Journal of Quantitative Criminology

, Volume 31, Issue 1, pp 93–123 | Cite as

Is the Shape of the Age-Crime Curve Invariant by Sex? Evidence from a National Sample with Flexible Non-parametric Modeling

Original Paper



Prior theoretical scholarship makes strong assumptions about the invariance of the age-crime relationship by sex. However, scant research has evaluated this assumption. This paper asks whether the age-crime curve from age 12–30 is invariant by sex using a contemporary, nationally representative sample of youth, the National Longitudinal Survey of Youth 1997 cohort (NLSY97).


To address the limitations of the existing empirical literature, a novel localized modeling approach is used that does not require a priori assumptions about the shape of the age-crime curve. With a non-parametric method—B-spline regression, the study models self-report criminal behavior and arrest by sex using age as the independent variable, and its cubic spline terms to accommodate different slopes for different phases of the curve.


The study shows that males and females have parallel age-crime curves when modeled with self-report criminal behavior variety score but they have unique age-crime in the frequency of self-report arrest. Group-based trajectory analysis is then used to provide a deeper understanding of heterogeneity underlying the average trends. The onset patterns by sex are quite similar but the post-peak analyses using the early onset sample reveal different patterns of desistance for arrest by sex.


The study found evidence of relatively early and faster desistance of arrest among females but little difference exists for the variety of criminal behaviors. Implications and future directions are discussed.


Age-crime curve Sex Non-parametric Spline regression Group-based trajectory modeling 



The author would like to thank Shawn Bushway, Justin Pickett and the anonymous reviewers of this manuscript for their advice and helpful comments on this research.


