Diego Farren - Thesis Short

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UNIVERSIT ¨ AT ZU K ¨ OLN Violence, Self-Control and Morality: A Dual-System Perspective by Diego Farren A thesis submitted in partial fulfillment for the degree of Master of Science (M.Sc.) in the Wirtschafts- und Sozialwissenschaftliche Fakult¨at (WISO) Institut f¨ ur Soziologie und Sozialpsychologie (ISS) Supervisor: Prof. Dr. Clemens Kroneberg October 2014

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Diego Farren - Thesis Short

Transcript of Diego Farren - Thesis Short

  • UNIVERSITAT ZU KOLN

    Violence, Self-Control and Morality: ADual-System Perspective

    by

    Diego Farren

    A thesis submitted in partial fulfillment for the degree ofMaster of Science (M.Sc.)

    in theWirtschafts- und Sozialwissenschaftliche Fakultat (WISO)

    Institut fur Soziologie und Sozialpsychologie (ISS)Supervisor: Prof. Dr. Clemens Kroneberg

    October 2014

  • Sometimes I am two people.

    Johnny is the nice one.

    Cash causes all the trouble.

    They fight.

    - Johnny Cash

    i

  • UNIVERSITAT ZU KOLN

    Abstract

    Wirtschafts- und Sozialwissenschaftliche Fakultat (WISO)

    Institut fur Soziologie und Sozialpsychologie (ISS)

    Supervisor: Prof. Dr. Clemens Kroneberg

    Master of Science (M.Sc.)

    by Diego Farren

    An exercise of theoretical elaboration (Thornberry 1989) from a control perspective is

    pursued using mainly inputs from the General Theory of Crime (GTC; Gottfredson

    and Hirschi 1990), the Situational Action Theory (SAT; Wikstrom et al. 2012; Wik-

    strom 2006), the Model of Frame Selection (MFS; Kroneberg 2006), and the Reflective-

    Impulsive Model (RIM; Hofmann et al. 2009; Strack and Deutsch 2004). The capability

    of the final model of action proposed to predict acts of violence is tested through mul-

    tilevel analyses using data from the International Self-Report Study of Delinquency 2

    (ISRD-2; Enzmann et al. 2010; Junger-Tas et al. 2012, 2010). The results point in the

    expected direction, i.e. action can be modeled through the suggested framework. Theo-

    retical, methodological and policy implications derived from the adoption of the proposed

    model are discussed. Limitations of the analyses applied and ideas to overcome them in

    future researches are also presented.

    ii

  • Acknowledgements

    The biggest thanks of all to my boss and friend Dirk Enzmann for all the dedication,

    discussions, good advice, good sense of humor and unconditional support.

    Also thanks to my college Ilka Kammigan and to the whole Uni Hamburg crew, lead

    by Peter Wetzels and Sylvie Billon - thanks for fitting me in, for your support, and for

    creating such a nice atmosphere.

    Thanks to those who enlighten my way in those dark moments of doubt, whether its

    with theory or with statistics or with Stata and R - thanks to Clemens Kroneberg,

    Alexander Schmidt and Bernd Wei.

    Also thanks to Hans-Jurgen Andre, Ravena Penning and Hawal Shamon for the amaz-

    ing two years of profound learning I had as a tutor.

    A big thanks to all my friends around the world and especially to my Kumpel David

    Bruder, my beloved classmates, and to all the amigos at the Mauer in Koln. And my

    special gratitude to Birgit Kastner and Lena Taube for accommodating me in the last

    phase of this project, when I no longer had a home.

    Last but not least, I thank my family for their support, example and wisdom. Mother

    and father, you are both my favorite people in the world.

    iii

  • Contents

    Abstract ii

    Acknowledgements iii

    List of Figures v

    List of Tables vi

    Abbreviations vii

    1 Introduction 1

    2 Theoretical Background 3

    2.1 Theoretical integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    2.2 Dual-system perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2.3 Conceptualization and measurement . . . . . . . . . . . . . . . . . . . . . 13

    2.4 Research question and hypotheses . . . . . . . . . . . . . . . . . . . . . . 17

    3 Methods 20

    3.1 Data source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3.2 Operationalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3.3 Statistical analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    4 Results 42

    5 General Discussion and Conclusion 56

    Bibliography 63

    Appendix A: Correlations 74

    iv

  • List of Figures

    1.1 Study goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    2.1 SAT & MFS complemented . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    2.2 Clusters of attributes associated with dual systems of thinking . . . . . . 12

    2.3 The Reflective-Impulsive Model (RIM) . . . . . . . . . . . . . . . . . . . . 16

    3.1 Histogram: impulsive determinants of behavior . . . . . . . . . . . . . . . 24

    3.2 Histogram: reflective determinants of behavior . . . . . . . . . . . . . . . 25

    3.3 Histogram: school disorganization scale (agg.) . . . . . . . . . . . . . . . . 27

    3.4 Mediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

    3.5 Observable and unobservable outcomes . . . . . . . . . . . . . . . . . . . . 39

    4.1 Predicted probabilities (95% CI) . . . . . . . . . . . . . . . . . . . . . . . 45

    4.2 Marginal probability effects (95% CI) of impulsive determinants of behavior 47

    4.3 Predicted probabilities (95% CI) over intoxication . . . . . . . . . . . . . 49

    4.4 Discrete probability change (95% CI) over intoxication . . . . . . . . . . . 50

    5.1 RIM and SAT/MFS compared . . . . . . . . . . . . . . . . . . . . . . . . 56

    v

  • List of Tables

    2.1 Impulsive and controlled outcomes: four scenarios . . . . . . . . . . . . . 18

    3.1 Sample description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    3.2 Violence related prevalences by country . . . . . . . . . . . . . . . . . . . 22

    3.3 Descriptive statistics: impulsive determinants of behavior (scale) . . . . . 23

    3.4 Descriptive statistics: reflective determinants of behavior (scale) . . . . . 24

    3.5 Descriptive statistics: life-time intoxication (scale and items) . . . . . . . 25

    3.6 Descriptive statistics: school disorganization scale . . . . . . . . . . . . . . 26

    3.7 Descriptive statistics: control variables . . . . . . . . . . . . . . . . . . . . 28

    4.1 Regression results (main regressions) . . . . . . . . . . . . . . . . . . . . . 43

    4.2 Explained variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    4.3 Predicted probabilities (95% CI) over impulsive determinants of behaviorcompared (M1 vs M4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    4.4 Marginal probability effects (95% CI) of impulsive determinants of be-havior compared (M1 vs M4) . . . . . . . . . . . . . . . . . . . . . . . . . 48

    4.5 Predicted probabilities (95% CI) over intoxication compared (M2 vs M4) . 48

    4.6 Discrete probability change (95% CI) over intoxication compared (M2 vsM4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    4.7 Regression results (KHB mediation) . . . . . . . . . . . . . . . . . . . . . 52

    4.8 Mediation analysis with impulsive determinants of behavior as treatmentvariable (counterfactuals; no interactions) . . . . . . . . . . . . . . . . . . 53

    4.9 Mediation analysis with school disorganization as treatment variable (coun-terfactuals; no interactions) . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    4.10 Mediation analysis with impulsive determinants of behavior as treatmentvariable (counterfactuals; with interactions; intoxication = 0) . . . . . . . 54

    4.11 Mediation analysis with impulsive determinants of behavior as treatmentvariable (counterfactuals; with interactions; intoxication = 1) . . . . . . . 54

    4.12 Mediation analysis with school disorganization as treatment variable (coun-terfactuals; with interactions) . . . . . . . . . . . . . . . . . . . . . . . . . 54

    A.1 Descriptive statistics and correlations: self-control/impulse related items . 74

    A.2 Descriptive statistics and correlations: violence attitude/reflective deter-minants of behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

    A.3 Descriptive statistics and correlations: school climate related items (schooldisorganization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

    A.4 Descriptive statistics and correlations: neighborhood climate related items 75

    A.5 Descriptive statistics and correlations: family bonding related items . . . 76

    A.6 Correlations of all variables used in the regressions . . . . . . . . . . . . . 76

    vi

  • Abbreviations

    GTC General Theory of Crime

    ISRD International Self-Report Study of Delinquency

    MFS Model of Frame Selection

    RIM Reflective-Impulsive Model

    SAT Situational Action Theory

    vii

  • Dedicated to my father Fernando Farren

    viii

  • 1. Introduction

    A dual-system perspective is proposed to test the hypothesis that acts of violence can

    be modeled as an outcome that depends mainly on self-control, morality, situational

    moderators, and their interplay. Theoretical elaboration (Thornberry 1989) from a con-

    trol perspective is applied to develop an action theory that can serve to understand and

    predict acts of violence. Data from the International Self-Report Study of Delinquency

    2 (ISRD-2; Enzmann et al. 2010; Junger-Tas et al. 2012, 2010) representing populations

    of grade 7 to grade 9 (mostly 12 to 14 years students) from 30 different countries is

    analyzed. Statistical methods used belong mainly to the family of multilevel logisitc re-

    gression models. Also a counterfactual perspective is adopted to test hypotheses about

    mediation (see e.g. Imai, Keele and Tingley 2010).

