PREDICTING THE RECIDIVISM OF SERIOUS YOUTHFUL OFFENDERS USING SURVIVAL MODELS*

PREDICTING THE RECIDIVISM OF SERIOUS YOUTHFUL OFFENDERS USING SURVIVAL MODELS*

CHRISTY A. VISHER PAMELA K. LATTIMORE RICHARD L. LINSTER

National Institute of Justice

Increases over the past decade in the number and seriousness of crimes committed by young offenders have resulted in renewed interest in control of the serious, violent, or chronic youthful offender. Recent research has established a number of theoretically relevant variables associated with persistent offending and ofleially defined recidivism. Few studies, however, have examined the individual characteristics that might predict the timing of youthful recidivism. This paper seeks to fill some gaps in knowledge of the serious youthful offender by estimating a multivariate survival model for a sample of youths paroled from California Youth Authority institutions. The model’s results are then used to develop risk-assessment profiles for the sample. We suggest that these profiles may provide a reasonable approach for establishing treatment protocols or supervision requirements for paroled youths.

INTRODUCTION In recent years, studies of youthful crime have produced few results that

focus on the practical aspects of controlling criminal activity by serious youthful offenders. This may be, in part, a consequence of predictions in the mid-1970s that juvenile crime would decline. But, in fact, juvenile arrests remained nearly constant between 1978 and 1982 (Cook and Laub, 1986). By the early 198Os, national data on juvenile crime indicated that more youths were being formally referred to court and that the nature of their offenses was more serious (Krisberg et al., 1986). Between 1985 and 1989, total arrests of persons under age 18 and arrests for index offenses among this group increased 2.3% and 3.0%, respectively, and arrests for violent crimes rose 15.5% (Federal Bureau of Investigation, 1990:Tables 29 and 31).1

As the number of youths engaged in crime increased, many in the research

* We would like to acknowledge the valuable comments of three anonymous reviewers. Points of view are those of the authors and do not necessarily represent the official position of the U.S. Department of Justice or the National Institute of Justice.

In this paper, we use the term youthful offender to encompass adolescents and young adults under the age of 25. Not only do states have different policies with respect to

1.

CRIMINOLOGY VOLUME 29 NUMBER 3 1991 329

330 VISHER ET AL.

community suggested that rehabilitation programs for juveniles did not work (Sechrest et al., 1979; Wright and Dixon, 1977). Thus, in 1984 a national committee recommended that the federal effort in the area of delinquency prevention be redirected toward control of the serious, violent, or chronic offender (see National Advisory Committee, 1984; Regnery, 1986).

It is widely recognized that most juvenile offenders do not commit serious crimes repeatedly and do not commit crimes as adults (see Blumstein et al., 1986). Recent data suggest that a small group of offenders (less than one- third) appear to be responsible for about 60% of all offenses committed by those under the age of 18 (Bureau of Justice Statistics, 1988). Additionally, juvenile offenders with extensive prior records appear to have high probabilities of reoffending. Analyses of the 1945 and 1958 Philadelphia birth cohort data show that after three offenses, the probability of committing a fourth is about 0.72 and the recidivism probability is quite stable for subsequent offenses (see Winer, 1989:Table 2.12).

The juvenile justice system, however, does not appear well equipped to handle increases in serious offending (Cronin et al., 1988). Many experts on youthful offending agree that the existing correctional options for serious, persistent youthful offenders are inadequate (Bishop et al., 1989; Krisberg et al., 1986; Speirs, 1988). Typical probation is generally considered to be ineffective because supervision is minimal and youths do not view probation as punishment. The use of detention or other secure placement for youths is rising (Krisberg et al., 1986) and is accompanied by severe institutional crowding in some states (e.g.,California). Given this dismal picture of juvenile justice, it is not surprising that recidivism among moderately serious, adjudi- cated youthful offenders is high-67% in one 1982 study of more than 3,000 male youths committed to probation camps in California who were followed for 24 months (Palmer and Wedge, 1989).

