Developmental Trajectories of Delinquent Behavior

Abstract

A latent class growth analysis (LCGA) of self-reported involvement in delinquency was performed on a sample of 1,414 boys and girls from the 1997 version of the National Longitudinal Survey of Youth. The LCGA results revealed the presence of three trajectories (high, medium, and low elevation). The three-trajectory and three-class posterior probabilities models were subsequently compared to a simple dimensional model composed of the sum of all delinquent acts reported in a 7-year period. Analyses revealed that the simple dimensional model correlated significantly better with measures of delinquency initiation and severity than the three-trajectory and posterior probabilities models. The fact that a categorical model created from the results of an LCGA analysis and posterior probabilities of class membership experienced significantly weaker effect sizes than a simple dimensional model suggests the absence of a nonarbitrary division between the trajectory groups identified in this study.

Keywords

developmental trajectories delinquency latent class growth analysis

Trajectories of antisocial behavior are currently among the most popular theoretical constructs in research studies on crime and delinquency. Whether theoretically or empirically derived, trajectories are the impetus behind much of the developmental research currently being conducted in the fields of criminology and criminal justice. The best-known theoretically derived model is probably Moffitt’s (1993) three-part developmental taxonomy. In her theory, Moffitt proposed the existence of three trajectories: life-course-persistent (LCP) delinquency, adolescence-limited (AL) delinquency, and nondelinquency (ND). The LCP pattern is thought to have its origins in early behavioral and developmental problems and allegedly extends from childhood or early adolescence to middle adulthood. The delinquent careers of those following the AL path to antisocial behavior are relatively brief by comparison, starting in middle adolescence and ending in late adolescence or early adulthood. Of the two patterns, AL delinquency is the more prevalent and comes with fewer early developmental, behavioral, and environmental problems than LCP delinquency. These individuals, according to Moffitt (1993), learn crime by observing and modeling the behavior of LCP adolescents. Moffitt asserts that these two trajectories have different causes, correlates, and outcomes, which is, in part, the foundation of her theory that LCP and AL delinquency are separate categories of behavior.

Trajectories can also be empirically derived. Rather than creating the categories a priori, empirically minded researchers rely on statistical techniques like latent class growth analysis (LCGA; Nagin, 1999) and growth mixture modeling (GMM; Muthén & Muthén, 2004) to determine the number of trajectories. Nagin and colleagues (Nagin, 2005; Nagin & Odgers, 2010; Nagin & Tremblay, 1999) used LCGA to identify trajectories empirically. Several different models have been proposed on the basis of these analyses but most involve either three or four trajectories. Using Farrington and West’s (1990) London data, Nagin and Odgers (2010) illustrate how four trajectories fit the data and account for important differences between participants. The high rate chronic trajectory contained the highest proportion of cases with low IQ, poor parenting, high risk taking, and parental criminality. The low rate chronic trajectory had about the same number of cases with low IQ as the high rate chronic trajectory but fewer cases of poor parenting, high risk taking, and parents with criminal records. Participants in the AL trajectory began engaging in delinquency later and ended their delinquency earlier than participants in the two chronic trajectories. Risk taking and parental criminality were more prevalent in the AL group than in the low-chronic trajectory but less prevalent than the high-chronic trajectory. A fourth trajectory, nondelinquency, not only was the most prevalent pattern but also displayed the fewest number of cases of low IQ, poor parenting, high risk taking, and parents with criminal records.

Research has not always supported the existence of three (Moffitt, 1993) or four (Nagin, 2005) trajectories. Two to four trajectories were extracted from samples participating in a multisite study by Broidy and colleagues (2003). In other studies, as many as five (Hoeve et al., 2008), six (Lacourse et al., 2002), and seven (Bushway, Thornberry, & Krohn, 2003) developmental trajectories have been uncovered. Even more disconcerting than the wide variation in the number of classes obtained in research on developmental trajectories of crime (see Van Dulmen, Goncy, Vest, & Flannery, 2009) is the possibility that the research methodology (LCGA, GMM) was responsible for some of the trajectories observed in these studies. Although LCGA and GMM are not identical, they both derive from a clustering algorithm. To the extent that most longitudinal and time series data in the behavioral sciences are moderately to highly skewed (Shumway & Stoffer, 2006), data clustering procedures like LCGA and GMM have a tendency to overestimate the correct number of components in a mixture (Bauer & Curran, 2003). Furthermore, because data clustering procedures assume that a distribution is heterogeneous, model misspecification is common when data are drawn from a homogenous or dimensional distribution (McLachlan & Peel, 2000).

