two normal distributions will hold at least (see Table 1 for summary statistics for the variables).
approximately or at least not lead one astray. If the A one-component (conventional) regression model
normal regression model holds, the slope distribution and two-component mixture of regressions were ap-
is normal (for example, Freedman 2005), so this result plied to the data. Model selection employed Schwarz’s
would give some hope for the appropriateness of the (1978) Bayesian Information Criterion denoted as
component conditional normality assumption in (1). BIC(LL; k; n), where LL is the loglikelihood, k the num-
The regression mixture procedure provides esti- ber of estimated parameters, and n sample size. The
mates for three λ, two σ² and 2(p+1) estimates of β. model with the largest BIC is taken as the best-suited
The number of covariates p varies, which means the model (taking the largest BIC following Schwarz). For
sample size n varies as well because as already noted, the one- and two-component regression models BIC
only complete data are admissible under the reg- (–346.21, 6, 235) = –362.39 and BIC(–316.86, 13, 235) =
mixEM routine. –351.46. Thus, the mixture model was selected. See
Collectively, the adolescents participating in our Table 2 for the corresponding parameter estimates.
study show different longitudinal trajectories consid- The standard errors in parentheses were obtained us-
ering change of offending versatility, hence, adoles- ing standard bootstrap observed data resampling pro-
cents’ trends of offending versatility over time are
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cedures (Efron and Tibshirani 1993). In addition, λ0 = functions are nearly identical. Acceptance of violence,
0.540(.020). for component j = 1, β11,acc is negative, and significantly
Table 1: Summary statistics for the predictor variables acceptance of violence, impulsivity, peer delin-
quency, and corporal punishment (first time point, t1)
y acc imp pee pun
variable range -7 to 2.5 0 to 29 0 to 35 0 to 28 0 to 16
mean -.87 11.47 17.50 5.02 1.34
var 1.80 38.29 44.90 26.57 9.24
Notes: Predictor variables: acc: acceptance of violence, imp: impulsivity, pee: peer delinquency, pun: corporal pun-
ishment. These statistics are all based on n = 237, representing complete data for all five variables.
Table 2: Two-component multivariate mixture of regressions estimates with four predictors: accep-
tance of violence, impulsivity, peer delinquency, and corporal punishment (standard errors in paren-
theses)
Components
Component 1 (j = 1): Component 2 (j = 2):
Predictors
Decreasing Offending Versatility Increasing/Stable Offending Versatility
^
j 0.228(0.094) 0.232(0.094)
^
j 1.391(0.258) 0.282(0.180)
^
j0 0.881(0.264) –0.495(0.057)
^
Acceptance of violence j1,acc –0.099(0.017) –0.013(0.004)
^
Impulsivity j 2,imp –0.021(0.015) 0.005(0.003)
^
Peer delinquency j 3,pee –0.077(0.018) 0.007(0.005)
^
Corporal punishment j 4,pun 0.002(0.032) 0.024(0.007)
Notes: Parameter estimates relating to the predictors: Values marked in bold are statistically significant (at least
at the 0.05 significance level).