What are the characteristics of persistent youthful offenders? In a review of risk-assessment instruments developed for use with juveniles in several states, Baird et al. (1984) identified eight factors associated with continued criminal involvement for juveniles: age at first adjudication, frequency and severity of prior criminal behavior, prior institutional commitments, alcohol and drug abuse, poor family relationships, negative peer influences, and school problems. However, no follow-up data or tests of the predictive accuracy of those factors were provided.

More sophisticated studies generally agree with this characterization of the influential life experiences of persistent youthful offenders, albeit with some variations. These studies often incorporate extensive information about the

the age of majority, but many states are developing programs and policies specific to youthful offenders.

RECIDIVISM OF YOUTHFUL OFFENDERS 33 1

youth’s family, which allows further specification of the relevant family characteristics. These family influences include criminal parents or siblings; poor parenting, often involving ineffective supervision; and family conflict or dis- ruption in family structure (see Blumstein et al., 1986; Elliott et al., 1985; Greenwood, 1986 Loeber and Stouthamer-Loeber, 1986). These studies also find that deprived background (low social class, poor housing, large family size), poor school performance, early antisocial behavior (lying, stealing, act- ing out), and prior victimization are characteristic of serious youthful offenders.

In a study of 107 Arizona juvenile parolees that compared the accuracy of three risk-assessment models, criminal history variables (i.e., prior arrests or referrals) were again the strongest predictors of recidivism. Other important predictors included age at first arrest, parole violations, and “family dynam- ics” (Ashford and LeCroy, 1990).

Other research has explicitly studied the factors that may predict recidivism (measured by some official action, such as rearrest). One recent study of young parolees (aged 17 to 22) describes the criminal activities over a six-year period of more than 1 1,OOO young offenders paroled in 1978 from prisons in 22 states (Bureau of Justice Statistics, 1987). The study found that, overall, 69% had been rearrested, but that recidivism rates were highest in the first two years: 32% rearrested within one year and 47% within two years. Moreover, the length of the parolee’s prior record was related to when the rearrest occurred: Those with four prior arrests were twice as likely to be rearrested within the first year as those with one or two prior arrests. Higher rates of recidivism were also found for parolees who were incarcerated for a property offense, had a prior arrest for at least one violent offense, had been younger than age 17 when first arrested as an adult, had not completed high school, or were under age 19 when paroled. Time served in prison, however, was not related to the likelihood of rearrest after parole.

Thus, it appears that much of the research on serious youthful offending has consistently identified a set of variables that are associated with persistent offending and/or officially defined recidivism. What has been lacking in prior research is a flexible analytic approach that can examine juvenile recidivism in its complexity. The challenge is to develop methods for managing serious offenders in the juvenile system. Several experts have suggested that the juvenile justice system and serious offenders, in particular, could benefit from some of the correctional innovations that have been introduced in the adult system in recent years (Baird et al., 1984). For example, risk assessment is widely used in the adult system, both for initial placement/classification and release. An extensive literature exists on the use of offender classification for adults in the criminal justice system (see, e.g., Farrington and Tarling, 1985; Gottfredson and Tonry, 1987). But little is known about using risk assessment and classification systems in juvenile justice decision making, especially

332 VISHER ET AL.

for serious offenders. Moreover, those systems that are in use may be flawed because of their dominant concern with service needs and inattention to recidivism risk (Guarin+Ghezzi and Byrne, 1989). Although methodological issues are likely to be similar in adult and juvenile classification, substan- tive differences may well exist.

This paper seeks to fill some of the gaps in knowledge about the serious youthful offender. We use a multivariate survival model to examine recidivism patterns among a sample of youths released from California Youth Authority (CYA) institutions and attempt to explain the patterns using a wide range of social characteristics and offending history variables. The resulting model is then used to develop risk-assessment profiles for the sample and for selected individuals within the sample. We suggest that these risk functions may provide a reasonable approach for establishing treatment protocols or supervision requirements for paroled, high-risk youths.