Walters (2011) used the taxometric method (Meehl, 1995) to assess whether Moffitt’s (1993) theory was a true taxonomy by examining previously collected maternal ratings of childhood conduct disorder, hyperactivity, and oppositional defiant disorder in individuals who later reported engaging in delinquency between the ages of 15 and 21. The results of this study failed to show evidence of heterogeneity in the distribution of early behavioral problems (a major premise of Moffitt’s theory), thereby raising questions about the taxonomic status of Moffitt’s three-class model and denoting that individual differences in early behavioral problems are quantitative (different degrees) rather than qualitative (different kinds) in nature. Determining whether developmental patterns of criminality differ between males and females is also an important research topic. Walters (2011) observed dimensional latent structure in both male and female participants in his study. In four of the six samples included in a multisite study by Broidy et al. (2003), separate analyses were conducted for males and females. In each instance, trajectories of male and female offending were similar in number and pattern, although the male trajectories tended to be more highly elevated than the female trajectories. This latter finding is consistent with research showing that males engage in more delinquent behavior than females (Tracy, Kempf-Leonard, & Abramoske-James, 2009).

The Present Study

A core assumption of Moffitt’s (1993) theory is that LCP and AL delinquents display divergent patterns of delinquent behavior: LCP delinquents having an earlier onset and longer course and AL delinquents having a later onset and shorter course. This assumption could not be tested in the Walters (2011) investigation because the indicators were cross-sectional rather than longitudinal. No attempt, in fact, has ever been made to apply the taxometric method to longitudinal or time series data. In the absence of empirical support for the use of taxometrics with longitudinal data, an alternative approach was sought. Semiparametric group-based analysis (Nagin, 1999), also known as latent class growth analysis, is currently the procedure most often used by researchers interested in identifying trajectories of delinquent behavior. Using LCGA to identify trajectories of delinquent behavior, a categorical model was created. This categorical model and the three-class posterior probabilities from this model were then compared to a dimensional model formed from the sum of all delinquent acts originally used to identify the trajectories. This is similar to how Prisciandaro and Roberts (2009) compared dimensional and categorical models of unipolar depression. It was predicted that the dimensional model would correlate better with external measures of delinquency initiation and severity than the categorical model and three-class posterior probabilities in both male and female participants.

Method

Participants

The National Longitudinal Survey of Youth 1997 (Center for Human Resource Research, 2009) is a nationally representative sample of 8,984 U.S. residents born between 1980 and 1984. Black and Hispanic participants were oversampled to facilitate statistical analysis of these groups, and male and female participants were equally represented. All participants were initially interviewed in 1997, and approximately one fifth of the sample, 1,771 respondents, had been born in 1984. This was the target group for the current investigation because the majority of these individuals had been interviewed annually between the ages of 13 and 19. Complete data were available for 1,414 (79.8%) of the respondents born in 1984, and these individuals served as participants in this study. The gender breakdown for the sample was 714 males and 700 females. Racially, more than half the sample was White (53.4%), followed by Black (24.4%), Hispanic (21.1%), and mixed (1.1%) ethnicity respondents. Analyses revealed no gender or racial differences (p > .10) between the 1,414 participants and 357 individuals who were removed from the sample because of incomplete data.

Measures

Longitudinal delinquency indicators for this study were seven delinquency involvement scales derived from an interview conducted annually when respondents were between the ages of 13 and 19. The same five delinquent behaviors were covered in each interview: carried a weapon, purposely damaged or destroyed property not belonging to the respondent, stole something worth $50 or more, attacked or assaulted someone, and sold or helped to sell marijuana, hashish, or hard drugs. A respondent was asked if he or she engaged in any of these behaviors in the past 12 months and was awarded one point for each behavioral category he or she acknowledged engaging in at least once. The ranges, means, standard deviations, skew, and kurtosis of these seven indicators are listed in Table 1.