    This study has three goals (see Figure 1.1): first, a discussion of the conceptual meaning

    of self-control and its place in crime causation. Inputs from different theories in criminol-

    ogy and social-psychology will be taken into consideration with the goal of contributing

    to a theory of action that can be used as a roadmap for the development of valid mea-

    sures and understanding of the variables of interest. An important part of this goal is to

    integrate approaches of different disciplines, in this case psichological and criminological

    theories (also referred as a postmodernist perspective on integration Barak 2010). In

    order to be clear about the type of integration proposed, part of the theoretical chapter

    is dedicated to clarifying the meanings of theoretical integration and its state of the art.

    Figure 1.1: Study goals

    THEORY

    Goal 1:Theoretical

    model

    Goal 2:Measuring

    instruments

    Goal 3:Statisticalanalysis

    ANALYSIS

    Once the proposed theory of action has been explained, the next step is to give guidelines

    on how to measure the most relevant concepts involved in it. The second goal of this

    study is, accordingly, to critically revisit the existent measuring instruments for the key

    concepts of the described theory of action. The logical conclusion at this stage, would

    be to choose the best measures or to develop new ones and analyze them. Nevertheless,

    the data in this case has already been collected, so that no changes to the measuring

    1

  • Introduction 2

    instruments can be made. That is, although a critical revision of the instruments being

    used to measure the concepts of interest can be done, the data analyses must still rely

    on existing instruments. The main intention of the second goal is then, to state the ideal

    conditions under which the theoretical model developed in goal one should be tested.

    In this sense, the theory of action to be proposed is expected to set the standards for

    the measurement of its main concepts. This is considered a relevant goal to avoid mis-

    understandings about the meaning of relevant concepts in the guiding theory of action.

    Finally the model proposed in goal one will be statistically tested using state of the art

    multilevel models. The results will be described and interpreted with special emphasis

    on their theory, methodology and public policy implications. It is of main importance to

    keep theoretical abstraction and methodological sophistication connected to the prag-

    matic goals of public policy. In other words, particular attention will be payed to the

    consequences of the proposed theory and methodology for policies to reduce crime and,

    specifically, acts of violence.

    The next chapter presents the necessary discussion about theoretical integration that

    should give the reader a general notion about the meaning of such an exercise and its

    relevance for the development of social science. A proposition for theoretical integration

    follows, using inputs from relevant criminological and psychological theories. First the

    original theories are summarized and then the proposed integrated theory of action is

    explained in detail. The chapter ends with the explicit exposure of the research question

    and hypotheses to be tested in order to check the predictive power of the action theory

    as developed in the previous section.

    The methodological chapter presents a short description of the data to be used to test

    the model proposed. Also the operationalization of the variables is explained and mea-

    sures of reliability are presented. The chapter ends with a general description of the

    statistical methods implemented to test the hypotheses.

    The results chapter presents the statistical analyses and tests of hypotheses. The findings

    are critically discussed in the concluding chapter. The consequences for criminology

    theory, methods of data collection and analysis, as well as for public policy, will be

    discussed in the final chapter as well.

  • 2. Theoretical Background

    The analysis of crime has been characterized by many competing, and at times con-

    flicting perspectives on crime and delinquency (Elliott et al. 1979, 3) that deal with

    different aspects and levels of reality. Control theories are an important part of crimino-

    logical studies. With all the changes they have gone through, they share the same main

    proposition: everyone is capable of committing crime and control prevents him/her from

    doing so (Bernard et al. 2010, 203f.).

    Since the publication of A general theory of crime (GTC; Gottfredson and Hirschi

    1990), control theories have placed special attention on self-control. Much has been

    discussed about self-control as a predictor of crime (see e.g. Goode 2008; DeLisi and

    Vaughn 2007; Geis 2000). Although many scholars criticize this theory, the fact is that

    studies including its measure more often than not prove it as a significant predictor of

    problematic conduct (for a meta-analysis see Engel 2012).

    It seems clear that self-control plays a key role in crime causation. But there are at

    least two critical points to be clarified. First, the meaning of self-control is still con-

    troversial and should be refined. It is now a commonplace in criminology to state that

    Gottfredson and Hirschi (1990) failed to precisely define self-control, and just rested on

    a description of behaviors that reflect intrinsically low self-control (e.g. Wikstrom and

    Treiber 2007, 243; Tittle et al. 2004, 147).1 Moreover, Gottfredson and Hirschi (1990)

    tend to ignore the potential inputs of the conceptualization given by psychological the-

    ories of self-regulation. The problem of conceptualization is a critical one, because any

    comprehensive test of a theory relies on the congruence between theoretical derivation

    and operationalization (Marcus 2004, 35f.). Because Gottfredson and Hirschi (1990)

    give no operational definition of self-control (Akers 1991, 204), researchers have been

    forced ... to interpret the concept of self-control in their own manner, ... and come

    up with their own measures of self-control. (Piquero 2008, 26f.). Although Hirschi

    1Gottfredson and Hirschi (1990) define low self-control as the tendency to pursue immediate gratifica-tion while not taking possible negative long-term consequences into account. They characterize peoplehaving low self-control as being impulsive, insensitive, physical (as opposed to mental), risk-taking,short-sighted, and nonverbal (p. 89f.).

    3

  • Theoretical Background 4

    and Gottfredson (1993) do manifest preference for behavioral measures of self-control

    (p. 48), Akers (1991) makes the point that if offenses themselves were used as measures

    of self-control, this would create a problem of tautology (p. 204).

    The second critical point refers to integrating self-control theory with other explana-

    tory theories that have proved to be good predictors of crime. Theoretical integration

    has been fueling discussion for a long time in criminology (see e.g. Bernard et al. 2010,

    327f.; Bernard 2001; Bernard and Snipes 1996; Messner et al. 1989). Those in favor of

    it (e.g. Elliott et al. 1979) see it as an alternative to theoretical competition and fal-

    sification, as this last strategy has failed to reduce the number of criminology theories

    (Bernard 2001, 335). However, those opposed to it (e.g. Hirschi 1979) see no compati-

    bility between the basic models of delinquency theories -i.e. control, strain, and cultural

    deviance models (Kornhauser 1978, 21ff.)- and therefore no possibility of theoretical in-

    tegration.

    In this chapter the state of the art in the debates about these two critical points is

    presented. First the problem of theoretical integration in criminology is revisited to

    conclude that a theory of action is needed. Next, a dual-system perspective is proposed

    as a suitable theory of action to be applied on acts of crime and violence. In order to

    support this statement, a summary of already existing dual-process theories in crimi-

    nology is presented and a dual-system model of self-control derived from psychology is

    described. The theoretical and methodological benefits of such a perspective are summa-

    rized and a revision of existent measuring instruments is presented. Finally, through the

    adoption of a dual-system model of self-control, the research questions and hypotheses

    will be derived.

    2.1 Theoretical integration

    Theoretical integration is defined by Thornberry (1989) as the act of combining two

    or more sets of logically interrelated propositions into one larger set of interrelated

    propositions, in order to provide a more comprehensive explanation of a particular phe-

    nomenon. (p. 52, italics from original). The essential and most difficult aspect of

    this task is that theoretical integration can only be achieved when many theories form

    a new theory that retains the premises of each theory (Bernard and Snipes 1996, p.

    308). According to Liska et al. (1989) there are two types of theoretical integration:

    propositional and conceptual.

  • Theoretical Background 5

    Conceptual integration is when the theorist equates concepts in different theories, argu-

    ing that while the words and terms are different, the theoretical meanings and operations

    of measurement are similar and is seen by the authors as useful only as a means to

    propositional integration (p. 15). Bernard and Snipes (1996) put this nicely into

    words: conceptual integration is nothing but playing games with words and meanings

    (p. 308).

    Hirschi (1979) defines three forms of propositional integration: end to end different

    theories get sorted in a sequential order, so that the dependent variable in some prior

    theory, becomes the independent variable in a new more general integrated theory (p.

    34f.) , side by side the dependent variable of interest is divided into disjunctive parts,

    e.g. different types of crimes that can each be explained by different theories (p. 35f.)

    and, up and down there is one main theory, and other theories can be subsumed to

    it (p.36) . These three types of integration can be further applied to the micro-level,

    macro-level, or cross-level (Liska et al. 1989, 5).

    Because of the difficulty of achieving propositional integration, some authors have pro-

    posed changes or even alternatives to it. Liska et al. (1989) describe the possibility of

    a middle range integration, i.e. a more flexible form in which propositions of differ-

    ent theories are used to build a new theory, without necessarily retaining all the main

    premises or the original definitions of the concepts from each original theory:

    We can easily borrow ideas (concepts and propositions) from different theo-

    ries and explore how they fit. Some propositions of different theories may be

    incompatible because they are tightly linked to incompatible assumptions.

    Other propositions, however, may not be so tightly linked to such assump-

    tions, and some propositions of different theories may be deduced from a

    common set of assumptions, even if they were originally derived from incom-

    patible assumptions. (p. 17)

    Thornberry (1989) even comes up with an alternative to theoretical integration, i.e.

    theoretical elaboration:

    Rather than starting with multiple theories and attempting to reconcile their

    differences to generate a comprehensive model, theoretical elaboration explic-

    itly starts with a particular theoretical model. Accepting its assumptions,

    level of explanation, and causal structure, it attempts to build a more and

    more comprehensive model by the logical extention of the basic propositions

    contained in the model. (p. 56)

  • Theoretical Background 6

    Finally, Bernard and Snipes (1996) defend a substantial reinterpretation of criminology

    theories (p. 332). They argue that criminology theories should be interpreted and

    classified in terms of their location of independent variation and direction of causation

    giving raise to two categories of criminology theories: individual difference theories

    and structure/process theories (Bernard et al. 2010, 338f.).2 Under this perspective,

    full integration could be achieved through a single theory of crime that incorporates

    the structural conditions that are associated with higher crime rates, the processes that

    explain why normal individuals who experience these structural conditions are likely

    to engage in crime, and the individual characteristics that make it more or less likely

    that an individual will engage in crime regardless of structural conditions. (Bernard

    and Snipes 1996, 342). They also state that although such a full integration should

    be theoretically possible, it may not necessarily be desirable, so that it may be best

    to attempt integration only within each category of theories, and not between them

    (Bernard and Snipes 1996, 304).