DATA

The subjects of this study are members of a randomly selected cohort of male youths (adolescents and young adults under the age of 2 5 ) released to parole in California between July 1, 1981, and June 30, 1982.2 These data were selected for three reasons: First, as previously noted, relatively little research has focused on the recidivism of high-risk youth-the 88% rearrest rate of this sample clearly characterizes these youths as high risk. Second, the purpose of the paper is to develop an application of the model and, perhaps, gain some insights on serious youthful offending. Third, this data set contains a rich set of variables that have been linked either empirically or theoretically to recidivism.

The 1981-1982 CYA release cohort was 96% male, and this research focuses on the 1,998 male offenders in the CYA release cohort. Information on one or more variables was missing for 49 observations (less than 3% of the sample); thus, the final sample size was 1,949.3

2. The data were originally gathered to develop a risk-prediction instrument for the Youthful Offender Parole Board (California Department of Youth Authority and National Council on Crime and Delinquency, 1987). Funding and support for the collection of these data were provided by the Florence Burden Foundation, the David and Lucille Packard Foundation, the California Youth Authority, and the National Council on Crime and Delinquency.

3. Information on prior commitments was missing for 23 subjects. Data on one or more other independent variables were missing for another 15 subjects. The dependent variable in the analyses is time to failure (arrest or parole revocation) or censoring. Six subjects died during the follow-up period and were dropped from the sample because the date of death could not be accurately assessed. Four subjects’ first arrest “following release” occurred before release and the reason for failure for three subjects could not be determined; these were also excluded.

RECIDIVISM OF YOUTHFUL OFFENDERS 333

FAILURE CHARACTERISTICS

Follow-up data were collected from California records, and thus, failure indicators (e.g., subsequent arrest) are for the state of California only. Fol- low-up data were available for at least three years for all subjects.4

Eighty-eight percent of the sample (1,7 10 of 1,949 subjects) “failed” during the follow-up period. The failure event was defined as the first rearrest or parole revocation after release. (For convenience, failure is subsequently discussed asfirst rearrest.) Of the 1,710 failures, 234 subjects (13.7%) failed due to revocation of parole. The most common reason for failure was an arrest for either a violent offense or robbery (33.7%). For those who failed, the mean time to failure was 306 days; the median was 204.5 days; and the modal failure time was 43 days (14 subjects).

SUBJECT CHARACTERISTICS

A variety of socioeconomic and criminal history variables that have been theoretically or empirically linked to offending are included in the analyses. The values of those variables provide a concise characterization of the CYA sample. Table 1 lists the variables and their respective means and standard deviations.5

Criminal History Variables

Focusing first on criminal history variables, it is apparent that as a group these youths began crime at an early age and were fairly active. The average age at first arrest was 14.2 years, and the average time between the first arrest and the instant CYA commitment (INCRIME) was 4.1 years. The subjects had been arrested an average of 7.58 times and more than 80% had four or more arrests. About two-thirds (63.9%) had previously been committed to custody for a stay of more than 10 days; the mean number of previous commitments was 1.17. Most (53%) of the subjects had not previously violated parole, although numerous parole violations by some subjects resulted in a mean number of violations of 1.03.

Individual criminal history score variables were developed for the subjects

4. The length of time to failure or censoring ranged from 1 day to 1,619 days. For the subjects who did not fail, the length of the follow-up period was determined to be the number of days between release and September 30, 1985. The records were searched during the last few months of 1985. According to CYA officials, (1) the length of time between arrest and the submittal of arrest records to the state vanes among the local jurisdictions and (2) September 30, 1985, was a “safe” censoring date in the sense that all arrests occur- ring on or before that date should have been entered into the state system.

A full discussion of subject characteristics and bivariate correlations in the data is available elsewhere (Linster et al., 1990).

5 .

