Towards an Explanatory Taxonomy of Adolescent Delinquents: Identifying Several Social-Psychological Profiles

Abstract

Taxonomic structure is examined in two large samples of delinquent youth in a domain of socio-psychological and personality factors. This paper offers a partial empirical test of the overlapping theoretical taxonomies of Moffitt (Pshycol Rev 100:674–701, 1993), Lykken (The antisocial personalities, 1995) and Mealey (1995). The first sample consisted of juvenile offenders (n = 1,572) from three state systems. Multiple cluster analysis methods were applied (Wards method, standard K-means, bootstrapped K-means and a semi-supervised pattern recognition technique). Core or exemplar cases were identified by means of a voting procedure. Seven clusters recurrently emerged across replications. While clear analogues of Moffitt’s two main categories were found, several additional stable subtypes emerged that were clearly reminiscent of Lykken’s sociopathic, neurotic-internalizing and “normal” types. However, boundaries between types were fuzzy and unstable, and many unclassified cases existed. Internal validation was assessed by cross-method verification. External validation assessed type differentiation on several delinquent behaviors. Finally, generalizability was assessed by repeating the clustering on a large replication sample (n = 1,453) from another state. Six of the seven initial types re-emerged.

Appendices

Appendix A

Youth COMPAS

The following briefly describes the Youth COMPAS scales. Scale name abbreviations and factor loadings (in parenthesis) for selected key items in each scale are indicated. Full psychometric characteristics and theoretical justifications for each scale are available from the first author.

Antisocial Opportunity (CrimOpp): Hang around with friends (.66), parties w/o adults (.69).

Absence of prosocial engagement (LowProsoc): Church activities (.66), sports, music/hobbies (.66), school activities (.70).

Anti-social peers (CrimAssoc): Friends use drugs (.75), friends arrested (.70), friends dropped out (.65).

Social isolation (SocIsolate): Has trouble making friends (.77), no close friends (.62)

Common drugs (ComDrug): Alcohol use (.81), marijuana use (.78).

Hard drugs (HardDrug): Used cocaine (.72), used heroin (.62), has injected (.48).

Substance abuse trouble (SubTrbl): Poor judgment when high (.87), violent feelings when high (.83)

Sexual promiscuity (Promiscty): Frequency of intercourse (.78), number of partners (.68).

Impulsivity (Impulsiv): Takes risks (.64), makes quick decisions (.76), seen as reckless (.73).

Manipulative-dominance (Manipulate): Good at talking one’s way out of trouble (.67), easily lies and gets away with things (.73), can dominate/threaten others (.55).

Empathy (LowEmpath): Feels sad when seeing other people cry (.81), guilt feelings when breaking a promise (.84).

Aggression/anger (Agress): Quick temper (.79), History of fights (.66), stays calm in arguments (.53).

Tolerance of violence(ViolTol): How wrong it is to hit someone to win an argument (.50), hit someone to teach them a lesson (.76).

Lack of remorse (LowRemor): Blames others/situation (.72), doesn’t express regret (.63).

Negative social cognitions (NegCognit): Kids put you down (.78), few kids can be trusted (.63).

Academic failure/success (AcadFail): Usual grades (.79), number of classes failed (.80), times grade repeated (.57).

Attention problems (AttProbs): Trouble paying attention (.85), easily bored (.71).

Educational aspirations (LowGoals): Intends to graduate (.72), education is important (.81).

School behavior (SchoolBeh): Suspended (.72), argues/fights with students (.67), conflict w. teachers (.74).

Family discontinuity (FamDisc): Multiple caretakers (.64), separated from natural parent (.61), out-of-home placements (.72).

Social class and poverty (LowSES): Family receives social assistance/subsidized housing (.68), parent has unstable/low wage employment (.81), difficulty paying bills (.87).

Family criminality (FamCrime): Mother arrested (.62), father jailed (.60), sibling drug use (.51).

High crime neighborhood (Nhood): Friends or family assaulted (.73), drug sales (.84), witnessed fights/gunfire (.87).

Parental conflict/domestic violence (ParentConf): Parents threaten each other (.84), parents yell/fight (.78), parents attack each other (.82).

Inconsistent discipline (InconDiscp): parents have clear rules (.72), perceived fairness (.72), clear reasons for punishments (.75).