    The last argument does not mean that theories at one level can not include arguments of

    other levels, on the contrary this may be desirable. With respect to individual difference

    theories that include macro variables, Bernard and Snipes (1996) declare:

    While integrating previously existing theories across levels of explanation

    may be undesirable, new theories that incorporate arguments at both of

    these levels of explanation may be both useful and feasible....

    Such theories explain individual-level variation in criminal behavior using

    both individual differences and the interaction between individual differ-

    ences and structural position. When explaining individual differences with

    a combination of individual and structural explanations, it is easy to avoid

    committing an ecological fallacy. (p. 343)

    As can be concluded from the exposition so far, what is meant by theoretical integra-

    tion is already not always agreed and rarely made explicit (see e.g. Liska et al. 1989,

    1; Thornberry 1989, 52). A truly propositional cross-level integration can be thought

    as the gold standard. Nevertheless, achieving such an integration is very unlikely and

    probably not worth the investment. In other words, cross-level integration in the terms

    of Bernard and Snipes (1996) -i.e. a full integrated theory capable of explaining varia-

    tion in both crime rates and individual likelihood of engaging in criminal behavior- may

    2In the same direction, Nagin and Paternoster (1993) write that [c]riminological theory has developedalong two separate and distinct tracks: in one time-stable individual differences distinguish offendersfrom nonofenders, while other theories attribute crime to circumstances and situations in the socialsetting that are external and proximate to the offender (467f.).

  • Theoretical Background 7

    be too complex at the moment and not necessarily useful (p. 342f.).3 But at the same

    time, development of theories at the level of the individual needs to account for the

    impact that the environment has on the individual differences (Wikstrom et al. 2010,

    56). In other words, a general theory of crime should not only explain why people have

    different probabilities of committing crime, but need to also account for the role that

    the environment has in influencing individual differences and as a trigger that allows

    probabilities to become action.

    The alternatives to the most purist views on theoretical integration already discussed

    here, seem to be closely related to the actual stand of theoretical progress in criminology.

    By relying on theories of action, newly developed theories of crime causation integrate

    the statements of many existing theories into one theoretical frame. By doing so, they

    do not necessarily retain the premises of each original theory. Integration through the

    reliance on a theory of action seem much more flexible than a propositional integration

    and allows e.g. some modifications to the original concepts and propositions taken from

    existing criminology theories.

    The next section describes two newly developed theories of action that have been ap-

    plied to the explanation of crime. Finally, a dual-system perspective is presented and

    promoted as a suitable theory of action to explain acts of violence.

    2.2 Dual-system perspective

    The demand for a theory of action in social science is not a new one. Coleman (1986)

    critically revisited post-Parsonian social theories, and concluded by declaring that a

    theory of purposive action that can relate individual actions to systemic functioning

    is needed (p. 1332). In criminology, Bernard (1989) made the case for relying on the

    relations that different component theories have to a theory of action as a way of in-

    tegrating them (p. 140). As stated by Wikstrom et al. (2012), explaining the actual

    causal process that directly links a person (crime propensity) and a setting (criminogenic

    exposure) to an act of crime ... requires the integration of causally relevant personal and

    environmental factors and analysis of their interaction within the context of an adequate

    3Bernard and Snipes (1996) state: The integration of individual difference and structure/processtheories is theoretically possible but remains a long-range goal pending the development of more advancetheoretical arguments and statistical techniques. (p. 304). Although such a full integration is not theintention of this study, it is worth mentioning two examples of statistical and theoretical developmentsthat might point at the advance meant by Bernard and Snipes (1996).In the statistical field, Goldstein et al. (2009) present a multivariate-multilevel model that allows for theinclusion of more than one dependent variable at more than one level of analysis.In the theoretical field, Messner (2012) made a proposal for a cross-level integration between Wik-stroms Situational Action Theory (e.g. Wikstrom et al. 2012; Wikstrom 2006) and his and RosenfeldsInstitutional Anomie Theory (e.g. Messner and Rosenfeld 2007, 2001).

  • Theoretical Background 8

    action theory. (p. 5f.), so that an action theory is a theory that details the process

    (the mechanism) that produces action. (p. 8).

    Understanding the mechanism that produce action, means understanding how society

    models individual perception and, in turn, how individual action models society (i.e.

    the macro-micro-macro relations, see Coleman 1986, 1322ff.). Rational choice theory is

    considered to be the first theory of action to integrate person and situation in a con-

    vincing way (Lindenberg 2008, 669). Classical criminology has also relied on a reasoning

    actor who can estimate costs and benefits when deciding to (or not to) commit crime

    (see e.g. Bernard et al. 2010, 14ff.). But because actors do not always act in a rational

    way, psychologists have been developing theories that can explain action as the result

    of a process that only sometimes follows a rational calculation (see e.g. Chaiken and

    Trope 1999; Kahneman 2003; Smith and DeCoster 2000). In criminology this has lead

    to some attractive discussions and propositions about the role of human agency in crime

    causation (see e.g. Gottfredson 2011; Kroneberg et al. 2010; McCarthy 2002; Paternoster

    and Pogarsky 2009; Wikstrom and Treiber 2007). As a consequence, some new theories

    of action have been lately proposed that share the reliance on what has been called

    variable rationality (see e.g. Kroneberg 2006, 2).

    Psychological theories explaining variable rationality are usually labeled as dual-process

    theories (see Chaiken and Trope 1999). According to Smith and DeCoster (2000) what

    these theories share, is that they all try to explain three main components: how people

    process in quick-and-dirty fashion, how they process when willing and able to engage in

    extensive thought, and what conditions encourage such effortful processing (p. 108).

    On the other side, the main difference between dual-process theories is the temporal and

    logical relation assumed between types of process, i.e. whether they occur simultane-

    ously or in a sequential way or even in an alternative way (p. 125).

    In criminology, Wikstrom and colleagues developed their own theory of action: the Situ-

    ational Action Theory (SAT; see e.g Wikstrom 2006; Wikstrom et al. 2012). SAT defines

    two perception choice processes that precede action: habit and rational delibera-

    tion (Wikstrom et al. 2012, 19ff.). The situation is seen as the core unit of analysis

    in criminology, and defined as the perception of action alternatives and process of

    choice that follow from the interaction between person and setting (environment is

    understood as everything outside the person, so that the analysis should be limited to

    the setting, i.e. the part of the environment that is accessible through senses to the

    person; Wikstrom et al. 2012, 15). The situation then demarcates how much agency

    an actor may apply to the process of action selection, i.e. the situation determines the

  • Theoretical Background 9

    likelihood of an action followed by habit or by rational deliberation.

    If the situation is at the center of interest, the next step would be to disentangle the

    essential elements that conform it. According to Wikstrom et al. (2010) these are: at

    the level of the person its crime propensity and, at the level of the setting its crimino-

    genic exposure. Both elements can be further decomposed into morality and control.

    If the morality of the person and the morality of the context correspond (i.e. both

    encourage or both discourage an act of crime4), then the likelihood of an action in the

    same direction as the correspondence is high. If the setting encourages acts of crime but

    the persons morality discourages it, self-control comes into play. Finally if the context

    discourages acts of crime but the persons morality encourages it, then social control in

    the form of deterrence plays a role (p. 61).

    Following Wikstrom and Treiber (2007), morality is the key individual aspect that filters

    what action alternatives an actor will take into consideration in a given situation. If the

    setting is familiar to the actor, he or she will tend to act out of habit. But if the setting

    is not familiar to the actor, he or she will tend to choose an action after some delib-

    eration and self-control may be a part of this process. especially, as stated previously,

    when there is a conflict between the moral rules of person and setting in the form of a

    setting that encourages an act of crime and a person whos moral rules discourage it,

    self-control will be involved in the process of deliberation (p. 245ff.).

    In sum, SAT understands that the primary way in which morality causally affects crime,

    is by filtering what action alternatives a person will perceive in a given situation, and

    only in a secondary order (i.e. when already involved in deliberation) it also affects (to-

    gether with controls) the way in which a person chooses between alternatives for action

    (Wikstrom 2010, 222).

    Another newly developed theory of action that has been applied to crime, is Kronebergs

    Model of Frame Selection (MFS; see e.g. Kroneberg 2006, 2007; Kroneberg et al. 2010).

    The MFS has emerged as an answer to the absence in social science of a clear definition

    of the situation and of variable rationality within a model of action (Kroneberg

    2006, 9). Similarly to SAT, it specifies under what conditions behavior follows from

    a cost-benefit calculus and under which it will be the result of an automatic reaction

    (Kroneberg et al. 2010, 265). This is done by identifying three selections that precede

    behavior in any given situation. First an actor needs to make a frame selection in

    4Wikstrom (2006) defines act of crime as the act of breaking a moral rule defined in criminal law,where a moral rule is a prescription of what is right and what is wrong in a given context (p. 63).