  1. Andersson F, Levander S, Svensson R, Levander MT (2012) Sex differences in offending trajectories in a Swedish cohort. Crim Behav Ment Health 22(2):108–121CrossRefGoogle Scholar
  2. Apel R, Kaukinen C (2008) On the relationship between family structure and antisocial behavior: parental cohabitation and blended households. Criminology 46(1):35–70CrossRefGoogle Scholar
  3. Apel R, Sweeten G (2010) Propensity score matching in criminology and criminal justice. In: Weisburd D, Piquero AR (eds) Handbook of quantitative criminology, 1st edn. Springer, New YorkGoogle Scholar
  4. Apel R, Paternoster R, Bushway SD, Brame R (2006) A job isn’t just a job: the differential impact of formal versus informal work on adolescent problem behavior. Crime Delinq 52(2):333–369CrossRefGoogle Scholar
  5. Apel RJ, Bushway SD, Brame R, Haviland A, Nagin DS, Paternoster R (2007) Unpacking the relationship between adolescent employment and antisocial behavior: a matched samples comparison. Criminology 45(1):67–97CrossRefGoogle Scholar
  6. Apel R, Bushway SD, Paternoster R, Brame R, Sweeten G (2008) Using state child labor laws to identity the causal effect of youth employment on deviant behavior and academic achievement. J Quant Criminol 24:337–362CrossRefGoogle Scholar
  7. Beck AJ, Shipley BE (1989) Recidivism of prisoners released in, 1983. U.S. Department of Justice: Bureau of Justice Statistics, Washington, DCGoogle Scholar
  8. Bergman LR, Andershed A (2009) Predictors and outcomes of persistent or age-limited registered criminal behavior: a 30-year longitudinal study of a Swedish urban population. Aggress Behav 35:164–178CrossRefGoogle Scholar
  9. Bersani BE (2012) An examination of first and second generation immigrant offending trajectories. Justice Q iFirst Article, 1–29Google Scholar
  10. Bishop DM, Frazier CE (1992) Gender bias in juvenile justice processing: implications of the JJDP Act. J Crim Law Criminol 82(4):1162–1186CrossRefGoogle Scholar
  11. Block CR, Blokland AAJ, van der Werff C, van Os R, Nieuwbeerta P (2010) Long-term patterns of offending in women. Fem Criminol 5(1):73–107CrossRefGoogle Scholar
  12. Blokland AJ, Nieuwbeerta P (2005) The effects of life circumstances on longitudinal trajectories of offending. Criminology 43(4):1203–1240CrossRefGoogle Scholar
  13. Blokland AJ, Nagin DS, Nieuwbeerta P (2005) Life span offending trajectories of a dutch conviction cohort. Criminology 43(4):919–954CrossRefGoogle Scholar
  14. Brame R, Piquero AR (2003) Selective attrition and the age-crime curve. J Quant Criminol 19(2):107–127CrossRefGoogle Scholar
  15. Britt C (1992) Constancy and change in the US. Age distribution of crime: a test of “Invariant hypothesis”. J Quant Criminol 8(2):175–187CrossRefGoogle Scholar
  16. Britt C (1994) Model specification and interpretation: a reply to Greenberg. J Quant Criminol 10(4):375–379CrossRefGoogle Scholar
  17. Bushway SD, Sweeten G, Nieuwbeerta P (2009) Measuring long term individual trajectories of offending using multiple methods. J Quant Criminol 25:259–286CrossRefGoogle Scholar
  18. Chow GC (1960) Tests of equality between sets of coefficients in two linear regressions. Econometrica 28(3):591–605CrossRefGoogle Scholar
  19. de Boor C (2001) A practical guide to splines. Springer, New YorkGoogle Scholar
  20. DeFleur LB (1975) Biasing influences on drug arrest records: implications for deviance research. Am Sociol Rev 40(1):88–103Google Scholar
  21. DeLisi M (2002) Not just a boy’s club: an empirical assessment of female career criminals. Women Crim Justice 13(4):27–45CrossRefGoogle Scholar
  22. D’Unger A, Land K, McCall P (2002) Sex differences in age patterns of delinquent/criminal careers: result from poisson latent class analyses of the Philadelphia cohort study. J Quant Criminol 18(4):349–375CrossRefGoogle Scholar
  23. Edin K, Kefalas M (2005) Promises I can keep: why poor women put motherhood before marriage. University of California Press, BerkeleyGoogle Scholar
  24. Eggleston EP, Laub JH (2002) The onset of adult offending: a neglected dimension of criminal career. J Crim Justice 30(6):603–622CrossRefGoogle Scholar
  25. Eilers PHC, Marx BD (1996) Flexible smoothing with b-splines and penalties. Statist Sci 11(2):89–102CrossRefGoogle Scholar
  26. Farrington D (1986) Age and crime. Crim Justice 7:189–250CrossRefGoogle Scholar
  27. Farrington DP, West DJ (1995) Effects of marriage, separation, and children on offending by adult males. Curr Perspect Aging Life Cycle 4:249–281Google Scholar