Table 1:

Descriptive Statistics for the Seven Longitudinal Indicators

Year (age)	Range	M	SD	Skew^a	Kurtosis^b
1997 (13)	0–5	0.47	0.79	1.91	4.14
1998 (14)	0–5	0.43	0.82	2.35	6.43
1999 (15)	0–5	0.37	0.77	2.62	7.91
2000 (16)	0–5	0.34	0.76	2.86	9.88
2001 (17)	0–5	0.27	0.68	3.17	11.79
2002 (18)	0–5	0.24	0.62	3.21	12.18
2003 (19)	0–5	0.20	0.56	3.57	16.16

Note. Year (age) = year and age when the interview took place; M = total sample mean based on the results of a 6-point (0–5) rating scale; SD = standard deviation; N = 1,414.

The standard error of measurement for skew was .065.

The standard error of measurement for kurtosis was .130.

Four external self-report correlates of delinquency initiation/severity were examined in this study: running away from home, school suspensions, percentage chance of being arrested in 5 years, and subsequent arrests. Running away from home may be an early precursor of delinquency and is one of the criteria for childhood conduct disorder (American Psychiatric Association, 2000). It has also been found to correlate with delinquency and may partially mediate the relationship between early physical and psychological abuse and later delinquency (Kim, Tajima, Herrenkohl, & Huang, 2009). In the current study running away from home was evaluated as present (1) or absent (0) prior to age 14 and from age 14 to 18 in yearly intervals for a total possible score of 6.

School suspension is a fairly common consequence of school-based antisocial behavior, especially in the United States, and correlates moderately well with delinquency (Hemphill et al., 2007). Accordingly, the total number of days participants spent at home as a result of being suspended from school over the course of their entire school career served as an external correlate of delinquency in this study.

Anticipation of future legal troubles is another correlate of delinquency. Using three waves of a longitudinal panel study, Brezina (2000) demonstrated that adult constraints created a state of low personal control that was partially assuaged by future delinquent involvement. In the current study, anticipation of future legal troubles was measured with a self-report item that asked the respondent to assess his or her anticipated odds of being arrested within the next 5 years, an assessment made when the individual was 16 years old.

Delinquency has been found to exert both direct and indirect effects on adult criminal behavior (Mason et al., 2010). Hence, one of the best predictors of future criminal behavior is past criminal behavior. The future arrests variable was the sole prospective correlate examined in this study. Although all the other correlates were collected contemporaneous to the period covered by the delinquency indicators (i.e., ages 13–19), self-reported arrests were assessed on a yearly basis from age 20 to age 24 and then summed.

Analysis

LCGA for categorical data was performed on the seven longitudinal indicators with Mplus 5.0 (Muthén & Muthén, 1998–2007). The estimator used in these analyses was maximum likelihood with robust standard errors. Beginning with a one-class model, an additional class was added to the model in a stepwise fashion until the stopping rule was achieved. Stopping rules for the current study included trivial change in the Bayesian information criterion (BIC) and group size. Each participant was assigned to the class for which he or she had the highest posterior probability. Once class assignments had been made, an ordered categorical model was created from all possible combinations of the classes in the best fitting solution. The ordering that achieved the highest effect sizes across the four external criteria (i.e., 1 = low elevation, 2 = moderate elevation, 3 = high elevation) was selected for implementation. Correlations between the ordered categorical model and external criterion variables were subsequently compared to correlations between the simple dimensional model (sum of the five delinquent acts considered over the seven periods, for a maximum score of 35) and these same criterion variables. It was reasoned that if the categorical model was meaningful and useful, then the ordered categorical–criterion correlations should equal or exceed the dimensional-criterion correlations.

Results

LCGA

An LCGA of self-reported delinquent involvement revealed the presence of two reasonably well fitting models: a three-class model and a four-class model. The four-class model achieved a lower BIC than the three-class model, but the change in BIC (<100) between the two models (see Table 2) could be considered trivial in a sample as large as the current one (see McGrath & Walters, in press). In addition, the four-class model contained two moderate-delinquency groups that essentially emerged from a single moderate group in the three-class model, and the three-class model correlated slightly better with the external measures of delinquency initiation and severity than the four-class model. Accordingly, the three-class solution served as the categorical model in this study. Figure 1 depicts the three trajectories in the three-class model, which were subsequently labeled high, moderate, and low elevation.