  • Theoretical Background 10

    order to define the situation. That is, through situational objects an actor must get an

    idea of in what kind of a situation he or she finds him-/herself. Once the actor has a

    general idea of where he or she is, he or she must do a script selection. In this step he

    or she searches for possible actions to choose from a list of actions that correspond to

    the already selected frame and to his or her interpretation of how he or she is expected

    to behave (i.e. that correspond to his definition of the situation). Finally follows an

    action selection, i.e. he or she must choose to act (or not to) by selecting one of the

    alternatives the chosen script presents (Kroneberg 2006, 10f.).

    According to Kroneberg (2006), the way in which each of these selections is done can be

    more or less conscious, so that the level of elaboration needed to produce action may vary.

    This variation in levels of elaboration is dependent on the modes of information process-

    ing (or mode selections in short), which can follow either an automatic-spontaneous

    mode (i.e. as-mode) or a reflecting-calculating mode (i.e. rc-mode). Depending on vari-

    ables of the situation, the selection will tend to be made in an as-mode or in a rc-mode.

    For example, a higher level of familiarity with the situation promotes an automatic an-

    swer (i.e. ready-to-use programs are easy to access). Also pressure for a fast reaction will

    result in less elaborated selections. On the contrary, being highly motivated to choose

    wisely because e.g. of the cost of wrongdoing, will promote the use of the extra effort

    needed to apply selections in a rc-mode (p. 11f.). In the case of crime acts, strongly

    internalized moral norms will lead to automatic answers (Kroneberg et al. 2010, 261).

    MFS and SAT share many arguments and many differences are only terminological. For

    example, the modes of selection described by the MFS are equivalent to the forms of

    action defined by the SAT. That is, habitual form of action and deliberation in

    SAT equate the as-mode and rc-mode in MFS, respectively (Messner 2012, 13).

    Also both theories assume that only when values are not strongly internalized, people

    proceed to evaluate the possibility of committing crime (Kroneberg et al. 2010, 264).

    In this sense, according to both theories action or inaction is primarily an automated

    response that depends on the socialization of the individuals and only secondly on vari-

    able characteristics of individuals and contexts (Kroneberg et al. 2010, 261).

    As can be seen in Figure 2.1, the connection between individual and environment is

    already very convincingly explained by the SAT with its definition of the situation. One

    particularly interesting consequence of the SAT is that it faces in a very convincing

    way the problem of linking self-control with social control as stated by Taylor (2001).

    This is done by defining self-control not as a trait -like Gottfredson and Hirschi (1990)

    do in their GTC- but as a situational variable (Wikstrom and Treiber 2007, 243). As

  • Theoretical Background 11

    Figure 2.1: SAT & MFS complemented

    Morality/Norms

    Frames/Scripts

    situational self-control(executive capabilities)

    Mode Selection

    CriminogenicExposure

    -moral rules of setting-level of enforcement(deterrence)

    SAT(situation)

    MFS(variable rationality)

    EnvironmentalCharacteristicscauses of the causes

    (crime propensity)

    behavioraloutcome

    social/selfcontrol link

    stated previously, according to the SAT self-control is the capability to resist temptation

    in a situation where the contexts morality promotes an action that conflicts with the

    individuals belief of what is good or bad. According to Wikstrom and Treiber (2007),

    self-control will vary depending on the situation, but what remains mostly constant is

    the trait responsible for the ability to exert self-control, i.e. the executive capability (p.

    251). The representation of the environment the person creates is particularly depen-

    dent on this capability, too, so that the perception of deterrence will be influenced by

    the levels of self-control an individual possesses in a given situation (p. 253).

    One essential contribution that the MFS adds to the SAT is a deeper explanation of the

    process through which action alternatives get filtered (Messner 2012, 13). The process

    which is triggered by Morality/Norms in Figure 2.1 takes place inside the head of

    a person. The frames and scripts as defined by MFS are to be found here. The way in

    which selections are made, is a consequence of the situation, i.e. depends on character-

    istics of the setting and of the person. The individuals morality operates as a filter

    of the frames and scripts that a person is going to consider in his selection process, and

    also of the way in which these selections will be done (i.e. in a rc-mode or as-mode).

    In social and cognitive psychology different dual-process and dual-system models have

    been proposed to deal with variable rationality (see e.g. Chaiken and Trope 1999; Evans

    2008; Kahneman 2003; Smith and DeCoster 2000). Dual-process theories share the idea

    that there are two ways of processing information, with one being slow, conscious and

    deliberative, and the other being rapid, unconscious and automatic (Evans 2008, 256).

  • Theoretical Background 12

    Whether only different processes are recognized or also different underlying cognitive

    systems, distinguishes dual-process from dual-system theories. One of the most influ-

    ential works in this area is the one by Kahneman (2003). The author refers to both

    systems as system 1 and system 2 (see Figure 2.2). While the names of the systems vary

    between theories, the main idea is that system 1 is the more automatic one and system

    2 the more reflective one.

    Figure 2.2: Clusters of attributes associated with dual systems of thinking

    System 1 System 2

    Clu

    ster

    1

    (Con

    scio

    usn

    ess)

    Unconscious(preconscious)

    Implicit

    Automatic

    Low effort

    Rapid

    High capacity

    Default process

    Holistic, perceptual

    Conscious

    Explicit

    Controlled

    High effort

    Slow

    Low capacity

    Inhibitory

    Analytic, reflective

    Clu

    ster

    2

    (Evo

    luti

    on)

    Evolutionarily old

    Evolutionary rationality

    Shared with animals

    Nonverbal

    Modular cognition

    Evolutionarily recent

    Individual rationality

    Uniquely human

    Linked to language

    Fluid intelligence

    Clu

    ster

    3

    (Fu

    nct

    ion

    alch

    arac

    t.) Associative

    Domain specific

    Contextualized

    Pragmatic

    Parallel

    Stereotypical

    Rule based

    Domain general

    Abstract

    Logical

    Sequential

    Egalitarian

    Clu

    ster

    4

    (In

    div

    .d

    iff.)

    Universal

    Independent ofgeneral intelligence

    Independent ofworking memory

    Heritable

    Linked togeneral intelligence

    Limited by workingmemory capacity

    Source: Evans 2008, 257

    One very interesting theory in this field, is Stracks and Deutschs Reflective-Impulsive

    Model (RIM; see e.g. Strack and Deutsch 2004). The authors base their model on

    the statements of Smith and DeCoster (2000), who identify two different memory sys-

    tems that store different information and also operate in divergent ways. According to

    the authors, there is the slow-learning system that operates through an associative

    processing mode, and a fast-learning system that operates through a rule-based

  • Theoretical Background 13

    processing mode (p. 110). Although the associative processing mode depends only on

    the slow-learning system, the rule-based processing mode depends on both systems (p.

    111). The general idea of RIM is that by defining two different systems that operate in

    parallel and that may operate in accord or conflict with each other, variable rationality

    can be explained (Strack and Deutsch 2004, 221f.).

    According to Hofmann et al. (2009) the impulsive system is generating impulsive behav-

    ior that is the result of the activation of an associative cluster in the long-term memory.

    The reflective system, on the other hand, complements the functions of the impulsive

    system by adding higher order mental process, like the ones involved in executive func-

    tions and deliberation. The RIM also states that in a final step, both systems access the

    motor cortex to activate behavior. So that both system are in a constant competition

    to trigger behavior and who wins this competition will be decided in this final step and

    depends on the strength of the activation of each system and on situational moderators

    that may shift the degree of activation in favor of one system (p. 164f.).

    In sum, the RIM as defined by Strack and Deutsch (2004) states that behavior follows

    from the activation of determinants in an impulsive system or in a reflective system (p.

    222). While the impulsive system is always activated and is responsible for automatic

    answers applied to familiar settings, the reflective system may be disturbed through

    situational moderators (p. 223). Hofmann et al. (2009) conducted a few experiments

    to show under what conditions the capability of the reflective system to restrain stan-

    dards may be altered. They show that the self-regulatory resources the reflective system

    possesses at a given moment can be depleted through repetitive use. This implies that,

    keeping everything else constant and within a close time period, with each new similar

    impulse that has to be inhibited, the self-regulatory resources get reduced and the likeli-

    hood that a new impulse can be inhibited decreases. The authors also show that alcohol

    consumption alters the functioning of the reflective system but not of the impulsive one,

    so that under the influence of alcohol restraint standards may be affected (p. 168ff.).

    2.3 Conceptualization and measurement

    One of the influences that the SAT and the MFS have generated is that more and more

    studies including some measure of morality or acceptance of norms and also some mea-

    sure of deliberation, like self-control or cost-benefit calculation, are been published in

    criminology (see e.g. Cops and Pleysier 2014; Kroneberg et al. 2010; Pauwels and Svens-

    son 2011; Pauwels 2013; Pauwels and Svensson 2011; Pauwels 2013; Svensson et al. 2010;

    van Gelder and deVries 2014; Wikstrom 2009; Wikstrom and Svensson 2010; Wikstrom

  • Theoretical Background 14

    2012). Self-control and morality tend to be measured through self-reports (for the op-

    erationalization applied by Wikstrom and colleagues in most of their publications, see

    Wikstrom et al. 2012, 132ff.). Self-control is mostly analyzed using adapted versions of

    the scale proposed by Grasmick and colleagues (Arneklev et al. 1993; Grasmick et al.