334 VISHER ET AL.

in an effort to capture both the nature and extent of past criminal activity.6 These variables condense all previous arrest charges (up to three per arrest) into five “score” variables: VIOLENCE, ROBBERY, BURGLARY, OTH- PROP (other property), and GENDELQ (general delinquency).’ Each of these score variables is a weighted sum of the number of charges for offenses of each of the five types. The weight is a function of the number of days between the offense and the instant commitment to CYA. All charges filed within two years (730 days) of the instant commitment are given a weight of 1; earlier charges are downweighted by the ratio 730/(number of days from arrest on that charge to instant CYA commitment).s The rationale for the weighting scheme is that offenses that occurred more than two years earlier might reasonably be assumed to have less bearing on current criminal propen- sities than those that occurred more recently.

The highest mean score (2.19) occurred in the GENDELQ category; values on that score ranged from 0 to 19.6. Considerable past involvement in more serious offending was also indicated by the mean scores for BURGLARY (1.66), OTHPROP (1.33), and VIOLENCE (1.22). These values indicate that, on average, members of this cohort had more than one previous arrest charge for crimes within each of these categories.

Current Commitment

Information on the instant offense and the behavior of the individuals while committed for the instant offense was also available. The variable MWF refers to the most serious charge that led to the CYA commitment. An MWF value of 1 indicates that the offense was a misdemeanor and a value of 3 indicates a felony. The intermediate score of 2 is defined as a “wobbler,” in other words the offense can be either a misdemeanor or a felony. The mean value of MWF was 2.39; the modal value was 2 (57.7%). Less than 2% of

6. Any criminal history score function will necessarily be somewhat arbitrary. For a recent comparison of a variety of operational definitions of prior criminal history, see Nel- son (1989).

7. Violent offenses included homicide, assault, rape, weapons, and kidnapping. Rob- bery and burglary included those offenses as well as attempts. Other properry offenses included grand theft, auto theft, possession and sale of drugs, and arson. Other offenses, which were classified as general delinquency, included miscellaneous assault (e.g., child endangering, riot, false imprisonment), petty theft, receiving stolen property, statutory rape, contributing to the delinquency of a minor, under the influence of drugs or alcohol, escape, miscellaneous felonies or misdemeanors, and welfare and institutional offenses.

8. The equation used to calculate criminal history scores is ZI = I Nk(i) * w(i),

where ZI = criminal history score for crime type k; k = VIOLENT, ROBBERY, BUR- GLARY, OTHPROP, or GENDELQ; Ndi) = number of charges of type k at arrest i; and w(i) = 730/Days(i), where Days(i) = number of days between arrest i and instant CYA commitment or = 730 if Days(;) < 730.


Table 1. Subject Characteristics

Variable Criminal History

AGEFIRST INCRIME ARRESTS PPARVIOL PRCOMMIT Scores VIOLENCE ROBBERY BURGLARY OTHPROP GENDELQ

Description

Age at first arrest (years) Time between first arrest & instant commitment (years) Number of previous arrests Previous parole violations Previous commitments (number > 10 days)

Violent criminal history score Robbery criminal history score Burglary criminal history score Serious property offense score General delinquency offense score

Current Commitment MWF CYAVIOL

Offense type (1 misdemeanor, 2 “wobbler”, 3 felony; Aggressive acts/threats during commitment (0 none, 1 minor act or threat, 2 minor act and threat, 3 major act or threat, 4 major act and threat)

INFRRATE Infraction rate (#infractions/TIMEIN) TIMEIN Length of confinement (years) AGEOUT Age at release (years)

ALCOHOL DRUGS GANG DROPOUT SCHDISC

FAMSIZE FAMVIOL

Substance Abuse and School Problems Alcohol abuse (0 none, 1 minor, 2 major) Drug abuse (0 none, 1 minor, 2 major) Gang involvement (0 none, 1 minor, 2 major) School dropout (0 no, 1 yes) School discipline problems (0 none, 1 minor, 2 major)