Table 2:

Summary of Latent Class Growth Analysis Results for the Seven Longitudinal Indicators

K	LL	PAR	BIC	ΔBIC
1	−7249.59	6	14542.71
2	−6709.45	9	13484.18	−1058.53
3	−6632.37	12	13351.79	−132.39
4	−6598.34	15	13305.49	−46.30
5	−6589.41	18	13309.40	+3.91

Note. The number of random starts was set at 100 during the initial stage, and the number of optimizations was set at 10 during the final stage. k = number of components or classes in the model; LL = log likelihood value; PAR = number of free parameters; BIC = Bayesian information criterion (smaller values indicate better fit); ΔBIC = change in BIC (− = current model has a better fit; + = previous model has a better fit); N = 1,414.

Figure 1:

Mean Delinquency Scores for the Three Trajectories

Male and female data were fit separately to the three-class model. Similarities were noted in the pattern (high, moderate, and low elevation) and size (the high elevation group had the smallest membership and the low elevation group had the largest membership) of the three latent categories for males and females, although the male trajectories were slightly more elevated than the female trajectories.

Comparing The Categorical and Dimensional Models

A three-class model was formed by assigning three points to participants with posterior probabilities that placed them in the high elevation trajectory, two points to participants with posterior probabilities that placed them in the moderate elevation trajectory, and one point to participants with posterior probabilities that placed them in the low elevation trajectory. This three-class model was then compared to the dimensional model (sum total of the five offenses across the seven periods). Using Steiger’s (1980) z test procedure for dependent correlations (see Table 3), the dimensional model was found to have a significantly higher effect size than the categorical model in relationship to the four external variables (runaway, school suspensions, rated likelihood of future arrest, and subsequent arrests) in all three samples (males, females, total).

Table 3:

Effect Sizes Recorded by the Dimensional and Categorical Models as Correlates of Delinquency-Related Outcomes for the Total Sample and by Gender

Criterion	Range	M	SD	Dim r	(95% CI)	Cov	Cat r	(95% CI)	Cov	z	%imp
Total sample (N = 1,414)
Runaway from home	0–5	0.28	0.64	.407	(.363–.449)	0.82	.342	(.296–.387)	0.14	4.85***	19.0
School suspensions	0–447	5.48	20.21	.300	(.252–.346)	19.20	.243	(.194–.291)	3.09	4.09***	23.4
Chance future arrest	0–100	13.48	20.52	.362	(.316–.406)	23.52	.315	(.268–.361)	4.08	3.45***	14.9
Subsequent arrests	0–13	0.37	1.24	.300	(.252–.346)	1.18	.251	(.202–.299)	0.20	3.52***	19.5
Males (n = 714)
Runaway from home	0–5	0.23	0.54	.446	(.385–.502)	0.84	.337	(.270–.400)	0.05	5.81***	32.3
School suspensions	0–447	7.53	24.48	.299	(.231–.364)	25.47	.244	(.174–.312)	3.94	2.81**	22.5
Chance future arrest	0–100	16.57	22.32	.334	(.267–.398)	25.94	.289	(.220–.355)	4.26	2.32*	18.9
Subsequent arrests	0–13	0.59	1.59	.295	(.226–.330)	1.63	.247	(.177–.315)	0.26	2.44*	19.4
Females (n = 700)
Runaway from home	0–5	0.33	0.54	.456	(.395–.513)	0.65	.415	(.351–.474)	0.13	2.14*	9.9
School suspensions	0–181	3.39	14.32	.267	(.197–.334)	10.13	.205	(.133–.275)	1.67	2.98**	30.2
Chance future arrest	0–100	10.33	17.98	.354	(.287–.417)	16.87	.297	(.228–.363)	3.04	2.82**	19.2
Subsequent arrests	0–7	0.15	0.66	.236	(.165–.305)	0.41	.189	(.116–.259)	0.07	2.24*	24.9

Note. Criterion = external criterion measure; run away from home = received one point for running away from home before age 14 and one additional point for every year between the ages of 14 and 18 when ran away from home at least once; school suspensions = total number of days participant suspended from school across the entire school career; chance future arrest = self-report of the estimated percentage chance of arrest in the next 5 years taken at age 16; subsequent arrests = total number of self-reported arrests between the ages of 20 and 24; range = range of scores in the current sample; SD = standard deviation; Dim r (95%CI) = correlation and 95% confidence (in parentheses) of the dimensional model; COV = covariance between Dim or Cat and external criterion measure; Cat r (95%CI) = correlation and 95% confidence interval (in parentheses) of the three-class ordered categorical model; all Dim and Cat correlations were significant (p < .001); z = z test of the difference between the correlations for the dimensional and categorical models (Steiger, 1980); %imp = percentage improvement in effect size (r) when transitioning from a categorical model to a dimensional model; correlations between Dim and Cat = .851 (total sample), .850 (boys), and .837 (girls).

p < .05, two-tailed. **p < .01, two-tailed. ***p < .001, two-tailed.

