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Self-Control Theory and Nonlinear Effects on Offending

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Abstract

Objectives

This paper examines Gottfredson and Hirschi’s (A general theory of crime. Stanford University Press, Stanford, 1990) self-control theory and develops theoretical arguments for why self-control may have a differential effect on offending depending on the level of self-control.

Methods

We test the argument that the association between self-control and violent offending (n = 5,681) and non-violent offending (5,672) is nonlinear by using generalized propensity score analyses of data from the National Longitudinal Study of Adolescent Health.

Results

The results indicate that self-control and offending are nonlinearly related in a manner that involves two thresholds. Specifically, among individuals at the high end of the self-control spectrum, there was little evidence of an association between variation in self-control and offending. However, among individuals in the middle part of the self-control spectrum, a positive association obtained—that is, the greater the level of low self-control, the greater the likelihood of offending. Finally, among individuals at the low end of the self-control spectrum, there was, once again, little evidence of an association.

Conclusions

A nonlinear association between self-control and offending may exist and have implications for self-control theory and tests of it. Studies are needed to investigate further the possibility of a nonlinear association and to test empirically the mechanisms that give rise to it.

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Notes

  1. Hirschi (2004: 548) has stated that “[a] change in the conceptualization of the sources of self-control and the cognitive processes it involves should have little effect on the empirical predictions derived from the theory.” Similarly, Piquero and Bouffard (2007: 7) have emphasized that the restatement does not fundamentally “change the general theory of crime.”

  2. Accordingly, Hirschi and Gottfredson (2008: 220), commenting on the suggestion that in some studies (e.g., Grasmick et al. 1993) opportunity measures outperform self-control measures and that self-control theory is thereby weakened, have observed: “Per contra, we would say, these findings show that the measure of opportunity is the better measure of control.”

  3. Some scholars have suggested that Gottfredson and Hirschi (1990) treat self-control as a dichotomy—one is either low in self-control or high in self-control (Tittle 1995)—but their description of self-control clearly suggests a concept that is continuous (Goode 2008: 13), which is how it is almost invariably measured in empirical research.

  4. Agnew (2005: 136) has argued that “while plausible, I tend to reject this [ceiling effect] argument based on the assumption that few people reach such extreme positions.” In reality, ceiling effects, as with “tipping point” effects, simply require, as a general matter, that some threshold be reached. The threshold does not have to be extreme.

  5. An extensive literature on self-control exists in psychology. Within this literature, there is not a universally agreed upon definition or measurement of self-control. Even so, Gottfredson and Hirschi’s (1990) discussion of self-control and their reconceputalization (Hirschi 2004; see also Hirschi and Gottfredson 2008) accords with many of the descriptions of self-control prevalent within this field (see, e.g., Hassin et al. 2010; Vohs and Baumeister 2011).

  6. There is no negative binomial option within Stata’s generalized propensity score procedure. To check that the results would be unlikely to be affected by use of the truncated measure, we compared results from regression models that used the truncated and untruncated measures, respectively, with those from negative binomial models using the truncated and untruncated measures, respectively. No appreciable difference in the results surfaced.

  7. Model fit was assessed using R2 (.069 for non-violent offending and .027 for violent offending). We compared specifications that included polynomials for self-control and the generalized propensity score and interactions between self-control and the generalized propensity score. The model in the paper was both the most parsimonious and had the best fit.

  8. We conducted ancillary analyses using a traditional regression modeling approach, including self-control and control variables and polynomial terms for self-control. When these results were graphed, they largely mirrored the generalized propensity score results shown here. We proceed with the latter modeling approach because it more directly addresses and highlights potential imbalances in covariates and makes no assumption about the functional form of the self-control and offending relationship (Hirano and Imbens 2004). In our study, the use of dichotomous or count measures of offending do not impose nonlinearity precisely because of this feature of the generalized propensity score approach (see, e.g., Doyle 2011; Kluve et al. 2012).

  9. The prediction model for self-control is provided in “Appendix 2”. As noted above, the model accords with that found in other studies of self-control using the same data. To conserve space, therefore, our discussion centers around the generalized propensity score results.

  10. The protocol outlined in discussions of generalized propensity score analyses involve “blocking on the score,” that is, dividing the treatment measure at two cut points to create three groups (see, e.g., Hirano and Imbens 2004; Bia and Mattei 2008; Kluve et al. 2012). We experimented with other cut-offs, creating, for example, five groups. The balance on covariates was largely the same regardless, suggesting that the balance was not sensitive to these cut points.

  11. The generalized propensity score procedure allows for specifying ordinal logistic regression models. We compared the results presented here with those using ordinal regression. The same pattern surfaced. However, with the latter approach, separate figures are generated for each level of the outcome (i.e., 0, 1, 2, 3, 4+). Given the similar results, we proceeded with the ordinary least squares estimates because they are simpler to present and discuss.

