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

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An Erratum to this article was published on 25 May 2014

Abstract

Objectives

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).

Methods

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.

Results

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.

Conclusions

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.

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Notes

  1. Some scholars report that a higher percentage of females had their first offense in adulthood, compared to male who take up a higher proportion in adolescent first offense (Bergman and Andershed 2009; Eggleston and Laub 2002). Within sex groups, however, both males and females are predominantly adolescent onsetters. Onset difference may also be driven by the use of samples of serious offenders. DeLisi (2002) used a recidivist sample of at least 30 arrests per respondent, and found the mean age of arrest onset was 18 and 20 for males and females, respectively. It is possible that chronic male offenders tend to initiate delinquent behavior earlier than chronic female offenders. Stattin et al. (1989) found that females have a peak age of onset around 21–23 for first conviction, compared to males at 15–17. In this study, the key variable is conviction. Compared to self-reported data, this may reflect that more serious female offenses were sanctioned later in the youthful time rather than early on in adolescence.

  2. This could certainly be the result of differential treatment of women by the criminal justice system. Studies of extra-legal variation in sentencing outcomes routinely reveal large unexplained differences in the treatment of men and women in the criminal justice system (for a review, see Mitchell 2005).

  3. NLSY97 uses a total of 147 of primary sampling units from NORC’s 1990 national sample. These units are Standard Metropolitan Statistical Areas (SMSAs) or non-metropolitan counties. These SMSAs and counties were stratified by region, age, and race before selection to ensure representation. See https://www.nlsinfo.org/content/cohorts/nlsy97/intro-to-the-sample/sample-design-screening-process for more detailed information on sampling process.

  4. See NLSY97 Online Users’ Guide for sample description: http://www.nlsinfo.org/nlsy97/nlsdocs/nlsy97/97sample/introsample.html, http://www.nlsinfo.org/nlsy97/nlsdocs/nlsy97/maintoc.html.

  5. Respondents who were incarcerated during the time of interview were also interviewed either by phone or in person. These respondents do not exceed 1.5 % of the sample based on the details of the reason for non-interview item (Question name: RNI). This item specifies the number of respondents interviewed during incarceration beginning in Round 10, with respondents’ age ranging from 21 to 27. Thus it is reasonable to assume that the prevalence of incarceration is also similar to this rate before Round 10, which is not considered an issue for current analysis.

  6. See “Appendix 1” for an attrition analysis.

  7. Imputation is done on these event history variables on arrest in the dataset for missing values. The NLSY97 documentation from NORC is forthcoming.

  8. Not all arrests are followed with detailed questions in each survey round.

  9. Refer to de Boor (2001: 114) for detailed explanation of this method.

  10. Typically for B-spline, scholars who use large number of knots (k > 20) have developed penalties to accommodate overfitting (Eilers and Marx 1996; Opsomer, et al. 2008). In the current study, only 3 internal knots are used. Thus, no penalty is incorporated.

  11. The three steps are: choose the initial optimal number of internal knots; the stepwise knot deletion, and the stepwise knot addition in S-PLUS program. The latter two steps involve comparison of change in Akaike information criterion (AIC) when a knot is removed (or added).

  12. One way to produce interpretable confidence intervals for nonparametric estimates is by bootstrapping (Wang and Wahba 1995). Bootstrapping is a resampling technique that is used to obtain inferential information on the distribution of an estimator (Hardle and Bowman 1988). Thus, bootstrapping standard errors are obtained here for the purpose of estimating statistical significance when comparing the curves by sex.

  13. Stata Program does not allow weight in bootstrapping command due to varying sample composition from bootstrapping process.

  14. Round 1 sampling weight is used throughout the entire process by assigning this weight to all data across rounds. This practice has been adopted to NLSY97 by Sweeten and Apel (2007), Apel et al. (2006, 2007, 2008), to list just a few.

  15. The average values of the “weighting ratios” range from 0.92 to 1.12.

  16. The desistance analysis uses similar spline regression specifications as that of the general analysis. Difference lies only in the sample size, and the knot points for the age variable (See Table 3 for knots of general and desistance analysis).

  17. Stata Software user-written package (“traj”) for trajectory analysis is used. It is written by Bobby L. Jones, based on his work with Daniel Nagin (http://www.andrew.cmu.edu/user/bjones, see Jones et al. 2001 for methodology discussion).

  18. The 30-years old respondents are fewer than 15, and are thus dropped from descriptive analysis. However, they are included in the spline regression.

  19. Confidence intervals of all estimated curves are calculated and adjusted with design effect. They are available upon request. It is not shown on the graphs due to indiscernible difference from the estimated curves in current scale.