It could be argued that correlation coefficients are limited for the purpose of comparing model-criterion relationships because categorical and dimensional models typically exhibit widely divergent variances. For this reason, the covariances of these relationships were also calculated and compared. The results, which are reported in Table 3, indicate that the dimensional-criterion covariances were 5 to 11 (modal value = 6) times higher than the categorical-criterion covariances.

The dimensional-criterion correlation was also superior to the multiple correlation coefficient obtained when the external criteria were regressed on the posterior probabilities for the three-class model. All four external criteria correlated significantly better with the dimensional model than with the three-class posterior probabilities model: runaway (.407 vs. .392, z = 2.05, p < .05), school suspensions (.300 vs. .285, z = 1.97, p < .05), chance of future arrest (.362 vs. .342, z = 2.68, p < .01), and subsequent arrests (.300 vs. .284, z = 2.10, p < .05). The dimensional model also achieved significantly higher effect sizes than the posterior probabilities for two of the external criteria in the male subsample (runaway, chance of future arrest) and one of the external criteria in the female subsample (school suspensions).

Discussion

The purpose of this study was to test the trajectory hypothesis by subjecting a large group of male and female youth to LCGA analysis. An LCGA of these data revealed the presence of a four-class model similar to the four-class models identified in past longitudinal research on delinquency (Broidy et al., 2003; Nagin, 1999) and a three-class model that bore some resemblance to Moffitt’s (1993) three-group typology. Because dividing the moderate group in the three-class solution into two subgroups in the four-group solution did not improve on the categorical model’s ability to correlate with external criteria of delinquency involvement/severity, the more parsimonious three-class model was selected as the categorical model for this study. When the three-class ordered categorical model was contrasted with a simple dimensional model (total number of self-reported delinquent involvements), the dimensional model correlated significantly better with all four markers of delinquency initiation and severity. The same outcome was observed when posterior probabilities of class membership replaced the three-class model, although the gap between the two sets of correlations closed some in the latter analyses. It should be noted that although the results of this study are not unequivocal proof of a single age–delinquency trajectory, they bring into serious question the utility and meaningfulness of multitrajectory models and the wisdom of dividing the age–delinquency relationship into subtypes. If the current results are cross-validated, one area for future research would be determining the number of dimensions that make up this single trajectory.

The fact that the current sample was fairly evenly divided between boys and girls made it possible to conduct secondary analyses on the basis of gender. Male and female participants were accordingly subjected to separate three-class LCGA analyses. The results revealed gender similarities in pattern and proportion and gender differences in elevation and absolute size for male and female participants. The three-class models for boys and girls were both ordered by elevation (low, moderate, high), and relative trajectory size was comparable across gender, with the greatest proportion of participants in the low elevation group and the smallest proportion of participants in the high elevation group. Conversely, the group elevations were slightly higher for boys than for girls, and a greater proportion of boys than girls fell into the high elevation group. Significantly stronger correlations between the dimensional model and criterion measures than between the categorical model and criterion measures, however, were recorded for both males and females. The finding that gender appeared to have only a small impact on the pattern and composition of the trajectories observed in this and other (Broidy et al., 2003) studies should not be taken as evidence that there are not significant gender differences in delinquency. The well-documented fact that more crimes are committed by males than females and certain factors (early sexual abuse, current substance misuse, relationship issues) are more important to female offending than to male offending suggests the existence of gendered pathways to crime and delinquency (Tracy et al., 2009).