Number of siblings (0 <4, 1 > =4) Intrafamily violence or abuse (0 none, 1 minor violence or abuse, 2 major violence or abuse, 3 major violence and abuse) Parental alc/drug dep. (0 none, 1 minor, 2 major) Parental criminality (0 none, 1 minor, 2 major) Sibling criminality (0 none, 1 minor, 2 major) Parental neglect/pwr supervision (0 none, 1 minor neglect or supervision, 2 major neglect or supervision, 3 major neglect and supervision)

Family Background

PARALCH PARCRIM SIBCRIM WEAKMOM

Environmental (Subject’s County of Commitment) PCLRATE Property crime clearance rate PCRATE Property crime rate VCLRATE Violent crime clearance rate

Mean/S.D.

14.19/(2.81) 4.1442.56) 7.58/(4.64) 1.034 1.43) 1.174 1.20)

1.22/(1.43) 0.58/(0.87) 1.664 1.7 1) 1.33/(1.56) 3.24/(2.83)

2.39/(0.52) 0.854 1.30)

0.82/( 1.18) 1.13/(0.61) 19.454 1.84)

0.84/(0.81) 1.02/(0.80) 0.47/(0.79) 0.55/(0.50) 0.8 V(0.82)

0.48/(0.50) 0.40/(0.79)

0.46/(0.80) 0.32/(0.68) 0.65/(0.86) 1.04/( 1 .oo)

0.17/(0.03) 65.244 10.66) 0.5 W(0.09) 14.95A4.49) VCRATE Violent crime rate ~I

NOTE: N = 1,949.

the cohort’s most serious commitment offenses were classified as misdemeanors.

Two variables provided insight into the behavior of the subjects during their confinement in CYA facilities. The first, INFRRATE, measured the number of disciplinary infractions as a function of time in custody. The

336 VISHER ET AL.

cohort averaged 0.82 infractions per year. The second variable, CYAVIOL, combined measures of overt aggressive behavior and threats made during confinement (see Table 1 for coding). For most subjects (1,214, 62.3%), the records indicated no aggressive behavior or threats during confinement. Finally, the average length of confinement in CYA facilities was 1.13 years and the average age at release was 19.45.

Substance Abuse, School Problems, and Family Background

The data suggest that, on average, most of the subjects were not seriously involved in substance abuse or gangs prior to their instant CYA commitment. The means of the variables ALCOHOL, DRUGS, and GANG were 0.84, 1.02, and 0.47, respectively. (These indicator variables were scored in the original case files as 0 if there was no evidence of the behavior, 1 if there was evidence suggesting minor involvement or problems, and 2 if there was evidence suggesting major involvement or problems.) About one-third of the sample had major problems with drugs, and 26% had major problems with alcohol. In addition, 29% of the cohort had some (either minor or major) association with a gang prior to confinement. Fifty-five percent of the subjects had quit school and slightly more than half (55.4%) had records suggesting school disciplinary problems.

Six variables provided information on the characteristics of the subjects’ families. The subjects were as likely as not to have four or more siblings (the mean of the dichotomous variable FAMSIZE was 0.48). For 62.1% of the sample, there was evidence of some parental neglect or poor parental supervision. The variable FAMVIOL provided a measure of evidence of intrafamily violence (any family members) and subject-specific abuse; there was no evidence of violence or abuse for 75.9% of the subjects. Also, most subjects’ records indicated no evidence of parental alcohol problems (PARALCH = 0 for 73.1 %) or parental or sibling involvement in crime (PARCRIM = 0 for 79.8%, SIBCRIM = 0 for 60.7%).

Environment

A final group of variables included in the analysis were two types of “environmental” variables. The first type comprised the county-level Uniform Crime Report crime and clearance rates for property and violent index offenses. Values for these variables were associated with each subject by his county of commitment. The mean property crime and crime clearance rates (PCRATE and PCLRATE) were 65.24 crimes/1,000 population and 0.17 clearances/reported crime, respectively. The mean violent crime and crime clearance rates (VCRATE and VCLRATE) were 14.95/1,000 population and 0.5 1 clearances/reported crime, respectively. The values of these variables varied considerably between countries with, for example, the violent crime


rate ranging from 4.82 to 26.42 and the violent crime clearance rate ranging from 0.19 to 0.82.