    1993). Morality on the other side, tends to be measured with much more heteroge-

    neous instruments. Usually, people are asked how good or how bad they find a

    given behavior and/or how ashamed they would feel if getting caught doing some-

    thing wrong (see e.g. Wikstrom and Butterworth 2006).

    The problems of self-reports, especially when it comes to measuring sensible topics

    through surveys, are quite known (see e.g. Tourangeau 2000, 255ff.). Also particular

    problems with the Grasmick et al. (1993) self-control scale and with other instruments

    used in criminology to measure self-control, have been largely acknowledged (see e.g.

    Marcus 2004; Piquero 2008; Schulz and Beier 2012; Tittle et al. 2004). The first step in

    developing good measures is to clearly define the concepts of interest (see e.g. Groves

    2004, 50ff.). If the main interest lies in the interaction of some concepts, then both con-

    cepts need to be clearly defined as well as their interaction. The SAT makes a nice work

    in defining individual morality and self-control and also how they interact. According

    to Wikstrom and Treiber (2007) when an actor exerts self-control in the process of de-

    liberation, his or her executive capabilities in conjunction with situational variables will

    define the levels of self-control he or she possesses, and these executive capabilities reside

    in the brains prefrontal cortex. The prefrontal cortex can be further subdivided into

    two parts responsible mostly for habit -i.e. the dorsolateral prefrontal cortex (DLPFC)-

    and another responsible mostly for deliberation -i.e. the orbital frontal cortex (OFC)-

    (p. 253). These two subdivisions are then jointly responsible for the level of agency an

    actor will put into action.

    Keeping the interaction between propensity and exposition as explained by SAT, RIM

    adds a different interpretation of the interaction between self-control and individual

    morality. Explained through RIM, what is always activated is the impulsive system

    or the long-term memory. The associations created by this system are slowly learned

    through the history of the organism and provide quick answers to the environment de-

    pending on its needs and learning experiences (Hofmann et al. 2009, 164f.). In other

    words, the learned associative clusters are primarily dependent on experience and repe-

    tition and only secondarily on the reflective adherence to moral norms. In this sense, the

    tendency to impulsive behavior is closer to the perspective of Gottfredson and Hirschi

  • Theoretical Background 15

    (1990) on self-control as a trait responsible for criminality.5

    The premise made by Smith and DeCoster (2000) that the reflective system operates

    as a rule-based processing mode means that the reflective system uses symbolically

    represented and intentionally accessed knowledge as rules to guide processing (p. 111).

    These internalized rules are socially learned and culturally shared (p. 112), so that they

    can be in part equated to the morality and norms in the SAT and the MFS, respectively.

    What people believe to be good or bad (independent of their actual behavior) is stored

    in this system. The reflective system is also responsible to inhibit impulsive behavior

    when necessary (Hofmann et al. 2009, 165), so that the executive functions defined by

    SAT (i.e. as the capability to apply self-control when the morality of an actor contra-

    dicts the morality of the setting) would be part of this system (see also: Hofmann et al.

    2012). That is, self-control as defined by SAT would be the result of operations by the

    reflective system, while self-control (or low self-control) as seen by the GTC would be a

    consequence of how the impulsive system operates.

    In opposition to SAT and MFS, RIM defines no moral filter but an always activated

    impulsive system that may or may not trigger behavior depending on the strength of the

    activation of both systems and on situational moderators. In other words, there are two

    ways of processing information that operate in parallel. Whether the action selection

    process follows an automatic response or deliberation will normally depend on which sys-

    tem triggers action. The impulsive system is responsible for automatic responses while

    the reflective is responsible for deliberation and may be more easily disturbed through

    situational moderators (Strack and Deutsch 2004, 223).

    The last statement can be seen as contradictory with regard to SAT and MFS, because

    according to RIM moral norms get stored in the reflective system that is responsible

    for deliberation, whereas the SAT and the MFS state that strongly internalized moral

    norms would predict automatic action selection. This contradiction might be explained

    through a theoretical and a methodological argument.

    From a theoretical point of view, the reflective system relies on the impulsive one to

    operate (but not the other way around; Strack and Deutsch 2004, 223). This means

    that the reflective system is in part defined by the impulsive one. Strong internalized

    values are expected to be stored in both systems (for a very nice in deep discussion

    about how rational contents can get stored in the impulsive system and still be seen

    5It should be noted that according to Hofmann et al. (2009), trait self-control and impulsive determi-nants of behavior are two different things (p. 170). Nevertheless Gottfredson and Hirschi (1990) includeimpulsive behavior as one of the manifestations of low self-control (p. 90).

  • Theoretical Background 16

    as rational, see: Sauer 2012). And even in cases of modifying routines, according to

    the RIM the links made in the impulsive system are stable but can be changed gradually

    through learning (Strack and Deutsch 2004, 223). This can be achieved through repe-

    tition and through a process that is referred as the process of consolidation, i.e. the

    process through which newly formed memory is transferred by repeated presentation

    from the fast binding to the slow-learning system (Smith and DeCoster 2000, 110).

    Kahneman and Frederick (2002) also make the case for the transmission of contents

    between systems: complex cognitive operations eventually migrate from System 2 to

    System 1 as proficiency and skill are acquired (p. 51).

    It can be hypothesized that newly learned moral norms can get strongly internalized

    through this process of consolidation that changes the impulsive system. Consequently,

    it would be expected that someone who strongly supports right and wrong as defined by

    society should also have low impulsivity with respect to the particular behavior, which

    leads to the methodological argument. In order for a measure of impulsivity to be valid

    it needs to be specific to the temptation of interest, in this case violence, and each sys-

    tem should be measured by employing different instruments (Hofmann et al. 2009, 167f.).

    Figure 2.3: The Reflective-Impulsive Model (RIM)

    ReflectiveSystem (RS)

    (executive capabilities)

    ImpulsiveSystem (IS)(trait impulsivity)

    RS*IS*SM(state self-control)

    self-control

    outcome

    social/selfcontrol link

    SituationalModerators (SM)

    EnvironmentalCharacteristics

    situation

    variablerationality

    process ofconsolidation

    The model to be tested in this study is summarized in Figure 2.3. In short, the impulsive

    system produces impulsive behavior that can be restrained by the reflective system.

    The outcome of this fight is also affected by situational and dispositional moderators

    (Hofmann et al. 2009, 168ff.). The trait responsible for the ability to exert self-control

    are the executive capabilities as defined by SAT. The trait responsible for the tendency

    to act impulsively, is the trait of impulsivity and can be equated to the underlying

  • Theoretical Background 17

    definition of self-control in GTC.6 Impulses (as opposed to trait of impulsivity) arise

    when a latent motivation ... meets an activating stimulus (Friese and Hofmann 2009,

    796). This implies that measures of impulsive determinants of behavior need to be

    specific to the temptation of interest (Hofmann et al. 2009, 167). In the same way, state

    self-control is dependent on the characteristics of the situation. Ideal measures of the

    complete RIM should point at all these elements and their interplay so that states and

    their determinants can be assessed and their effect on crime understood.

    2.4 Research question and hypotheses

    The perspective on integration adopted in this study follows SATs and MFSs example,

    i.e. integration is pursued through the adoption of a theory of action, and not through the

    more pure forms of theoretical integration (like a propositional integration respecting

    each central argument of the component theories, and a cross-level integration capable of

    explaining crime at the level of individuals as well as crime rates). Of the alternatives to

    integration revisited in the previous pages, the one to be applied in this study resembles

    what Thornberry (1989) defines as theoretical elaboration because a control perspec-

    tive is chosen as a starting point. The dependent variable to be explained stays at the

    level of individuals but environmental and individual characteristics, proved by crimi-

    nology theories to predict crime, are to be linked through a dual-system theory of action.

    The theoretical framework to be applied centers on the interaction between individual

    and setting as explained by the SAT. However the interpretation of the interaction be-

    tween self-control and individual morality differs in the RIM. Although the concepts of

    self-control and morality and their operationalizations are similar to the ones applied by

    most previous studies and also by the SAT, the framework used here changes the order

    in which these factors predict acts of crime. The measure of self-control will be used

    as a proxy to impulsive determinants of behavior, while morality is considered to be a

    measure of the reflective determinants of behavior.7

    The main focus in this study is on the predictive capability of the measures of both

    systems (reflective and impulsive) and their interaction as shown in Figure 2.3. Acts of

    violence are to be predicted. Accordingly, the main research question is:

    6In order to prevent confusion, any use of the word control should be avoided when referring tothe impulsive system, because the reflective is the one that restrains. Nevertheless, whether to definethis trait as self-control or impulsivity is more a question of focus, because both look at the same coin,but from a different perspective (Friese and Hofmann 2009, 796).

    7It should also be stressed that according to the RIM impulsive determinants of behavior shouldnot be measured using self-reports. In this study classical measures of self-control are considered to beproxies to the determinants of impulsive behavior, but one should be cautious as to its assumptions.

  • Theoretical Background 18

    Can acts of violence be explained as outcomes of self-control that depend mainly on the

    interplay of three determinants: reflective and impulsive determinants of behavior and

    situational moderators?