Inadequate supervision (PoorSuper): Parents check when youth returns home (.84), parents check on youth’s friends (.65), parents monitor youth’s activities (.85).

Emotional bonding with parents (EmotBonds): Feels close to mother (.73), close to father (.51), feels close to sibling (.70).

Parental neglect (Neglect): Youth feels neglected (.80), parents show no interest (.71), parents rarely talk to youth (.79).

Physical abuse (PhysAbuse): Youth is scared of being hurt (.86), parents violent when high/drunk (.78), youth removed from home because of abuse (.73).

Emotional support (EmotSupp): Mother is hostile (.64), kicked out of the house (.50).

Sexual abuse (SexAbuse): Sexually abused by family member (.81), removed from home because of sexual abuse (.74).

Youth rebellion (YouthRebel): Youth intimidates parent/caretakers (.65), youth openly defies parents/caretakers (.82).

Appendix B

Algorithm

Given a set of points $X \in {\mathcal R}^{n \times m}$ and labels ${\mathcal L}=\{1,\cdots ,c\}.$ Let x _i denote the ith example. Without loss of generality the first l points (1 ...l) are labeled and the remaining points (l + 1 ...n) unlabeled. Define $Y \in {\mathcal N}^{n \times c}$ with Y _ij  = 1 if point x _i has label j and 0 otherwise. Let ${\mathcal F} \subset {\mathcal R}^{n \times c}$ denote all the matrices with nonnegative entries. A matrix $F \in {\mathcal F}$ is a matrix that labels all points x _i with a label $y_i = \hbox{arg max} _{j \le c} F_{ij}.$ Define the series F(t + 1) = αS F(t) + (1−α) Y with $F(0)=Y, {\alpha}\in (0, 1).$ The entire algorithm is defined as follows:

1. Form the affinity matrix $W_{ij}=exp(-\| x_i - x_j \|^2/(2\sigma^2))$ if i ≠ j and 0 otherwise. σ determines how fast the distance function decays.

2. Compute S = D ^−1/2 W D ^−1/2 with D _ii  = ∑ ⁿ_j=1 W _ij and D _ij  = 0, i ≠ j.

3. Compute the limit of series $\lim_{t \to \infty} F(t) = F^{\ast} = (I-\alpha S)^{-1} Y.$ α ∈ (0,1) limits how much the information spreads from one point to the other.

4. Label each point x _i as arg max_{j ≤ c} F ^* _ij .

The regularization framework for this method follows. The cost function associated with the matrix F with regularization parameter μ >  0 is defined as

$$ {\mathcal Q}(F) = {\frac{1}{2}} \left( \sum^{n}_{i,j=1} W_{ij} \Bigl\| {\frac{1}{\sqrt{D_{ii}}}} F_i - {\frac{1}{\sqrt{D_{jj}}}}F_j \Bigr\|^2 + \mu \sum^n_{i=1} \| F_i - Y_i \|^2 \right) $$

(1)

The first term is the smoothness constraint that associates a cost with change between nearby points. The second term, weighted by μ, is the fitting constraint that associates a cost for change from the initial assignments. The classifying function is defined as $F^{\ast} = \hbox{arg min}_{F \in {\mathcal F}} {\mathcal Q}(F).$ Differentiating ${\mathcal Q}(F)$ one obtains $F^{\ast} - {\frac{1}{1+\mu}}S F^{\ast} - {\frac{\mu}{1+\mu}}Y.$ Define $\alpha={\frac{1}{1+\mu}}$ and $\beta={\frac{\mu}{1+\mu}}$ (note that α + β = 1 and the matrix (I−αS) is non-singular) one can obtain

$$F^{\ast} = \beta \left( {I - \alpha S} \right)^{ - 1} Y$$

(2)

For a more in-depth discussion about the regularization framework and how to obtain the closed form expression F ^* see Zhou et al. (2004).

An unlabeled point is assigned to the class with the highest value in its row of F ^*, a n × c matrix. Note that the label assignment for each point depends on the initial marked points chosen and the parameters σ and α. In most cases one of the columns in F ^* is significantly larger than any other value for this point indicating a clear vote for one class. Since this depends on the parameters chosen and it is not obvious how to choose the parameters, we obtained several sets of labels by varying σ which defines the local neighborhood of a point.