  12. It bears noting that, as Kluve et al. (2012: 19), echoing Hirano and Imbens (2004), have noted, “whether all the estimated coefficients associated with the [generalized propensity score] terms are equal to 0 can indicate whether the covariates introduce any bias.” If there are statistically significant coefficients involving the generalized propensity score, that indicates that the generalized propensity score is helpful in removing potential bias that results from the covariates. In Table 3, the statistically significant coefficients involving the generalized propensity score thus can be viewed as evidence that the methodology helps to reduce covariate-related bias in the estimation of the effect of self-control on offending.

  13. Full descriptions of the generalized propensity score modeling steps and procedures are detailed elsewhere. Hirano and Imbens (2004) provide proofs for their extension of the propensity score matching methodology to continuous treatments. Bia and Mattei (2008) describe the methodology and its implementation within Stata. Other works (e.g., Kluve et al. 2012) describe the methodology in greater detail and describe the advantages of generalized propensity score matching as compared to conventional regression-based approaches to estimating treatment effects. The advantages parallel those identified in using propensity score matching to estimate binary treatment effects (Rosenbaum and Rubin 1983).

  14. We conducted ancillary analyses in which we focused only on individuals who reported engaging in a non-violent offense. The argument here is that perhaps unique selection effects exist among those who commit non-violent offenses as compared to those who commit no such offenses. The same basic, nonlinear pattern emerged; the results are available upon request.

  15. We used the empirical Bayes fitted value as an estimate of offending propensity for each individual. This variable had a mean of 0 and ranged from −1.03 to 5.10. The reliability score for the overall offending intercept in our HLM model was .63. This score is slightly lower than those reported by Osgood and Schreck (2007) but is higher than ones reported in other studies using the same IRT approach (see, e.g., Sullivan et al. 2009; McGloin et al. 2011).

  16. We thank one of the reviewers for suggesting these additional lines of investigation.

  17. With generalized propensity score analyses, one does not specify separate functional forms to test which best predicts the outcomes. Rather, the focus is on achieving balance on the covariates and then, conditional on the generalized propensity score, generating predicted values. The resulting predicted values conformed with what was anticipated with hypothesis 3.

  18. A reviewer suggested analyzing multiple data sets to verify the results reported here. We agree, as noted in the text, that replication of this study is needed, with replication focusing on these data but also on the wide range of other data sets that exist on self-control and offending (Pratt and Cullen 2000; Goode 2008). In our view, the importance of other researchers replicating the findings here, and doing so with a wide range of other data sets and analytic approaches, is essential. On occasions when researchers report results from multiple studies, we may have greater confidence in the results. At the same time, the risk exists that the different studies a researcher selects are not representative of what would emerge from analyses of the larger universe of data sets. A central justification of meta-analyses, which have become more common in the past two decades, is precisely that they provide a more objective foundation on which to base particular claims. More generally, scientific progress results when independent researchers examine the same data and other data sets and arrive at similar results or determine the conditions under which results may vary; doing so reduces, but does not eliminate, the risk of confirmation bias (see Ioannidis 2005; Littell 2008; Eisner 2009). When a large number of data sets exist for studying a phenomenon, as is the case with self-control theory (see, e.g., Pratt and Cullen 2000; Goode 2008), this approach is especially important to ensure that findings are consistent across a range of researchers, measures, populations, and analytic approaches, and, conversely, to avoid situations whereby researchers unintentionally select data, measures, model specifications, and analytic approaches that favor one finding over another.

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Acknowledgments

We thank Avi Bhati, Michela Bia, Sam Field, Alessandra Mattei, Sonja Siennick, and Brian Stults, and especially the editors and anonymous reviewers, for their helpful suggestions and guidance. This research 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. We thank Avi Bhati, Michela Bia, Sam Field, Alessandra Mattei, Sonja Siennick, and Brian Stults, and especially the editors and anonymous reviewers, for their helpful suggestions and guidance

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  1. College of Criminology and Criminal Justice, Florida State University, 634 West Call Street, Tallahassee, FL, 32306-1127, USA

    Daniel P. Mears, Joshua C. Cochran & Kevin M. Beaver

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Correspondence to Daniel P. Mears.

Appendices

Appendix 1

See Table 4.

Table 4 Low self-control scale items
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Appendix 2

See Table 5.

Table 5 Generalized propensity score predictive model for low self-control
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Mears, D.P., Cochran, J.C. & Beaver, K.M. Self-Control Theory and Nonlinear Effects on Offending. J Quant Criminol 29, 447–476 (2013). https://doi.org/10.1007/s10940-012-9187-5

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