    The first hypothesis to be tested is that the interaction between determinants of both

    systems predict acts of violence better than their non-interacted measures. This hy-

    pothesis relies also on the assumption that each system has a significant effect on acts of

    violence. With respect to the role of situational moderators, the effect of intoxication

    will be tested. It is expected that it has a significant effect on acts of violence and

    that the interaction between the determinants of behavior in both systems is moder-

    ated by this situational variable. Taking into account the arguments of SAT, MFS and

    RIM, this study considers four possible combinations between reflective and impulsive

    determinants of behavior that may lead to either more automatically or more controlled

    action selection (see Table 2.1). When the norms are strongly internalized (as verbalized

    through self-report) and the impulsivity is low, an automatic adherence to the moral

    rules of society is expected. When there is rejection to the norms of society and also high

    impulsivity, an automatic response is expected in the form of acts of violence. In the two

    remaining cases, i.e. strong acceptance of moral norms and high impulsivity, or strong

    rejection of moral norms and low impulsivity, a fight between systems is expected in

    order to decide who triggers action. As a consequence, a more influential moderation of

    situational variables is expected for these last two combinations. The second hypothesis

    deals with this idea.

    Table 2.1: Impulsive and controlled outcomes: four scenarios

    high impulsivity low impulsivity

    pro violence automatic (+) fight (social control)

    against violence fight (state self-control) automatic ()

    Because according to the RIM the impulsive system is always activated while the reflec-

    tive system may be disengaged from processing information (asymmetry as defined

    by Strack and Deutsch 2004, 223) and the associative processing mode draws solely on

    the slow-learning system, [while] the rule-based processing mode uses both memory sys-

    tems, not just the fast-learning one (Smith and DeCoster 2000, 111), it is assumed that

    the information stored in the impulsive system should precede the information stored

    in the reflective system. In other words, it is expected that the effect of the impulsive

    determinants of behavior is mediated by the reflective ones. This will be tested in the

    third hypothesis.

  • Theoretical Background 19

    With respect to the role of the environment, it has been largely argued that charac-

    teristics of the context, like school climate, have an impact on acts of crime (see e.g.

    Gottfredson 2001; Siegmunt 2012). In this study it is assumed that the school setting

    should have a direct effect on the reflective determinants of behavior but not on the im-

    pulsive ones. Specifically this means that characteristics of the environment, should have

    a direct effect on the morality of pupils (i.e. their opinion about right and wrong) and

    their morality should have a causal effect on acts of crime (moderated by self-control).

    This is the fourth and final hypothesis.

    Formally, the following hypotheses will be tested:

    H1: Reflective and impulsive determinants of behavior interact to predict self-control outcomes.

    H2: Intoxication moderates the interaction between impulsive and reflective de-terminants of behavior.

    H3: The effect of impulsive determinants of behavior is mediated by the reflectiveones.

    H4: School climate effect on acts of violence is mediated by reflective determinantsof behavior.

  • 3. Methods

    In this chapter the data used is described, the operationalization of variables is ex-

    plained and measures of reliability are investigated. Finally the statistical techniques

    implemented are generally described.

    3.1 Data source

    Data from the second International Self-Report Delinquency (ISRD-2) study is used

    (Enzmann et al. 2010; Junger-Tas et al. 2012, 2010). The ISRD-2 is the follower of the

    ISRD-1 (Junger-Tas et al. 2003). The ISRD project is a cross-national survey with a

    comparative design that collects data on juvenile delinquency and victimization (Mar-

    shall and Enzmann 2012a, 21ff.). In its second wave, comparability standards have been

    improved and assessed (see e.g. Enzmann 2013).

    The sampled population are classes of grade 7 to grade 9 (students mostly between 12

    and 14 years old) in schools of 30 different countries (see Table 3.1 for the descriptive

    values of the general sample and each country). The sampling units are the classes,

    weighted by number of pupils. Representation at the level of cities and not of countries

    is pursued, with a goal of at least two medium to large cities by country (with exception,

    see Table 3.1). In order to keep the results of the different countries comparable, a

    standardized self-report survey is applied with emphasis on standardization of meaning

    and not of words (see e.g. Harkness et al. 2010). One of the main objectives of the

    ISRD-2, is the explanation of delinquent and criminal behavior through the test of

    criminological theories (Enzmann et al. 2010, 161).

    3.2 Operationalization

    3.2.1 Dependent variable

    The dependent variable is the life-time prevalence of at least one of three acts of violence:

    assault, group fight, carrying a weapon. The prevalences for each question and for the

    20

  • Methods 21

    Table 3.1: Sample description

    Country Cities Schools Classes % Included N Included

    Armenia 5 15 93 .977 1,997Aruba 1 10 29 .833 587Austria 7 45 125 .956 2,863Belgium 4 43 149 .900 2,077Bosnia/H. 2 37 85 .875 1,764Cyprus 5 16 102 .858 1,981Czech Rep. 3 91 160 .941 3,055Denmark 1 65 81 .879 1,210Estonia 3 100 129 .889 2,320Finland 1 44 77 .999 1,363France 3 23 66 .893 2,141Germany 7 68 158 .941 3,271Hungary 2 101 109 .939 2,069Iceland 1 26 32 .927 548Ireland 7 37 73 .884 1,381Italy 15 95 273 .956 5,064Lithuania 5 47 93 .939 2,042NL Antilles 2 33 100 .919 1,583Netherlands 17 40 114 .946 2,204Norway 3 41 83 .867 1,468Poland 7 46 90 .937 1,366Portugal 3 57 120 .944 2,470Russia 5 41 121 .954 2,206Slovenia 5 41 117 .936 2,091Spain 4 80 80 .904 1,617Suriname 2 87 111 .900 2,158Sweden 3 74 119 .894 2,040Switzerland 3 70 205 .969 3,531USA 4 15 148 .888 2,132Venezuela 5 47 94 .758 1,760

    Total 135 1,535 3,336 .919 62,359

    prevalence of at least one of the three acts (called violence) can be seen in Table 3.2. The

    valid cases for each question vary, because of omissions of only particular questions. The

    final violence prevalence includes each case that answered at least one of the violence

    related questions. The questions were formulated as follows (in the english version for

    USA):

    assault: Did you ever threaten somebody with a weapon or to beat them up, justto get money or other things from them?

    gr.fight: Did you ever participate in a group fight on the school playground, afootball stadium, the streets or in any public place?

    weapon: Did you ever carry a weapon, such as a stick, knife, or chain (not apocket-knife)?

  • Methods 22

    Table 3.2: Violence related prevalences by country

    Country assault valid gr.fight valid weapon valid violence valid

    Armenia .014 1,996 .184 1,983 .057 1,994 .198 1,997Aruba .028 577 .125 584 .107 582 .174 587Austria .022 2,855 .115 2,850 .061 2,850 .146 2,863Belgium .020 2,048 .131 2,046 .104 2,059 .184 2,077Bosnia/H. .009 1,759 .112 1,748 .029 1,752 .120 1,764Cyprus .018 1,965 .124 1,938 .026 1,951 .132 1,981Czech Rep. .006 3,047 .109 3,036 .072 3,041 .158 3,055Denmark .013 1,202 .116 1,194 .110 1,199 .179 1,210Estonia .018 2,311 .074 2,300 .095 2,313 .152 2,320Finland .007 1,363 .072 1,363 .076 1,363 .125 1,363France .023 2,128 .190 2,106 .080 2,124 .218 2,141Germany .043 3,251 .130 3,252 .099 3,247 .191 3,271Hungary .011 2,057 .089 2,038 .061 2,046 .129 2,069Iceland .009 547 .059 546 .057 547 .099 548Ireland .026 1,367 .249 1,361 .122 1,369 .285 1,381Italy .015 5,034 .151 5,028 .050 5,047 .171 5,064Lithuania .009 2,034 .086 2,033 .081 2,031 .141 2,042NL Antilles .020 1,575 .081 1,562 .078 1,568 .137 1,583Netherlands .030 2,196 .154 2,194 .098 2,192 .201 2,204Norway .014 1,466 .057 1,466 .057 1,463 .089 1,468Poland .010 1,363 .073 1,359 .069 1,360 .119 1,366Portugal .005 2,456 .088 2,454 .036 2,464 .109 2,470Russia .011 2,204 .084 2,195 .053 2,200 .117 2,206Slovenia .007 2,079 .068 2,077 .052 2,084 .105 2,091Spain .010 1,600 .096 1,605 .048 1,609 .119 1,617Suriname .013 2,134 .069 2,133 .067 2,137 .113 2,158Sweden .015 2,024 .074 2,017 .064 2,020 .111 2,040Switzerland .013 3,493 .086 3,485 .077 3,499 .135 3,531USA .021 2,112 .094 2,117 .096 2,116 .154 2,132Venezuela .011 1,724 .077 1,732 .028 1,743 .090 1,760

    Total .016 61,967 .110 61,802 .069 61,970 .149 62,359

    3.2.2 Independent variables

    3.2.2.1 Impulsive determinants of behavior

    Impulsive determinants of behavior will be measured through a shortened version of the

    self-control scale by Grasmick et al. (see Grasmick et al. 1993; Arneklev et al. 1993

    for the original scale and Marshall and Enzmann 2012b,a for a detailed description of

    the psychometric properties of the questions included in ISRD-2). Although impulsive

    determinants of behavior should not be measured through self-reported data (Hofmann

    et al. 2009, 167f.), it is expected that the self-control scale can serve as a proxy. The

    exercise presented here should be considered as a preliminary test of a dual-system

    perspective. The questions and subscales are as follow (answer categories: 1.agree fully;

    2.agree somewhat; 3.disagree somewhat; 4.disagree fully):

    Impulsivity (IM):1. I act on the spur of the moment without stopping to think.

