Abstract
Objectives
Recognizing the inherent variability of drug-related behaviors, this study develops an empirically-driven and holistic model of drug-related behavior during adolescence using factor analysis to simultaneously model multiple drug behaviors.
Methods
The factor analytic model uncovers latent dimensions of drug-related behaviors, rather than patterns of individuals. These latent dimensions are treated as empirical typologies which are then used to predict an individual’s number of arrests accrued at multiple phases of the life course. The data are robust enough to simultaneously capture drug behavior measures typically considered in isolation in the literature, and to allow for behavior to change and evolve over the period of adolescence.
Results
Results show that factor analysis is capable of developing highly descriptive patterns of drug offending, and that these patterns have great utility in predicting arrests. Results further demonstrate that while drug behavior patterns are predictive of arrests at the end of adolescence for both males and females, the impacts on arrests are longer lasting for females.
Conclusions
The various facets of drug behaviors have been a long-time concern of criminological research. However, the ability to model multiple behaviors simultaneously is often constrained by data that do not measure the constructs fully. Factor analysis is shown to be a useful technique for modeling adolescent drug involvement patterns in a way that accounts for the multitude and variability of possible behaviors, and in predicting future negative life outcomes, such as arrests.
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Notes
This finding speaks to a larger potential for criminality to increase an individual’s embeddedness with a deviant subculture that normalizes drug use and drug selling. Certainly, for some individuals this may well be the case. As will be discussed in the methods section, this study is focused on the direction of association that posits drug-related behaviors influencing criminality.
Here, intensity is derived from frequency of use of crack cocaine, powder cocaine, heroin, and crystal methamphetamine, taken from data gathered in the Arrestee Drug Abuse Monitoring (ADAM) program.
Because of this oversampling, subsequent analyses are disaggregated by gender.
Both from Rochester Police Department (RPD) and the New York State Department of Criminal Justice Services (DCJS). Including both of these agencies assures that events occurring outside of Rochester will be included. Unfortunately, but data outside New York State are not available.
It should be noted that while the RYDS interviews ask each subject a battery of questions regarding drug use and selling, the prevalence of such behaviors in the sample is still low. The overwhelming majority of drug use, for example, is the use of marijuana. Nearly all of the rest is cocaine use. Nonetheless, previous drugs and crime research using RYDS data has proven quite fruitful, despite not having extreme variation on the drug offending measures.
A note on missing data is necessary prior to continuing. For the drug-related behaviors captured in the factor analysis below, it was possible to use the full sample of 881 subjects who remained in the RYDS study through the end of Phase 1. Missing data on these behaviors was caused by skip patterns in the data collection instrument. During interviews, subjects were first asked if they had engaged in a particular behavior. If the subject said they had, they were then asked follow-up questions, such as how many times they had engaged in the behavior. If the subject said they had not, the follow-up questions were skipped and are therefore missing. Since the methods used here involved counting the number of times a subject engaged in a variety of behaviors, if the subject was missing on a variable because he or she responded previously that they had not engaged in that behavior, they were recoded to a zero on the count variable. Models below are estimated on the full sample of subjects who remained in the study by the end of the phase.
More correctly, these represent concept areas, rather than specific variables. Each of these concepts are measured for each subject for each wave of data collection from Waves 1–9. When estimating the factor analysis, it will be fruitful to include both wave-specific and cross-wave variables, and to measure each of these concepts or constructs in multiple ways. This is because factor analysis requires there to be more cases than variables, and more variables than factors. Factor analysis does not extract the total possible factors that exist in the data. It instead stops when no additional significant or meaningful variance remains to be extracted (Rummel 1970, p. 169). To yield a sufficient number of factors for these purposes then, multiple measures of many constructs are necessary to include meaningful variation. The variables discussed in this section are intended to give the reader an understanding of the concept areas that will be included, rather than a precise list of variables and their construction. This caveat applies equally to the drug selling variables, and variables known to be salient.
Count variables such as this will be measured both across Phase 1 and specific to waves. Alternatively, these could be converted in frequencies per a given unit of time such as week or month (λ). As above, the goal is to provide sufficient variation to yield multiple factors describing adolescent drug behavior patterns.
Id est, drugs other than marijuana.
Dollar amount, either during a wave or across the Phase.
All data on drug behavior measures were drawn from the self-reported items in the RYDS dataset. These data allowed for roughly 300 unique drug measures to be created for each subject, although the majority showed remarkably little variation.
Orthogonal rotation imposes the requirement that factors be mutually uncorrelated, however oblique rotation explicitly recognizes correlation between factors.
Marijuana, by contrast, provided ample variation.
With 3 exceptions, detailed and discussed below.
The purpose of the unrotated factor analysis is to determine the correct number of factors. The first unrotated factor pattern identifies the largest pattern of relationships in the data. The second unrotated factor pattern identifies the next largest pattern of relationship in the data, independent of the first pattern. The third unrotated factor pattern identifies the next largest pattern, independent of the first and second patterns, and so on. Thus the amount of variation in the data explained each successive pattern decreases.