  28. Farrington DP, Loeber R, Elliott DS, Hawkins JD, Kandel DB, Klein MW, McCord J, Rowe DC, Tremblay RE (1990) Advancing knowledge about the onset of delinquency and crime. Adv Clin Child Psychol 13:283–342CrossRefGoogle Scholar
  29. Fry LJ (1985) Drug abuse and crime a Swedish birth cohort. Br J Criminol 25(1):46–59Google Scholar
  30. Gendreau P, Little T, Goggin C (1996) A meta-analysis of the predictors of adult offender recidivism: what works! Criminology 34(4):575–607CrossRefGoogle Scholar
  31. Gibbons JD (1993) Nonparametric statistics: an introduction. SAGE Publications, Newbury ParkGoogle Scholar
  32. Giordano PC, Cernkovich SA, Rudolph JL (2002) Gender, crime, and desistance: toward a theory of cognitive transformation. Am J Sociol 107(4):990–1064CrossRefGoogle Scholar
  33. Gove WR (1985) The effect of age and gender on deviant behavior: a biopsychosocial perspective. In: Rossi A (ed) Gender and the life course. Aldine Publishing Company, HawthorneGoogle Scholar
  34. Goethals J, Maes E, Klinckhamers P (1997) Sex/gender-based decision-making in the criminal justice system as a possible (additional) explanation for the underrepresentation of women in official criminal statistics—a review of international literature. Int J of Comp and Appl Crim Just 21(2):207–240Google Scholar
  35. Graham J, Bowling B (1995) Young people and crime. Home Office, LondonGoogle Scholar
  36. Greenberg DF (1977) Delinquency and the age structure of society. Crime Law Soc Change 1(2):189–223Google Scholar
  37. Greenberg DF (1994) The historical variability of the age-crime relationship. J Quant Criminol 10(4):361–373CrossRefGoogle Scholar
  38. Hagan J, Simpson J, Gillis AR (1987) Class in the household: a power-control theory of gender and delinquency. Am J Sociol 92(4):788–816CrossRefGoogle Scholar
  39. Hardle W, Bowman AW (1988) Bootstrapping in nonparametric regression: local adaptive smoothing and confidence bands. J Am Stat Assoc 83(401):102–110Google Scholar
  40. He X, Ng P (1999) COBS: qualitatively constrained smoothing via linear programming. Comput Stat 14(3):315–338CrossRefGoogle Scholar
  41. Hindelang MJ, Hirschi T, Weis JG (1981) Measuring delinquency. Sage Publications, Beverly HillsGoogle Scholar
  42. Hirschi T, Gottfredson M (1983) Age and the explanation of crime. Am J Sociol 89(3):552–584CrossRefGoogle Scholar
  43. Jennings WG, Maldonado-Molina MM, Piquero AR, Odgers CL, Bird H, Canino G (2010) Sex differences in trajectories of offending among Puerto Rican youth. Crime Delinq 56(3):327–357CrossRefGoogle Scholar
  44. Johnson WT, Petersen RE, Wells LE (1977) Arrest probabilities for marijuana users as indicators of selective law enforcement. Am J Sociol 83(3):681–699Google Scholar
  45. Jones BL, Nagin DS, Roeder K (2001) A SAS procedure based on mixture models for estimating developmental trajectories. Sociol Methods Res 29(3):374–393CrossRefGoogle Scholar
  46. Keele LJ (2008) Semi parametric regression for the social sciences. Wiley, West SussexGoogle Scholar
  47. Kerr DR, Capaldi DM, Owen LD, Wiesner M, Pears KC (2011) Changs in at-risk American men’s crime and substance use trajectories following fatherhood. J Marriage Fam 73:1101–1116CrossRefGoogle Scholar
  48. Kirk DS (2006) Examining the divergence across self-report and official data sources on inferences about the adolescent life-course of crime. J Quant Criminol 22(2):107–129CrossRefGoogle Scholar
  49. Kreager DA, Matsueda RL, Erosheva EA (2010) Motherhood and criminal desistance in disadvantaged neighborhoods. Criminology 48(1):221–258CrossRefGoogle Scholar
  50. Langan PA, Levin DJ (2002) Recidivism of prisoners released in, 1994. U.S. Department of Justice: Bureau of Justice Statitics, Washington DCGoogle Scholar
  51. Laub JH, Sampson RJ (2001) Understanding desistance from crime. Crime Justice 28:1–69Google Scholar
  52. Mazerolle P, Brame R, Paternoster R, Piquero A, Dean C (2000) Onset age, persistence, and offending versatility: comparisons across gender. Criminology 38(4):1143–1172CrossRefGoogle Scholar
  53. Mitchell O (2005) A meta-analysis of race and sentencing research: explaining the inconsistencies. J Quant Criminol 21(4):439–466CrossRefGoogle Scholar
  54. Moffitt TE (1993) Adolescence-limited and life-course-persistent antisocial behavior: a developmental taxonomy. Psychol Rev 100(4):674–701CrossRefGoogle Scholar
  55. Moffitt TE, Caspi A, Rutter M, Silva PA (2001) Sex differences in antisocial behaviour: Conduct disorder, delinquency, and violence in the Dunedin longitudinal study. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  56. Monahan TP (1970) Police dispositions of juvenile offenders: the problems of measurement and a study of Philadelphia data. Phylon (1960) 31(2):129–141Google Scholar