  • Methods 23

    2. I do whatever brings me pleasure here and now, even at the cost of some

    distant goal.

    3. Im more concerned with what happens to me in the short run than in the

    long run.

    Risk-taking (RT):4. I like to test myself every now and then by doing something a little risky.

    5. Sometimes I take a risk just for the fun of it.

    6. Excitement and adventure are more important to me than security.

    Self-centeredness (CE):7. I try to look out for myself first, even if it means making things difficult for

    other people.

    8. If things I do upset people, its their problem not mine.

    9. I will try to get the things I want even when I know its causing problems for

    other people.

    Volatile temper (TE):10. I lose my temper pretty easy.

    11. When Im really angry, other people better stay away from me.

    12. When I have a serious disagreement with someone, its usually hard for me

    to talk about it without getting upset.

    First the four sub-scales previously presented are constructed through simple row mean

    calculation. In order for a respondent to get a valid value in each of the sub-scales, he

    or she must have answered at least two of the three composing questions. The final

    impulse scale is the simple row mean of the sub-scales. For the final scale, only cases

    with valid answers in all the sub-scales are included. Finally the impulse scale is me-

    dian centered and rescaled to standard deviation unit (see Table 3.3 for the descriptive

    statistics of the final scale before and after being standardized, and Figure 3.1 for the

    scales histogram; the correlations between items including the final scale is shown in

    the appendix in Table A.1). The scale reliability coefficient (Cronbachs ) of the final

    scale is .823.

    Table 3.3: Descriptive statistics: impulsive determinants of behavior (scale)

    Variable Mean Std. Dev. Min Q.25 Median Q.75 Max

    impulse 2.165 .601 1.000 1.750 2.167 2.583 4.000impulse (std) -.002 1.000 -1.940 -.693 .000 .693 3.048

  • Methods 24

    Figure 3.1: Histogram: impulsive determinants of behavior

    mean = .002

    impulsivecontrolled

    02

    46

    perc

    ent

    2 1 0 1 2 3

    3.2.2.2 Reflective determinants of behavior

    As a measure of the reflective determinants of behavior, pro-violence values have been

    asked through 5 items (see Marshall and Enzmann 2012a, 57; answer categories: 1.agree

    fully; 2.agree somewhat; 3.disagree somewhat; 4.disagree fully):

    1. A bit of violence is part of the fun

    2. One needs to make use of force to be respected

    3. If one is attacked, one will hit back

    4. Without violence everything would be much more boring

    5. It is completely normal that boys want to prove themselves in physical fights with

    others

    The reflect scale is generated by calculating the simple row mean of the five items. Only

    cases with three or more valid answers are included. The reflect scale is then median

    centered and rescaled to standard deviation unit (see Table 3.4 and Figure 3.2 for a

    description of the final scale; the correlations between items and final scale is shown in

    the appendix Table A.2). The scale reliability coefficient (Cronbachs ) is .705.

    Table 3.4: Descriptive statistics: reflective determinants of behavior (scale)

    Variable Mean Std. Dev. Min Q.25 Median Q.75 Max

    reflect 2.998 .661 1.000 2.600 3.200 3.400 4.000reflect (std) -.305 1.000 -3.326 -.907 .000 .302 1.210

  • Methods 25

    Figure 3.2: Histogram: reflective determinants of behavior

    mean = .305

    reject viol.accept viol.

    05

    1015

    perc

    ent

    3 2 1 0 1

    3.2.2.3 Situational moderators

    Situational variables are those that may influence the fight between systems. In other

    words, variables that may shift the likelihood of triggering action in favor of one of both

    systems. Characteristics of the situation like friends pushing a classmate to do something

    wrong may be considered. In this study a variable measuring life-time intoxication is

    included under the assumption that the consumption of alcohol and/or drugs should

    alter the inhibiting capabilities of the reflecting system. A value of one or yes, is

    assigned to someone who has been at least one time drunk (2 items) or has taken drugs

    (4 items). Cases having answered at least one of the items are included (see Table 3.5

    for the descriptive statistics).

    Table 3.5: Descriptive statistics: life-time intoxication (scale and items)

    Variable Obs Mean Std. Dev.

    life-time prev intoxication (scale) 62,359 .274 .446life-time prev drunk beer/wine 61,641 .234 .423life-time prev drunk spirits 61,556 .163 .369life-time prev hash 61,917 .088 .283life-time prev XTC 61,863 .013 .115life-time prev L/H/C/her/co 61,879 .010 .100

    3.2.2.4 Environmental variables

    School climate related characteristics (i.e. school disorganization) will be included, ag-

    gregated at the level of the school. These characteristics should be capable of influencing

    the pro-violence values of the pupils -i.e. their reflective system- and also on the long

  • Methods 26

    run -through the process of consolidation- their impulsive system. The following four

    items are included (answer categories: 1.not at all true; 2.not true; 3.true; 4.very true):

    1. There is a lot of stealing in my school.

    2. There is a lot of fighting in my school.

    3. Many things are broken or vandalized in my school.

    4. There is a lot of drug use in my school

    A scale at the level of pupils is first generated through row means of cases with three

    or more valid answers. This scale has an value of .748. A linear multilevel regression

    is estimated with this scale as dependent variable and no predictors, in order to get the

    value of the scale or its ecological reliability (Raudenbush and Sampson 1999). The

    following formula is used:

    =2u

    2u + (2e/

    Nn )

    =.152

    .152 + (.407/61,9133,336 )= .874

    where 2u is the between variance, 2e the within variance, N the size of the complete

    sample included in the analyses, and n the number of clusters. This scale is further

    aggregated at the level of classes using group means. The final scale at level of classes is

    then median centered and standard deviation rescaled (see Table 3.6 and Figure 3.3 for

    the descriptive statistics of the scale and Table A.3 for the correlations between items).

    Table 3.6: Descriptive statistics: school disorganization scale

    Variable Obs Mean Std. Dev. Min Q.25 Median Q.75 Max

    school disorg. (L1) 61,913 2.127 .746 1.000 1.500 2.000 2.500 4.000school disorg. (L2) 62,359 2.127 .414 1.000 1.833 2.103 2.409 4.000school disorg. (L2; std) 62,359 .058 1.000 -2.663 -.651 .000 .739 4.580

    3.2.3 Control Variables

    To avoid spurious relations between the dependent variable and the independent vari-

    ables of interest, control variables will be included. The controls represent all relevant

    variables in the prediction of acts of violence at hand and also of the reflective determi-

    nants of behavior. This is because of the mediation analyses (see the next section).

    Controls included are:

    Characteristics of individuals: gender: Are you male or female? (1 = male; 0 = female).

    age: How old are you? (continuous; between 11-18).

  • Methods 27

    Figure 3.3: Histogram: school disorganization scale (agg.)

    mean = .043

    disorderorder

    02

    46

    perc

    ent

    4 2 0 2 4

    migration: Generated out of three questions (cases with at least one valid

    answer included): Where you born in this country?; In what country was

    your mother born?; In what country was your father born? (1 = at least one

    member of family born in another country; 0 = else).

    Family related variables: violence at home: Have you ever experienced any of the following serious

    events? Repeated serious conflicts or physical fights between your parents,

    by parents we also mean step- or adoptive parents (1 = yes; 0 = no).

    traditional family structure: Are you living with your own mother and

    father? (1 = Yes, I live with my own mother and father; 0 = other).

    family bonding: Scale out of two questions (cases with at least one valid

    answer included): How do you usually get along with the man you live with

    (father, stepfather....)?; How do you usually get along with the woman you

    live with (your mother or stepmother)? (1 = not well at all, 2 = not so well,

    3 = rather well, 4 = very well; row mean, median centered and rescaled to

    standard deviation unit).

    Others: neighborhood disorganization: Scale out of five questions (cases with at

    least three valid answers included): There is a lot of crime in my neighbor-

    hood; There is a lot of drug selling; There is a lot of fighting; There are a lot

    of empty and abandoned buildings; There is a lot of graffiti (1 = not at all

  • Methods 28

    Table 3.7: Descriptive statistics: control variables

    Variable Mean Std. Dev. Min Q.25 Median Q.75 Max

    male .486 .500 .000 .000 .000 1.000 1.000migration .230 .421 .000 .000 .000 .000 1.000age 13.948 1.146 11.000 13.000 14.000 15.000 18.000violence at home .110 .313 .000 .000 .000 .000 1.000family bonding 3.642 .535 1.000 3.500 4.000 4.000 4.000family bonding (std) -.669 1.000 -5.612 -.935 .000 .000 .000family structure .732 .443 .000 .000 1.000 1.000 1.000grade 8.019 .817 7.000 7.000 8.000 9.000 9.000neigborhood disorg. 1.631 .704 1.000 1.000 1.400 2.000 4.000neigborhood disorg. (std) .329 1.000 -.568 -.568 .000 .852 3.691

    true, 2 = not true, 3 = true, 4 = very true; row mean, median centered and

    rescaled to standard deviation unit).

    school grade: Meta-data (categorical variable; 7th -reference-, 8th, 9th)

    3.3 Statistical analyses

    3.3.1 Multilevel analysis

    ISRD-2 data is of a multilevel nature. At least five levels can be recognized, from the

    lowest to the highest these are: pupils, classes, schools, cities, countries. Also coun-

    try clusters could be defined, for example with respect to decommodification (Esping-

    Andersen 1990). In this study, the dependent variable is the life-time prevalence of

    acts of violence, i.e. the outcome of a Bernoulli trial or a dummy variable. Therefore

    nonlinear models are the better choice. Because non-linear models are already complex,

    extra complexity should be avoided. In this case, random intercepts only at the level of

    schools are included. By clustering at the level of schools, a very big sample size at each

    level can be achieved and a better homogenization of the environmental conditions (see

    e.g. Oberwittler and Wikstrom 2009).