so; thus increasing acceptance of violence is associ-
Recapitulating, the slopes are modelled as out- ated with decreasing offending versatility. Similarly
comes, whereas the chosen risk factors are predictors for peer delinquency, β13,pee < 0 and thus has a similar
within the regression mixture model. The first compo- interpretation (increasing peer delinquency scores as-
nent standard deviation is again much larger than sociated with decreasing offending versatility). Collec-
that of the second component, although the weight tively, the risk factors acceptance of violence and peer
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delinquency both have a significant negative effect on different trajectories of offending versatility constitut-
the emergence of offending versatility within the ing diverse patterns of risk in adolescence, so that the
group of adolescents with decreasing offending versa- divergent developmental pathways are differentially
tility, or in other words, the higher the acceptance of described and externally validated. Comparing our re-
violence in this group of adolescents, the smaller the sults with the results of other studies, certain similari-
offending versatility slope in this group. This means ties emerge. Referring to the fundamental work of
the higher the acceptance of violence, the more nega- Moffitt (1993), risks mostly related to adolescence lim-
tive the slope, thus the more decreasing adolescents’ ited antisociality (for example, delinquent peers) are
offending versatility over t2 and t3 in this group. Re- associated with the contemporary maturity gap in
latedly, the results concerning peer delinquency have adolescence, whereas individual risks (for example,
a similar interpretation. Corporal punishment is not concerning personality) and family risks (for example,
different from zero in component one. Impulsivity is concerning child-rearing practices) are particularly
not different from zero in either component, suggest- important in life-course persistent antisociality. In our
ing that this variable does not reflect any positive or study, we do not have self-report data before the age
negative trend when combined with other variables, of about 15 years and beyond the age of about 17
over the two-year period (t1 – t3). Collectively, com- years, so childhood and (young) adulthood have to be
ponent two seems to reflect small changes about zero, neglected and, consequently, certain statements be-
with corporal punishment significantly positive, and yond the very limited age period of adolescence are
acceptance of violence significantly negative. Accord- not possible here. Accordingly, the length of follow-up
ingly, corporal punishment has a significant positive is not adequate to allow extensive conclusions. It has
effect and acceptance of violence has a significant become apparent that peer delinquency has a signifi-
negative effect on the emergence of offending versatil- cant negative effect on the emergence of offending
ity within the group of adolescents with slightly in- versatility within the group of adolescents with de-
creasing or rather stable offending versatility. Peer creasing offending versatility – which assumedly
delinquency is not different from zero in component might be limited to adolescence and, hence, related to
two. Overall, our findings illustrate the importance of the late period of the adolescence limited pathway.
different developmental risks for diverging develop- Results suggest that with increasing peer delinquency
mental processes explicating risk-related variations in there is decreasing offending versatility. As outlined in
juvenile offending versatility trajectories. the introduction, the bio-psycho-social risk model of
Lösel and Bender (2003) describes different predictors
3 Discussion of serious and violent criminality. Delinquent peers
Evaluating the hypotheses set forth above, it becomes are a developmental risk mainly related to adoles-
apparent, as expected, that adolescents have different cence (for example, see Lösel and Bender 2003; Moffitt
longitudinal trajectories considering the change of 1993, 2006). As already sketched above (see introduc-
offending versatility. In addition to a non-delinquent tion), predictors of adolescence limited antisociality
group, our solution identified two diverging sub- (for example, peer delinquency), are mainly associated
groups of offending adolescents: Individuals with de- with the contemporary maturity gap in adolescence
creasing versus individuals with slightly increasing or (for example, Moffitt 1993; see also Odgers et al. 2008),
rather stable offending versatility over time. Gener- adolescent antisociality is often influenced by adverse
ally, regarding different antisocial outcomes, most peer contacts (for example, see Battin et al. 1998; Lösel
studies report three to four developmental trajectories and Bender 2003), and offending in adolescence is fre-
(for example, see Jennings and Reingle 2012). In our quently characterized by a high rate of peer delin-
study, comprising a quite limited two-year span of quency (offending in groups) and a high rate of co-of-
adolescence, three groups of adolescents emerged, in- fending (for example, Wallner and Weiss 2019). Re-
cluding the non-delinquents. Furthermore, also as ex- strictively, in the current work, we did not take into
pected, different risks contribute variably to these account whether the committed offenses were typical
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 12
vironmental Risks
juvenile offenses, which are often committed in regard to persistent antisociality. Generally, associa-
groups. Relatedly, however, our empirical findings in- tions between offending and risk might vary accord-
dicate that having delinquent peers might be associ- ing to the selected dependent variable: As described
ated with offending versatility which is likely to fade above (see measures section), we used offending ver-
in the course of adolescence. Further longer-term and satility, as a variety index that tends to cover the di-
more detailed analyses are required in this context versity of offending rather than the severity of the in-
(see above). Corporal punishment (as a familial risk dividual offenses, as may be the case with violent
factor relating to parental violence), has a significant crime, for example. It could be expected that the rela-
positive effect on the emergence of offending versatil- tionship between acceptance of violence and violence
ity within the group of adolescents with slightly in- in adolescence would possibly turn out more as ex-
creasing or rather stable offending versatility. Corrado pected. Following Dünkel and Geng (2003), the level
(2002, 2012) identifies different risks for serious and of acceptance of violence in youth is positively related
violent antisocial behavior, taking into account differ- to self-reported violent behavior (see measures sec-
ent risk domains (environmental, individual, family, tion). Overall, more specific analyses might be useful
intervention, and externalizing behavior; see also to enhance clarity.