  57. Moore W, Pedlow S, Krishnamurty P, Wolter K (2000) National Longitudinal Survey of Youth 1997 (NLSY97) Technical Sampling ReportGoogle Scholar
  58. Nagin DS (2005) Group-based modeling of development. Harvard University Press, CambridgeGoogle Scholar
  59. Nagin DS, Land K (1993) Age, criminal careers, and population heterogeneity. Criminology 31(3):327–362CrossRefGoogle Scholar
  60. Nieuwbeerta P, Blokland AAJ, Piquero AR, Sweeten G (2011) A life-course analysis of offense specialization across age: introducing a new method for studying individual specialization over the life course. Crime Delinq 57(1):3–28CrossRefGoogle Scholar
  61. Opsomer JD, Breidt FJ, Claeskens G, Jauermann G, Ranalli MG (2008) Nonparametric small area estimation using penalized spline regression. J R Stat Soc Series B Stat Methodol 70(1):265–286CrossRefGoogle Scholar
  62. Osborne MR, Presnell B, Turlach BA (1998) Knot selection for regression splines via the LASSO. Comput Sci Stat 30:44–49Google Scholar
  63. Paternoster R, Bushway S (2009) Desistance and the “feared self”: toward an identity theory of criminal desistance. J Crim Law Criminol 99(4):1103–1156Google Scholar
  64. Piquero AR, Chung H (2001) On the relationships between gender, early onset, and the seriousness of offending. J Crim Justice 29(3):189–206CrossRefGoogle Scholar
  65. Piquero A, Brame R, Moffitt T (2005) Extending the study of continuity and change: gender differences in the linkage between adolescent and adult offending. J Quant Criminol 21(2):219–243CrossRefGoogle Scholar
  66. Rowe DC, Osgood DW, Nicewander WA (1990) A latent trait approach to unifying criminal careers. Criminology 28(2):237–270CrossRefGoogle Scholar
  67. Sampson RJ, Laub JH (2005) A life-course view of the development of crime. Ann Am Acad Pol Soc Sci 602(12):12–45CrossRefGoogle Scholar
  68. Shannon SKS, Adrams LS (2007) Juvenile offenders as fathers: perceptions of fatherhood, crime, and becoming an adult. Fam Soc J Contemp Soc Serv 88(2):183–191Google Scholar
  69. Skardhamar T, Lyngstad TH (2009) Family formation, fatherhood and crime: an invitation to a broader perspective on crime and family transitions. Discussion Papers No. 579, Statistics Norway, Research DepartmentGoogle Scholar
  70. Stattin H, Magnusson D, Reichel H (1989) Criminal activity at different ages: a study based on a Swedish longitudinal research population. Br J Criminol 29(4):368–385Google Scholar
  71. Steffensmeier D, Allan E (1996) Gender and crime: toward a gendered theory of female offending. Ann Rev Sociol 22:459–487CrossRefGoogle Scholar
  72. Stolzenberg L, D’Alessio SJ (2004) Sex differences in the likelihood of arrest. J Crim Justice 32:443–454CrossRefGoogle Scholar
  73. Sweeten GA, Apel RJ (2007) Incapacitation: revisiting an old question with a new method and new data. J Quant Criminol 23(4):303–326CrossRefGoogle Scholar
  74. Sweeten G, Bushway SD, Paternoster R (2009) Does dropping out of school mean dropping into delinquency? Criminology 47(1):47–91CrossRefGoogle Scholar
  75. Sweeten G, Piquero AR, Steinberg L (2013) Age and the explanation of crime, revisited. J Youth Adolesc 42:921–938CrossRefGoogle Scholar
  76. Telesca D, Erosheva EA, Kreager DA, Matsueda RL (2012) Modeling criminal careers as departures from a unimodal population age-crime curve: the case of marijuana use. J Am Stat Assoc 107(500):1427–1440CrossRefGoogle Scholar
  77. Tittle CR, Grasmick HG (1998) Criminal behavior and age: a test of three provocative hypotheses. J Crim Law Criminol 88(1):309–342CrossRefGoogle Scholar
  78. Uggen C (2000) Work as a turning point in life course of criminals: a duration model of age, employment and recidivism. Am Sociol Rev 65(4):529–546CrossRefGoogle Scholar
  79. Uggen C, Kruttschnitt C (1998) Crime in the breaking: gender differences in desistance. Law Soc Rev 32:339–366CrossRefGoogle Scholar
  80. Wang Y, Wahba G (1995) Bootstrap confidence intervals for smoothing splines and their comparison to Bayesian confidence intervals. J Stat Comput Simul 51(2–4):263–279CrossRefGoogle Scholar
  81. Wiesner M, Capaldi DM, Kim HK (2007) Arrest trajectories across a 17-year span for young men: relation to dual taxonomies and self-reported offense trajectories. Criminology 45(4):835–863CrossRefGoogle Scholar
  82. Zara G, Farrington DP (2009) Childhood and adolescent predictors of late onset criminal careers. J Youth Adolesc 28:287–300CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Criminal JusticeUniversity at AlbanyAlbanyUSA

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