    Following Guo and Zhao (2000), the reliance on multilevel models has at least four ad-

    vantages: first multilevel analyses is the adequate framework for analyzing multilevel

    data, second it corrects for possible biases resulting from the clustering nature of the

    data, third it also corrects for standard errors, and fourth it allows to decompose the

    total variances of the dependent variable into variance explained at each level (p. 444f.).

  • Methods 29

    The estimator used in this study is maximum likelihood (MLE; see Winkelmann and

    Boes 2006, 44ff.).8 Under random sampling it is possible to assume independence be-

    tween observations and that all observations come from the same data generating pro-

    cess, so that they are identically independent distributed (iid). The probability of ob-

    serving yi given the unknown parameters can be described as the probability or density

    function of yi, i.e. f(yi; ). Because the observations are independent of each other, the

    joint probability function of the sample is the product of the individual probability func-

    tions, i.e. f(y1, ..., yn; ) =ni=1 f(yi; ).

    MLE changes the function of the random sample y1, ..., yn given , for a function of

    given the random sample y1, ..., yn. This leads to the likelihood function:

    L() = L(; y) =

    ni=1

    L(; yi) =

    ni=1

    f(yi; )

    where L(; yi) is the likelihood contribution of a given observation and L() = L(; y) =

    L(; y1, ..., yn) is the likelihood function of the whole sample.

    Once the likelihood function is defined, the estimation process consists of finding the pa-

    rameter estimates (i.e. ) that produce the maximum value for the likelihood function.

    The bigger the value of the likelihood function, the better the estimated parameters

    fit the sample. If the assumptions made for the maximum likelihood estimation are

    right, then maximum likelihood is consistent, asymptotic normal, and efficient (see e.g.

    Amemiya 1985, 115ff.).

    In the case of non-linear models, the reliance on multilevel models when the data is

    of a multilevel nature is more important than in linear models. The reason is that for

    non-linear models estimated with maximum likelihood, the consistency of the estimator

    depends on the likelihood function being specified correctly (see e.g. Greene 2012, 712ff.).

    In other words, heteroskedasticity in non-linear models does not only affect the standard

    errors, but also the consistency of the coefficients. Relying on robust standard errors is

    not really an option for non-linear models, because in the presence of heteroskedasticity

    the likelihood function is not specified correctly. While robust standard errors may cor-

    rect the standard errors, the coefficients may still be inconsistent. That is, while using

    robust standard errors for non-linear models that are correctly specified is not necessary,

    their use in models that are wrongly specified could produce an appropriate asymptotic

    8For the ease of explanation, a one level empty model is explained here (i.e. yi instead of yij andno covariates included). The same results applied here work if covariates are included (i.e. f(yi|xi; )).The extra difficulties of multilevel models are discussed later.

  • Methods 30

    covariance matrix for an estimator that is inconsistent (see Freedman 2006).

    At least two different formulations are commonly used to describe non-linear models: as

    random utility models for individual choice and as a latent regression model. Here the

    latent formulation is explained (taken mostly from Cameron and Trivedi 2005, 475ff.;

    Goldstein 2011, 111ff.; Greene 2012, 686ff.; Rabe-Hesketh and Skrondal 2012, 520ff.;

    Snijders and Bosker 1999, 223f.; Winkelmann and Boes 2006, 95ff.). The description

    that follows is limited to random intercept models only, i.e. each cluster (school) may

    differ with respect to the intercept but the slopes are fixed across clusters.

    Because the observed outcome is a binary response variable that has a Bernoulli prob-

    ability function, i.e.:

    f(yij |xij , uj) = piyijij (1 piij)1yij yij = 0, 1

    where piij = P (yij = 1|xij , uj), a link function is needed that allows to link thepredictions in the observed outcome to the expected value of a latent (unobserved)

    continuous variable:

    yij = xij + uj + eij

    where xij = 0 +1x1ij + ...+kxkij and xij can be a variable at the level of individuals

    or at the higher level (i.e. x.j or generally in the literature zj).

    The different models for binary response variables, differ in the way that piij is param-

    eterized through the assumption about the distribution of eij . The link between latent

    and observed models can be seen as follows:

    yij =

    1 if yij 00 if yij < 0where yij is the observed binary variable and y

    ij the latent one. It follows:

    piij = P (yij 0|xij , uj) = P (xij + uj + eij 0|xij , uj)

    = P (eij (xij + uj)|xij , uj)= 1 P (eij < (xij + uj)|xij , uj)

    where the last equality is valid for symmetric distributions and shows that the observed

    variable is used to model the probability of the latent equation of exceeding the threshold

  • Methods 31

    of zero9. When assuming that eij has a standard logistic distribution, i.e. a logistic

    distribution with mean 0 and variance pi2/3:

    P (eij < a) =exp(a)

    1 + exp(a)= (a)

    a multilevel logit model is relied on. The conditional function of the logit model is given

    by:10

    1 P (eij < (xij + uj)|xij , uj) = 1exp[(xij + uj)]

    1 + exp[(xij + uj)]=

    exp(xij + uj)1 + exp(xij + uj)

    so that

    piij = G(xij + uj) =

    exp(xij + uj)1 + exp(xij + uj)

    = (xij + uj)

    Applying some algebra,

    piij =exp(xij + uj)

    1 + exp(xij + uj)

    piij + piijexp(xij + uj) = exp(x

    ij + uj)

    piij = exp(xij + uj) piijexp(xij + uj)

    piij = exp(xij + uj)(1 piij)

    piij1 piij = exp(x

    ij + uj)

    ln

    (piij

    1 piij

    )= xij + uj

    The logit link function is then defined as logit(piij) = ln(piij/(1 piij)).

    This is only one of many possible functions G(xij+uj). For example, assuming that eijhas a standard normal distribution, leads to the probit model with the function (xij+

    uj). Independently of the assumption about the distribution of eij , the likelihood of

    cluster j would be

    nji=1

    [G(xij + uj)]yij [1G(xij + uj)]1yij

    If the random intercepts uj were observed, this likelihood would be enough to estimate

    the parameters in the model. But because they are unobserved, a solution is needed to

    solve for the fact that piij is conditional on uj , i.e. that piij = G(xij + uj) = P (yij =

    9Using zero as a threshold is an innocent assumption, as far as the model contains a constant term(Greene 2012, 686).

    10Keep in mind that,exp(a)

    1 + exp(a) 1

    1 + exp(a) .

  • Methods 32

    1|xij , uj). Treating the uj as an unobserved normally distributed and uncorrelated ran-dom variables, i.e. uj N(0, 2u),11 and relying on the theorem from Bayes,12 allows tointegrate the random intercepts out, so that piij is no longer conditional on uj (this solu-

    tion is known as the Butler and Moffitts method and is also applied to estimate random

    effects non-linear panel models; see e.g. Greene 2012, 582). Formally, the joint proba-

    bility of all responses for cluster j conditional on the random intercept and covariates is

    given by:

    P (yj |xj) =P (yj |xj , uj)(uj)duj

    However the density unconditional on uj , i.e. P (yj |xj), has no closed expression. Dif-ferent options exist to solve for this problem, e.g. numerical integration relying on

    quadrature approximation (like Gauss-Hermite). In this study mean-variance adaptive

    GaussHermite quadrature is used (the default in Stata), which has the advantage of

    relying on the maximum likelihood estimation, so that fit measures based on maximum

    likelihood can be used after estimation (e.g. BIC and AIC criterion).

    The marginal likelihood is finally given by the product of the marginal joint probabilities

    of the responses in each cluster:

    L(, 2u) =Nj=1

    P (yj |xj)

    With respect to the results presented in this study, three considerations should be kept

    in mind. First, multilevel models can produce predictions of: only the fixed part, only

    the random part, or both. In this study only the fixed part is included to estimate

    predicted probabilities and marginal effects. This implies fixing the random intercept at

    zero, its theoretical mean value.

    Secondly, the model is non-linear multiplicative (while OLS is linear additive), which

    implies that marginal effects are conditional on the values of the variable of interest and

    also on the values of all the other covariates in the model (see e.g. Winkelmann and

    11The assumption that E(uj) = 0 produce no loss of generality as long as an intercept is included inthe model (see: Wooldridge 2010, 612).

    12The theorem from Bayes states that, for two random variables X,Y , the conditional density of Xgiven Y = y, equals the joint density of X,Y divided by the marginal density of Y (see e.g. Mosler andSchmid 2006, 27ff.). Formally,

    fx|y(x, y) =fxy(x, y)

    fy(y)

    so that,fxy(x, y) = fx|y(x, y)fy(y)

  • Methods 33

    Boes 2006, 104f.). For continuous variables this looks as follows:13

    pi

    xh=G(x)xh

    =