Stemmler, Wallner, and Link 2018; Wallner et al. 2018). Additionally, general limitations of the present
Generally, parental corporal punishment and adverse study should be mentioned. First of all, the analyses
child-rearing practices are considered important fam- primarily focused on offending adolescents. A large
ily-based risks for long-term, persistent, and/or severe number of individuals with triple zeros on offending
antisociality (for example, see Corrado 2002, 2012; versatility measures were considered as a separate
Farrington, Ttofi, and Piquero 2016; Lösel and Bender component, as explicitly noted in equation 1 (see
2003; Moffitt 1993, 2006, 2018). In the context of physi- methods section). They may not be as interesting to
cal aggression in childhood, Côté and colleagues consider from a covariance perspective. Another way
(2006) identified three different trajectory groups (low to think about the triple zeros is that they follow a
desisting, moderate desisting, high stable) and different probability distribution (i.e., equation 2; see
showed that hostile/ineffective parenting predicted methods section). One general limitation relates to
the high-level group trajectory. With respect to both the attrition in the sample of our longitudinal study.
components as acceptance of violence increases, of- We assume that our results are tolerably robust con-
fending versatility decreases (as can be seen from the cerning dropout issues. However, we have to consider
significantly negative βs in Table 2). Therefore, unex- these issues, even though their influence seems to be
pectedly, acceptance of violence has a significant neg- minor (see methods section). Another important issue
ative effect on the emergence of offending versatility pertains to the sample which contains a high propor-
within the two groups of adolescents. Indeed, crimi- tion of students from lower-track schools, so that gen-
nological literature commonly suggests that individ- eral conclusions concerning the population are not
ual risk concerning deviant beliefs and attitudes to- possible on the basis of these unweighted data (see
wards delinquency is meaningful in the prediction of methods section; Wallner and Weiss 2019). Further re-
persistent antisocial outcomes (for example, see Lösel strictions are associated with the heterogeneity of our
and Bender 2003; Seddig and Reinecke 2017). How- sample: We did not conduct gender-specific analyses,
ever, a recent meta-analytic review on risk factors for partly because of the small numbers of individuals in
persistent delinquent behavior among adolescents single groups of offending adolescents. Moreover, the
(Assink 2017) revealed relatively small effects for, analyses do not consider other sociodemographic
amongst others, the attitude domain. Thus, substan- variables (such as migration background, school type,
tial and clear effects should not necessarily be as- socio-economic status). Additional analyses might in-
sumed in any case. Concerning our own results, the clude (at least) data concerning late childhood and
relatively short time span examined should also be early adolescence to enable more precise, complete
noted; for example, no statements can be made with findings relating to the developmental course of anti-
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Wallner, Thomas, Stemmler: Change in Juvenile Offending Versatility Predicted by Individual, Familial, and En- 13
vironmental Risks
sociality. Restrictions concerning the chosen measures variably to offending versatility pathways as mostly
have to be mentioned: The justification for the vari- expected, extensively more research concerning devel-
ables selected is based on theory (see introduction opmental criminology is needed to identify underly-
and methods section). Other or additional risks could ing risk patterns in the prediction of heterogeneous
certainly have been selected as independent variables antisocial pathways, especially concerning, for in-
(for example, see Farrington, Ttofi, and Piquero 2016; stance, the specific antisocial outcome, possible pro-
Lösel and Bender 2003; Wallner et al. 2018). Moreover, tective effects, and the individual’s age.
consideration of protective factors would have en-
abled more precise statements concerning buffering References
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kumentation der Schülerbefragung in Dortmund und Nürn-
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