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Investigating the Functional Form of the Self-control–Delinquency Relationship in a Sample of Serious Young Offenders

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Abstract

Objective

This work further examines the functional form of the self-control–delinquency relationship as an extension of recent work by Mears et al. (J Quant Criminol, 2013). Given the importance of the authors’ conclusions regarding the nonlinear relationship between these two variables and the recognition that there are some potential limitations in the sample and assumptions required for the analytic methods used, we apply both similar and alternative techniques with a data set comprised of serious youthful offenders to determine whether key findings can be replicated.

Methods

Data from the Pathways to Desistance study, which comprise extensive individual and social history interviews with 1,354 offenders over multiple waves spread out over 84 months, is utilized in this analysis. These data are well-suited to investigating the questions of interest as the target population comprises youth with offending histories that are more extensive than those likely to be found in general surveys of adolescents. The analyses consider the self-control–delinquency relationship in an alternative sample with the previously used Generalized Propensity Score (GPS) procedure, which requires strong assumptions, as well as nonparametric regression which requires far weaker assumptions to consider the functional form of the self-control–delinquency relationship.

Results

The results generally show that the identified functional form of the self-control–delinquency relationship seems to be at least partly dependent on aspects of the modeling of dose–response associated with GPS procedures. When nonparametric general additive models are used with the same data, the relationship between self-control and delinquency seems to be approximately linear.

Conclusions

Identifying functional form relationships has importance for many criminological theories, but it is a task that requires that the balance of model assumptions to exploratory data analysis falls toward the latter. Nonparametric approaches to such questions may be a necessary first step in learning about the nature of mechanisms presumed to be at work in important explanations for crime and criminality.

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Notes

  1. To be clear, it is likely that the ADD Health data have generalizability over the larger range of the self-control continuum, yet to more precisely identify a lower threshold, one would be interested in a very restricted range of this continuum, which would presumably be well-populated in an offender sample.

  2. An identification problem occurs when reasonable inferences cannot be drawn even when the researcher has access to very large (or infinite) sample sizes. This is in contrast to questions of statistical inference, which aim to draw weaker conclusions from finite samples.

  3. Some prior research has identified important distinctions in the self-control-delinquency relationship in offender samples as opposed to youth from general population samples suggesting a need to consider generalizability in the measurement and observed effects across subpopulations in a substantive sense (see, e.g., DeLisi et al. 2003).

  4. This is an extension of the analysis Mears and colleagues' describe where they removed 5 % of cases at either end of the distribution, which identified a similar trend to their Fig. 2. While it is somewhat unexpected, it is intuitive that a near-identical trend would still be seen when a relatively small proportion of cases is removed at either end of the distribution. However, reaching that same conclusion when restricting the analysis to the portion of the data that displayed a linear trend previously is counterintuitive as the process should not produce a similar trend if we are capturing an unfiltered picture of the relationship between self-control and delinquency without boundary bias.

  5. This sensitivity analysis approach in some sense parallels the approach taken by Kluve et al. (2012) in the “Robustness” section of their paper as far as considering the impact of removing certain covariates representing second-order moments from the dose–response model.

  6. Ostensibly, the use of more terms in the parametric specification would seem to imply greater flexibility and fewer assumptions (since the high degree of parameterization would presumably allow flexible results). Yet we seem to be observing the opposite, namely that the results are sensitive to the parameterization assumptions.

  7. Information regarding the rationale and overall design of the study can be found in Mulvey et al. (2004), while details regarding recruitment, a description of the full sample, and the study methodology are discussed in Schubert et al. (2004). All data used in this analysis are publicly available through Mulvey (2012) and our syntax is available upon request.

  8. Although there are limitations in dichotomizing key variables (MacCallum et al. 2002), the Mears et al. work was based on limited dependent variables (a truncated count and a dichotomy) so that approach was utilized here to ensure as much comparability as possible.