The second type of environmental variable is composed of four regional variables (LA, BAYAREA, SONOTLA, and NORCNTRL), which are also associated with county of commitment.9 These variables were included to capture the possible influence of differences in environment not measured by county-level crime and clearance rates. Approximately 40% of the subjects are from LA county and 20% are from each of the other regions.

These descriptive statistics are intended to convey some sense of the study population from the point of view of a number of variables of interest to criminological theory.10 The analytical task for the remainder of this paper is to assemble the information contained in the data into an “intelligible” score function that can be demonstrated to have some credibility as an assessment of a subject’s rearrest risk.

A HAZARD MODEL A variety of analytic methods have been used to determine how a set of

theoretically relevant, independent variables are related to an individual’s probability of recidivism (see Farrington and Tarling, 1985; Gottfredson and Tonry, 1987). In this paper, the analysis is based on the notion of the hazard function. In a hazard (or survival) model, the focus is on the temporal pat- tern of recidivism exhibited by the sample.11 In essence, the dependent variable is time to rearrest (or end of the follow-up period) rather than simply whether a subject was rearrested during some fixed period at risk. The hazard rate forthcoming from a hazard model provides, for any arbitrarily small time dt, the probability that a subject will fail in the period [t, t + dt) given that the subject has not failed prior to t.

Cogent arguments exist for the particular suitability of hazard analysis to the study of recidivism (Gruenewald and West, 1989; Maltz, 1984; Schmidt and Witte, 1988). Maltz (1984) argues that failure-rate measures of recidivism (i.e., the time to failure) provide more information than such typical

9. LA is only Los Angeles County; BAYAREA comprises the counties of Sonoma, Napa, Solano. Marin, Contra Costa, Alameda, San Francisco, San Mateo, and Santa Clara; SONOTLA includes the Southern California counties of Santa Barbara, Ventura, San Ber- nardino, Orange, Riverside, San Diego, and Imperial; NORCNTRL includes all other counties.

Because this paper focuses on the practical utility of using survival models for predicting recidivism, race was not included in the multivariate model.

This type of analysis is also called “survival” analysis because of its applications in biomedical research, in which the research question is often one of how long patients survive after a given treatment or intervention. Survival analysis is described in a variety of sources including Kalbfleisch and Prentice (1980) and Elandt-Johnson and Johnson (1980).

10.

11.

338 VISHER ET AL.

recidivism measures as the proportion of offenders who are rearrested (or reincarcerated) within some fixed time period. More important for our purposes, a “static” model, such as a logit, assumes that a first-day failure is completely equivalent to a failure on the last day of the observation period. However, it is more likely that the subpopulations of early and late failures have different characteristics. Hazard analysis is particularly useful in uncov- ering heterogeneity among subjects with respect to risk of recidivism and identifying covariates that tend to be associated with the time to failure. Thus, hazard analysis explicitly permits investigation of whether early and late failures have different characteristics. This information may be useful in planning and evaluating treatment and supervision programs for serious juvenile offenders.

The flexibility and efficiency of hazard analysis have resulted in this approach gaining rapid popularity as a research tool for studying recidivism. There has also been extensive discussion in the literature about the appropri- ate form of the hazard model: proportional hazards, exponential, Weibull, lognormal and “split-population’’ models (see Schmidt and Witte, 1988). Gruenewald and West (1989) specifically consider the proper form of the hazard model for studying juvenile recidivism. They reason that recidivism among juveniles is likely to vary by age (cohort). The implication is that a proportional hazards model cannot capture essential elements of the recidivism process. They compare fits of exponential, Weibull, and lognormal models and conclude that the lognormal model, which allows for increasing and then decreasing patterns of recidivism risk over time, provides the best fit to their data.

