This study revisits a familiar question regarding the relationship between victimization and offending. Using longitudinal data on middle- and high-school students, the study examines competing arguments regarding the relationship between victimization and offending embedded within the “dynamic causal” and “population heterogeneity” perspectives. The analysis begins with models that estimate the longitudinal relationship between victimization and offending without accounting for the influence of time-stable individual heterogeneity. Next, the victimization-offending relationship is reconsidered after the effects of time-stable sources of heterogeneity, and time-varying covariates are controlled. While the initial results without controls for population heterogeneity are in line with much prior research and indicate a positive link between victimization and offending, results from models that control for time-stable individual differences suggest something new: a negative, reciprocal relationship between victimization and offending. These latter results are most consistent with the notion that the oft-reported victimization-offending link is driven by a combination of dynamic causal and population heterogeneity factors. Implications of these findings for theory and future research focusing on the victimization-offending nexus are discussed.
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However, it is worth noting that the Schreck et al. (2006) study does control for one particularly prominent source of population heterogeneity, low self-control.
While we primarily focus on these two possibilities, other hypotheses may be relevant as well. Indeed, as we discuss in the conclusion section, there may be a number of interactive possibilities that deserve serious attention in subsequent research.
The response rate in the RSVP is generally consistent with other studies of students that employ active parental consent (see Ellickson and Hawes 1989; Esbensen et al. 1996). Nevertheless, the response rate obtained in the RSVP study calls into question whether the obtained sample is generalizable to the targeted population of adolescents. Past research suggests that active parental consent procedures often produce samples that are biased on racial characteristics (Kearney et al. 1983). However, comparing demographic characteristics from our sample to Kentucky Department of Education enrollment data for the 65 schools in our sample, we find that the racial composition of our sample is fairly close to the KDE population data. In Year 1 our sample percentage nonwhite is 9.55%, while the corresponding figure from the KDE data (which includes all kids in the selected schools, not just 7th graders) is 10.18%. In contrast, our sample does appear to under-represent males, with about 45.5% of the Year 1 respondents being male, compared to 51.9% for the KDE data. Given known gender patterning of delinquent behavior and victimization, we suspect that non-response may understate the prevalence and overall variability of victimization, delinquent behavior and perhaps other “anti-social” factors. Without explicit data on the non-responders, however, we cannot know with any certainty the extent to which they differ from responders.
For the specific variables used in our analysis, the proportion of cases with missing data ranges between 8 and 25.6%. But, when item non-response is considered across all variables simultaneously, it is the case that about 49% of the individuals in the sample have missing values on at least one variable for at least one of the measurement occasions. Consequently, the use of the listwise deletion method for missing data would result in a serious data loss. On the other hand, FIML uses all available information from complete cases as well as the cases with missing data on some (but not all) variables to derive parameter estimates. The inclusion of the information from the partially complete cases contributes to knowledge of the underlying marginal distribution of variables with missing data and thereby can reduce the bias introduced by listwise deletion of cases with missing data, while also improving the efficiency of the estimates. Greater detail on the computation of FIML as well as the advantages and limitations of FIML relative to other missing data procedures are discussed in Allison (2002), Arbuckle (1996), Wothke (2000) and Enders and Bandalos (2001).
Using Mplus, we computed two exploratory factor analyses on these items. In the first analysis, we treat the items as continuous variables. In the second, the items were specified as ordinal variables. Results from both analyses are similar and indicate that the items load on a single factor (e.g., in the latter specification, loadings range between .55 and .98 on a first factor with an eigenvalue of 4.1).
An exploratory factor analyses with these items specified as ordinal categorical indicators indicates that all items load highly on a single factor (loadings range: .72–.96; eigenvalue = 9.6).
In supplemental analyses available from the first author, we utilized “variety” indices that tap the number of different types of crime (rather than a sum of scores across the types) for both the offending and victimization variables. Results from those analyses are substantively identical to those reported below.
Zumbo et al. (2007) find that the traditional computation of alpha yields a negatively biased estimate of reliability when it is applied to ordinal (or binary) items. In contrast, an “ordinal” alpha reliability coefficient derived from a polychoric (or tetrachoric, for binary data) correlation matrix is found to be more accurate. For the multi-item indices utilized in our analysis, we report both the traditional Cronbach’s alpha as well as the ordinal alpha recommended by Zumbo et al.
The survey items and descriptive statistics for all the measures employed in the analyses are presented in “Appendix A”.
An additional benefit of using the structural equation modeling approach is that many SEM software packages (including Mplus, which we utilize) include the “full-information” maximum likelihood (FIML) estimation methods which, as noted, effectively include (rather than exclude) cases with missing data on some analysis variables. These FIML methods have long been known to produce unbiased parameter estimates under the assumption that data are missing at random (MAR). In contrast, listwise deletion of missing data yields unbiased estimates only under the much stronger assumption that data are missing completely at random (MCAR). Consequently, the FIML approach is widely regarded as a superior approach to handling missing data than more traditional approaches such as listwise deletion (e.g., see Enders and Bandalos 2001; Wothke 2000). Another approach to handling missing that has nearly as good statistical properties as FIML is multiple imputation (see Rubin 1987; Allison 2002). As a supplement to our use of FIML estimation, we also utilized the missing data imputation procedures available in Stata version 11 to create 5 imputed datasets. We then re-estimated the full models reported in Table 3 using each of these imputed datasets. As expected, the average parameter estimates from those supplemental analyses yield findings that are numerically very close, and substantively identical, to those reported in Table 3.
All reported results reflect maximum likelihood parameter estimates with robust standard errors that are adjusted for non-normality and the clustering of individuals within schools.
Standard chi-square difference tests are not appropriate when applied to model fit chi-square statistics obtained from maximum likelihood estimators that are robust to non-normality and clustering. Therefore, we utilize the Satorra-Bentler scaled chi-square difference test, which was developed to address this concern. Detail on this test can be found in Satorra (2000) and useful advice on its practical application can be found on the MPlus website at: http://www.statmodel.com/chidiff.shtml.
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This research was sponsored, in part, by grant DA-11317 (Richard R. Clayton, PI) from the National Institute on Drug Abuse. The authors would like to thank Richard R. Clayton, Scott A. Hunt, Kimberly Reeder, Michelle Campbell Augustine, Shayne Jones, Staci Roberts, and Jon Paul Bryan for their contributions to the Rural Substance abuse and Violence Project, which provides the data analyzed here.
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Ousey, G.C., Wilcox, P. & Fisher, B.S. Something Old, Something New: Revisiting Competing Hypotheses of the Victimization-Offending Relationship Among Adolescents. J Quant Criminol 27, 53–84 (2011). https://doi.org/10.1007/s10940-010-9099-1