As identified in the plot, the first factor has an eigen value of 11.35. Thus it explains the variance of a little more than 11 variables. Similar, with its eigen value of 4.41, the second factor explains the variance of about 4 and half variables. The eigen values for the third and fourth factors are 3.40 and 2.72, respectively. However, the fifth factor has an eigen value of only 1.82. It explains the variance of less than two variables.
For completeness, the subsequent analyses were estimated with 5 factors. The fifth factor added practically nothing to the analysis, and results were unchanged. Using four factors is therefore the more parsimonious choice.
Reliable here means that the results can be replicated with different data sets (Abdi 2003).
When vectors are highly positively related, the angular distance between them will be very small (i.e. close to 0°), and when they are highly negatively related, the angular distance will be near the other extreme (i.e. near 180°). When vectors are unrelated to one another, the angular distance between them is 90°.
Other methods include the Varimin, Quartimax, and Equimax. Because orthogonal rotation is not the focal rotation, these are not discussed.
This method proceeds in two steps. In the first step, a target matrix is identified using orthogonal rotation whose entries (values) are raised to a power between 2 and 4. Here, the first step rotation method is the Varimax rotation, and the entries are raised to the third power, forcing the values to become bi-polar. The second step is to compute a least squares fit to the Varimax solution.
Alternatively, the cosine of the angle between them is small.
Also included in this factor were two dummy variables for age of initiation for marijuana selling and age of initiation for hard drug selling. The factor analysis process discards cases listwise if a case is missing on any variable. This means that if a subject never sold hard drugs or marijuana, they would be deleted from the sample. To correct for this, subjects who never initiated were recoded on these variables to their current age. The dummy variables remove this correction, and their factor loadings can be ignored.
Recall that the original RYDS sample is 75 % male.
This finding adds to the understanding of the RYDS subjects, long known to be prone to the use of marijuana. The current research indicates that at least sporadic use of hard drugs is not as uncommon as previously thought.
Or, not at all. Dummy variables account and control for this possibility.
As is explained below, the arrests considered in the empirical models here exclude drug-related arrests, as the relationship between drug-related behaviors and drug arrests is already so well documented.
Because agreement between self-reported and official arrests in RYDS has been shown to be quite high (Krohn et al. 2013), using official data here presents little to no bias.
Arrests in this data set are highly skewed to the right end of the distribution. There are several corrections for this non-normal distribution, including Poisson or negative binomial regression. Poisson regression assumes the conditional variance of the outcome variable be equal to the conditional mean. In all of the arrest outcomes in this project, this assumption is violated. Specifically, the variances were much larger than the mean. The simplest correction proposed in situations like these is to take the natural log of the dependent variable, and this correction was used here. All arrests are in logged units. Because the remainder of the continuous outcome variables exhibit approximately normal distributions, ordinary least squares regression is appropriate.
This test amounts to an analysis of variance, distributed as F, with n–k degrees of freedom where n equals the sample size and k equals the number of independent variables. The null hypothesis for the test is one of no relationship, or that none of the factor scores are significantly different than zero.
For completeness, models identical to those presented below were also estimated including measures for drug use and drug selling at Phase 2 and Phase 3. These measures were created by counting the number of use and selling incidents for each subject across the phases. The rationale for their inclusion was that if past drug offending is predicted to be related to these outcomes, then it is reasonable to ask if contemporaneous drug use and drug selling could have a direct impact on the same outcomes. Surprisingly, these measures were never significant in any model, with one exception. Drug use was a significant predictor of arrests at Phase 2 for males. In all cases, the sizes of the coefficients were miniscule in comparison, all less than 0.002. Further, including these measures did not mediate the significance of the adolescent drug offending factor scores in any case. The likely reason is that by Phase 2 and Phase 3, there are so few subjects who continued to use and sell drugs that the variables did not have statistical power. For these reasons, the measures were dropped from the final models presented herein. At the introduction to the project, the competing hypotheses of offenders becoming entrenched in drugs versus aging out were discussed. The results here support the idea that the vast majority of the RYDS subjects aged out of crime by the time they reached adulthood.
Again, these are only arrests incurred during Phase 3.
The reader will recall that Factor 1 was not a significant predictor of arrests for female subjects at Phase 1. The significant finding here may signal that for problematic female offenders, drug selling has a longer lasting impact. We are grateful to an anonymous reviewer for suggesting this possibility.
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Acknowledgments
Support for the Rochester Youth Development Study has been provided by the Office of Juvenile Justice and Delinquency Prevention (86-JN-CX-0007), the National Institute on Drug Abuse (R01DA005512), the National Science Foundation (SBR-9123299), and the National Institute of Mental Health (R01MH63386). Work on this project was also aided by grants to the Center for Social and Demographic Analysis at the University at Albany from NICHD (P30HD32041) and NSF (SBR-9512290). We are most grateful to the many helpful comments and suggestions given by the anonymous reviewers on earlier versions of this paper.
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Phillips, M.D. A Factor Analytic Model of Drug-Related Behavior in Adolescence and Its Impact on Arrests at Multiple Stages of the Life Course. J Quant Criminol 33, 131–155 (2017). https://doi.org/10.1007/s10940-016-9286-9
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DOI: https://doi.org/10.1007/s10940-016-9286-9