In concluding that the age–crime relationship is invariant across a wide range of variables and conditions, Hirschi and Gottfredson (1983) started a controversy that continues to this day. In contrast to life span development theories of crime, in which multiple age–crime trajectories are identified and studied (Moffitt, 1993, 2007; Nagin & Tremblay, 1999; Piquero, 2008), Hirschi and Gottfredson reject the notion of multiple age–crime patterns. Sampson and Laub (2005) adopt a similar view. To the extent that developmental trajectories of delinquency may be artifacts of the procedures used to identify them (i.e., LCGA, GMM), it is imperative that they be thoroughly evaluated and rigorously tested. Otherwise, we run the risk of reifying results that owe their existence to the very method from which they were extracted. The taxometric method is generally effective for use with cross-sectional data, but it is uncertain whether it can be meaningfully applied to longitudinal data. This just said, there is a taxometric principle, which when applied to traditional mixture modeling analysis may help determine whether a construct is dimensional or categorical: that is, comparative analysis. Incorporating this principle into the current study, a three-class trajectory model composed of high, moderate, and low delinquency groups was found to achieve significantly smaller effect size correlations with external delinquency criteria than a simple dimensional model.

Dividing a continuous measure into discrete categories will result in a significant loss of information when the latent structure of the construct is dimensional. In situations where the latent structure of a construct is categorical, dividing a continuous measure into discrete categories should not make a difference with respect to the scale’s ability to correlate with and predict relevant criteria and may actually increase statistical precision by reducing measurement error (Ruscio, Haslam, & Ruscio, 2006). Hence, it was hypothesized that if a categorical system was to possess anything other than heuristic value, it would need to perform at least as well as a simple dimensional model. It may be unrealistic to expect a categorical variable derived from a continuous measure to significantly outperform the original continuous measure, but it is not unrealistic to expect a categorical variable to perform at least as well as the continuous measure from which it was derived and for the categorical model to possess incremental information above and beyond what is available from a simple dimensional model.

In the current study, the three-class ordered categorical model was constructed post hoc so that the highest correlations of all possible three-group category combinations were ensured. Posterior probabilities operate as continuous measures, and they can be sample dependent and inaccurate in small samples (Li & Lerner, 2011), but in the current study they benefitted from a large sample size. Despite these advantages and modifications, the effect sizes attained by the three-class ordered categorical model were 15% to 23% smaller than the effect sizes attained by the dimensional model. In the end, there was no evidence of a nonarbitrary break or discontinuity in the distribution of longitudinal delinquency scores in the current sample. These results are inconsistent with the multiple trajectory models of Moffitt (1993), Nagin (Nagin & Tremblay, 1999), and others (see Piquero, 2008) but consistent with prior research findings of dimensional latent structure when latent trajectory analysis has been applied to longitudinal data (Lahey et al., 2006), and taxometric analysis has been applied to cross-sectional data (Walters, 2011).

The current findings have potentially important theoretical and practical implications. Theoretically, the results suggest that delinquency may have an additive etiology rather than a specific, threshold, interactive, or bifurcating etiology. Meehl (1977, 1992) discussed four etiological pathways that frequently characterize categorical constructs: specific etiology, threshold effect, nonlinear interaction, and developmental bifurcation. Specific etiology is where the necessary and sufficient conditions for the development of a behavior are contained in a small set of biological or environmental factors. A threshold effect, on the other hand, begins as a dimension but then transforms into a category once it reaches a critical level of severity or vulnerability. The synergistic effect that occurs when certain variables interact can also give rise to a categorical construct, a process known as nonlinear interaction. Finally, categories are sometimes caused by a developmental bifurcation in which the behavior begins as a dimensional but then evolves into a category once certain developmental milestone are achieved. None of these causal explanations, however, appear to apply to delinquency. There are no necessary or sufficient causes of delinquency, just a large pool of partial causal factors, which when combined increase a person’s risk of future delinquency (Farrington, 1998). With additive etiology, it is possible for two equally serious cases of delinquency to be caused by two completely different sets of causal factors because it is the accumulation of factors rather than a specific factor that is at the etiological core of a dimensional construct.