  20. The B-spline method is argued to constrain the upticks often seen with cubic polynomial functions. Nevertheless, there are visible upticks in current Fig. 2a, b. It is important to bear in mind that the number of observations at extremities of the curve is much smaller compared to the main body of the curve due to the cohort structure of the NLSY97. This fact is reflected in the much wider bounds at the ends of the curves.

  21. These respondents are either non-offenders or offending once only very early in the survey history.

  22. Chow tests are also performed for the subsamples. All reject the null hypothesis that the coefficients of the combined model are the same as that of the separate models.

  23. Additional analyses on separate items of the self-report criminal behavior (vandalism, attacking someone, and a pooled three-item property offense) were conducted to compare the sex difference in the age-crime curves of different types of offenses, with an attempt to examine underlying heterogeneity. All three sets of curves show a similar pattern with males reporting a higher level for each variable and the male and female curves are parallel.

  24. Respondents’ arrest charges were analyzed to examine whether there is a sex difference by arrest charge type. The charges reported in NLSY97 include eight categories: robbery, assault, theft, burglary, vandalism, other property offense, drug trafficking, and drug possession. All eight curve-comparisons show an earlier peak and a lower level for females than males to a varying degree. Thus, the conclusion of current study remains consistent regardless of the types of arrests.

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Acknowledgment

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.

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  1. School of Criminal Justice, University at Albany, 135 Western Ave., Albany, NY, 12222, USA

    Siyu Liu

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Appendices

Appendix 1: Attrition

Attrition started to occur since Round 2. Thus, attrition analysis is used to examine whether the respondents who drop out from the survey at any given round, regarded as “the attritted group,” would indicate non-randomness among major dependent variables. Table 7 below provides a yearly description of the number of respondents and attrition rate, which is shown to peak around Round 9 (for 2005). The concern is that the attritted group may differ significantly from the retained group in items of interest, therefore undermining the representativeness envisioned during the initial sampling.

Table 7 Attrition rate by round
Full size table

The only round that has complete data on all measure—Round 1—is used for statistical comparison on surveyed and attrited respondents of subsequent rounds. For example, we know who were interviewed and who attritted at Round 5. So dividing the entire sample into these two groups, the Round 1 data on the interested items are compared and tested. It is shown that respondents who attrited at Round 5 are significantly more likely to be females and less likely to be involved in substance use. No significance on the t tests of other variables is present. Other rounds with these two changing groups of respondents can be interpreted similarly (Table 8).

Table 8 Attrition comparison using round 1 items
Full size table

Appendix 2: Period Effect

Period effect refers to the influence specific to a particular historical time period (Farrington, 1986, p203). Because of the unavailability of individual official record for the respondents in the NLSY97, I use the official arrest data obtained from the Bureau of Justice Statistics Data Analysis Tools (Snyder, 2011), then compare the trends of arrest rate by gender from 1999 to 2009 corresponding to the study period of 1997–2009. Figure 6 shows little fluctuation in arrest rates by year from the official data for both males and females (Age 0–17). This official UCR data suggests that the study sample is collected during a relatively stable time period in a national backdrop that would not confound the age-crime curve from self-reported data NLSY97. Therefore, no alarming period effect should be considered.

Fig. 6
figure 6

Prevalence of BJS arrest estimates by year and gender. Data source FBI, Uniform Crime Reporting Program (Snyder et al. 2012)

Full size image

These official data source also largely substantiate the self-reported arrest rate shown in Fig. 4b on frequency of arrest. The official estimates here shown in Fig. 6 for male are relatively lower than the NLSY97 estimates for the younger age group and higher for the older age group. For males, the official average arrest rate is 0.2 for 18–29 years old youth and .16 for self-report version. For females, the official rate on average is about 0.05 compared to the average rate of .04 for self-report. The officially defined “juveniles” who are the under-18 youth has an average of .05 for male and .02 for female. The corresponding group from NLSY97 reports an average of 0.1 for male and .05 for female.

Appendix 3: Cohort Effect

Cohort effect refers to the influence for a specific cohort due to the year they were born (Farrington, 1986, p203). To examine this, I break down the sample by five cohorts based on the year they were born (1985–1989). Figure 7 indicates two out of the five cohorts on the arrest rates by cohort and age. As it is clearly shown, for both male and female subsamples, the youngest and oldest cohorts overlap each other relatively well, implying little evidence for cohort-related bias. Similar conclusion is suggested for prevalence of marijuana use (figure not shown).

Fig. 7
figure 7

prevalence of self-reported arrest by sex and age: cohort 1985 versus cohort 1989

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Liu, S. Is the Shape of the Age-Crime Curve Invariant by Sex? Evidence from a National Sample with Flexible Non-parametric Modeling. J Quant Criminol 31, 93–123 (2015). https://doi.org/10.1007/s10940-014-9225-6

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