In this paper, we use an extremely flexible model that combines aspects of a variety of standard hazard functions.12 The choice of this model was moti- vated by three assumptions about an offender’s recidivism risk over time. First, risk is relatively low for most (but not all) subjects in the period immediately following release. In this early period, recidivism risk might increase as a positive power of the time since release. Second, subjects who have remained arrest-free for a long time are likely to have a lower risk of recidivism in the near future. This possibility is represented mathematically by including a term that may decrease exponentially with time. Third, both the level of risk and its variability in time are likely to depend on subject covariates.

The basic form of the hazard function is h(t,Z) = eZ’~’aeZ’b’ , (1)

where Z is the covariate vector and u, 6, and c are the parameter vectors to be estimated. The unit of time t is years. Since (h dr) is a conditional probability

12. (1990).

An application of this model to pretrial failure is given in Visher and Linster


and, therefore, dimensionless, the hazard function has the dimensions of 1 / years. This model allows, for example, the possibility that for some subjects the initial risk following release might well be high (Zb < 0) but that for other subjects the risk of rearrest may continue to increase throughout the

Equation 1 shows the basic form of the hazard model. As a final refine- ment to the model, we chose to use a hazard function in which the parametric form in the first 36 weeks at risk was allowed to differ from that in the subsequent period. The decision to model the hazard in two epochs followed the generation of preliminary results from a single-epoch model. These results, although providing a statistically good fit to the data, showed that the model was systematically underestimating failure in the early period following release.13 Thirty-six weeks was chosen as the point of division somewhat arbitrarily on the basis that about half of the 1,949 subjects (979) failed within the first 36 weeks (0.6904 years) following release. (These subsamples were also found to differ significantly on a variety of the measures discussed in the previous section; see Appendix A.) Thus, the final form of the hazard function was

follow-up period (Z’b > 0).

(2)

The form for the later epoch was chosen so as to exclude the singularity at 0 from the range of definition. Although the hazard function will in general have a discontinuity at 36 weeks, the survival function and all probabilities calculated over finite time intervals are continuous for all positive t.

Model parameters were estimated by likelihood maximization. Further discussion of the mathematical properties of the model and the estimation procedure are provided in Appendix B.

c 5 0.6904 t > 0.6904 ’

e Z ~ l t Z b ~ eZ’blt

e z C 2 (t - 0.6712)Zbz eZ’bz(t - 0.6712) h(t ,Z) = I

ESTIMATION RESULTS

The model coefficients and estimated t-statistics are given in Table 2.14 The first three columns present the estimates for the hazard model up to 36 weeks (includes all 1,949 subjects) and the last three columns present the estimates based on the 970 subjects who survived for more than 36 weeks. Blank spaces in the table correspond to parameters that were eliminated in the construction phase of model development (see Appendix B).

13. A likelihood-ratio test comparing the fit of the initial, single-epoch model with a “naive” model that assumed that the covariates contain no reliable information about rearrest risk resulted in a chi-squared value of 786. With 38 degrees of freedom, the probability under the null hypothesis is less than

Not all coefficients achieve traditional levels of significance as measured by the t- statistic. However, by the likelihood ratio test used to construct the model, the “nonsignifi- cant” terms retained in the model contribute “significantly” to the fit of the overall model.

14.

VISHER ET AL.

h W

'9 - v

6 h! - v

2 8 3

0 I

N

U

Q v z 8 W 00

i=' m 5 m m

I 8

00 - - I-- C I W

0 I I 8 8

QZ .?z vv

m w -9 w m 0 0

I

h 00 g 2 x

z m v

W m

2 I

h - 8 0

I

h m z v

m 2 m

'9 I -

h m '9 V - I-

8 I

I

*

WEA

KM

OM

-0

.035

(1

.69)

0.

067

(2.0

4)

PCL

RA

TE

2.

74

(2.2

1)

PCR

AT

E

0.03

2 (2

.55)

V

CL

RA

TE

1.