Proponents of the multiple trajectory approach contend that, if nothing else, trajectory models of delinquency have heuristic value (Nagin & Tremblay, 2005). We should not, however, sacrifice accuracy for heurism. How practical is a model that does not correlate or predict as well as the simple sum of previous delinquent behaviors? Change clearly occurs over the course of a person’s life, and such change can play an important role in both predicting delinquency and encouraging desistance (Sampson & Laub, 1993). These changes, however, are not well represented in most developmental trajectories of delinquent behavior. In the current study, as well as in much of the previous research (see Broidy et al., 2003), the trajectories differed primarily in magnitude or level (e.g., high, moderate, and low). There are situations, such as the current investigation, where trajectories exhibit an upward or downward slope or follow a curvilinear pattern, but these trends generally do not distinguish between the trajectories very well. For instance, all three trajectories in the current study displayed a declining slope, with the slope of the high elevation trajectory being greater than other two trajectories only because of a much higher peak. The practical value of the current study is that it illustrates how simple dimensional models are capable of outperforming more complex and sample-specific categorical models and in so doing may actually possess greater heuristic value than categorical models. The dimensional model does not need to be recalibrated with each new sample as the categorical model does. As long as prior delinquent/antisocial behavior has been measured, the dimensional model can be implemented and, if the current results are any indication, do a better job of assessing delinquency severity and predicting future criminal conduct than the categorical model.

There are several methodological limitations that need to be considered when interpreting the results of this study. First, the indicators used in this study catalogued whether participants engaged in any of five different delinquent acts at least once during the past year. As such, they had limited ability to capture the true extent and severity of antisociality engaged in by some of the more prolific delinquents in the same. Furthermore, these indicators were based solely on participant self-report. As Shadish, Cook, and Campbell (2002) note, the use of a single data source may introduce mono-operation bias into a study. In the future, researchers may want to consider using indicators from several different sources, such as the parental rating scales employed in the Walters (2011) investigation or the official arrest records that Wiesner, Capaldi, and Kim (2007) used to identify multiple trajectories in their study. Second, only the adolescent years were covered in the present study. Important developmental differences are believed to exist between AL and LCP delinquents, beginning in middle to late childhood, if not earlier. Accordingly, the current results need to be cross-validated in a sample where participants are followed beginning in elementary school rather than in junior high or middle school. A third potential weakness of this investigation is that participants were followed only to age 19. Moffitt (1993) contends that LCP delinquents continue to offend well into middle adulthood, whereas AL delinquent typically desist in their late teens or early 20s. Hence, the age range needs to be extended at both ends, running from middle childhood to age 30. It could be argued that results more congruent with the multiple trajectory hypothesis would have surfaced had a longer time span been utilized. It should be noted, however, that many of the cluster-based research studies on which multiple trajectory theories are based have used time frames that rarely extended beyond age 14 or 15 (see Broidy et al., 2003; Nagin & Tremblay, 1999).

Criticism can be directed at two of the decisions I made in constructing the trajectories for this study. First, issue can be taken with the fact that I employed LCGA rather than GMM or another potentially more appropriate procedure like count variable (Poisson or negative binomial) analysis. I chose LCGA over GMM because it is the most commonly used latent growth modeling approach in research on delinquency trajectories. The principal difference between LCGA and GMM is that GMM permits within-class variability and LCGA does not (Muthén & Muthén, 2004). Given the similarities between LCGA and GMM, it seems unlikely that a different conclusion would have been reached had GMM, or a count variable approach for that matter, been used instead of LCGA, but this is an empirical questions that requires further study. The second decision that could be questioned is my choice of the three-class model over the four-class model. I selected the three-class model because it was more parsimonious than the four-class model and the BIC improved only slightly when moving between the two models. Most important for the purposes of this study, the three-class model achieved slightly better effect size estimates than the four-class model, thereby providing the optimal categorical model. Although there is no way to know for sure whether the current distribution of cases contained a discontinuity, the fact that a dimensional delinquency model significantly outperformed a categorical delinquency model suggests that delinquency may follow one rather than several trajectories. Whether an actual taxonic boundary separates categories of delinquent behavior, however, requires a taxometric analysis of trajectory data and assurance that the taxometric method can be appropriately used with longitudinal indicators.

Footnotes

The author received no financial support for this work and has no affiliation or financial agreement with any organization whose financial interests may be affected by the material in this article.

Glenn D. Walters, PhD, is an assistant professor in the Department of Criminal Justice at Kutztown University in Kutztown, Pennsylvania. His research interests include the creation of a psychological theory of criminal behavior, assessment of psychopathy and criminal thinking, and application of the taxometric method to psychopathology and related psychological constructs. He has published more than 200 articles and book chapters and is the author of 15 books, including The Criminal Lifestyle (Sage, 1990) and Crime in a Psychological Context: From Career Criminals to Criminal Careers (Sage, 2012).

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