  9. Given the question of temporal order and the fact that Gottfredson and Hirschi (1990) view substance use as an “analogous behavior” and thus an outcome measure in their theory, we did not include alcohol use as in the Mears et al. study (see Caliendo and Kopeinig 2008; Rosenbaum 1984).

  10. For more detailed information on measures and constructs, interested individuals are encouraged to visit the study website (http://www.pathwaysstudy.pitt.edu).

  11. This parallels Berk’s (2004) suggested best practices for using multiple regression as a tool for description and learning about relationships as opposed to a method for causal inference.

  12. For further information on nonparametric regression, see Fox (2000a, 2000b).

  13. GAM generalizes the linear model by modeling E[Y|X] = s 0 + s 1(X), where s 1(·) is any smooth function, here estimated using smoothing splines.

  14. Balance is evaluated at three cut points in the GPS process such that the propensity score, comprising the potential treatment values, is segmented into intervals and then the median of the GPS for each of those groups is evaluated relative to the others in terms of the differences in covariate values for those that fall into the focal treatment interval and those that are assigned to that interval by virtue of their propensity score but actually belong to a different treatment interval (Bia and Mattei 2008; Hirano and Imbens 2004). Other authors stress the importance of assessing whether common support conditions are met in the context of GPS (Flores et al. 2012; Kluve et al. 2012) and recent work has attempted to integrate those tests into the Stata program as well (Bia et al. 2013).

  15. Two technical notes on estimation bear mentioning. First, since the outcome is dichotomized, we use a standard logit link function in the estimator. Second, a typical concern with many nonparametric estimators is over-fitting or under-fitting the model, either of which may obscure results. We address this issue by using cross-validation to ensure optimal fit in the R package, Mixed GAM Computation Vehicle with GCV/AIC/REML smoothness estimation and GAMs by REML/PQL (MGCV), developed by Wood (2006).

  16. In an effort to estimate GAM models that were similar to the parametric specification utilized in GPS, we did also analyze variants of the nonviolent and violent delinquency models that included an interaction term. That variable was treated parametrically in GAM due to the fact that it is a nonadditive term (see Fox 2008). The patterns in those plots were similar to those shown in Figs. 5, 6 and 7, except that there is a slight inflection for the upper range of self-control for nonviolent offending. That pattern becomes nearly linear when the interaction term is removed from the model (as shown in Fig. 7).

  17. When it is appropriate to the question, researchers applying a GPS-like method might look at the works by Flores et al. (2012) and Kluve et al. (2012) for advice on checking key assumptions and examining sensitivity.

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Acknowledgments

This study employs data from Mulvey, Edward P. Research on Pathways to Desistance (Maricopa County, AZ and Philadelphia County, PA): Subject Measures, 2000–2010. ICPSR29961-v2. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor], 2013-01-07. doi:10.3886/ICPSR29961.v2. We wish to thank Carol Schubert for her assistance in compiling and transferring the data and members of the Pathways to Desistance research group for helpful comments on an early concept paper and Ray Paternoster and the anonymous reviewers for useful feedback on later versions of this work. All interpretations and conclusions reached in this work are those of the authors. Additionally, a portion of this article uses data from ADD Health, a program project designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris, and funded by a Grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 17 other agencies. Special acknowledgment is due to Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Persons interested in obtaining data files from ADD Health should contact ADD Health, Carolina Population Center, 123 W. Franklin Street, Chapel Hill, NC 27516-2524 (addhealth@unc.edu). No direct support was received from Grant P01-HD31921 for this analysis.

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Authors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, USA

    Christopher J. Sullivan

  2. University of Maryland, College Park, MD, USA

    Thomas Loughran

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  1. Christopher J. Sullivan
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Correspondence to Christopher J. Sullivan.

Appendix

Appendix

See Table 4.

Table 4 Bivariate correlations for key study measures and covariates
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Sullivan, C.J., Loughran, T. Investigating the Functional Form of the Self-control–Delinquency Relationship in a Sample of Serious Young Offenders. J Quant Criminol 30, 709–730 (2014). https://doi.org/10.1007/s10940-014-9220-y

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