61

(3.1

9)

VC

RA

TE

-0

.087

(2

.41)

0.

023

(2.9

5)

0.00

7 (1

.91)

R

egio

n (N

OR

CN

TR

L =

Ref

eren

ce C

ateg

ory)

L

A

0.81

5 (4

.09)

0.

221

(2.4

0)

BA

YA

RE

A

0.76

5 (2

.69)

SO

NO

TLA

***

0.21

0 (2

.35)

Inte

rcep

t 5.

09

(2.1

5)

-10.

70

(2.7

3)

3.41

(4

.00)

-1

.20

(4.7

5)

N 1,

949

970

Com

pari

son

with

Nai

ve M

odel

Ln

L

- 79

2.4

- 10

35.2

D.F

. 38

N

ull H

ypot

hesis

Pro

babi

lity

< 10

-10

1.5X

lo-’

NO

TE

S:

***

Indi

cate

s var

iabl

es th

at w

ere

not r

etai

ned

in t

he fi

nal s

olut

ion.

M

axim

um-li

kelih

ood

solu

tion

for

the

two-

peri

od h

azar

d m

odel

of

equa

tion

2; s

ee T

able

1 f

or d

efin

ition

of

vari

able

s.

Q Y w f:

342 VISHER ET AL.

Since the variables are not standardized, the magnitudes of the coefficients in Table 2 cannot be compared directly. To interpret the variable coefficients, recall that the hazard function is log linear in the covariates. Each line of the model, when multiplied by the subject’s covariate value, in effect defines a covariate’s contribution to rearrest risk as a function of time since release. Specifically, rewriting equation (1) in terms of the log hazard for the kth covariate, zk9, at time t,

In h ( t , Z k ) = zk(Ck + bkt + a k h 2). (3) For example, let zk equal AGEOUT with a value equal to the sample mean of 19.45 years (see Table 1). Then, in the early period (t - < 0.6904 years), this variable would contribute [19.45( -0.356) + 19.45(0.417)t + 19.45(-OO.169)ln t] to the log of the hazard function, In h. This function is shown in Figure 1. Also shown is the contribution to the log hazard of each of the terms on the right-hand side of equation 3. As can be seen, the ah term contributes more to the hazard during the period immediately after release, and the bk term contributes more as t becomes large. Because ak and bk are opposite in sign, the hazard function will have an extremum at t* = bk/bd or, in this case, at t* = 0.41 years.15

In general, the criminal history variables and the variables describing the current commitment (see Table 1) have a larger impact on the hazard function than the other groups of variables. Nevertheless, after controlling for the official history factors, all five variables describing the youth’s substance abuse and school problems were significantly related to risk of recidivism. Moreover, several family background characteristics also affected risk. Finally, six of the seven variables describing the county-level property and violent crime and crime clearance rates and county of commitment for each subject affected recidivism risk in the follow-up period.

Four covariates designated by asterisks (* * *) were dropped completely during the model identification process and appear to have little independent influence on recidivism risk in this sample: number of arrests, violence criminal history score, family violence, and parental criminality (ARRESTS, VIO- LENCE, FAMVIOL, and PARCRIM). Although the number of (previous) arrests has generally been found in other studies to be a strong predictor of recidivism risk, we believe that this variable’s lack of contribution here is due to the high correlation between ARRESTS and other variables that offer considerable explanatory power in the model. Among these are the score variables, which provide a (weighted) summary of prior arrest charges for five

15. These properties are apparent in the first derivative of the log-hazard function with respect to time. Specifically, d In h(zbf)/dt = zA(bl + a,/?). As t becomes large, ak/t approaches 0. If bA and a, are opposite in sign (b, + a J f ) = 0 at t = !uk/bd. The extremum is a minimum (maximum) if br is greater than (less than) zero and uk is less than (greater than) zero.

RECIDIVISM OF YOUTHFUL OFFENDERS

I I I I I I I I I I I

0 W N r 4 W 0

I - I I 7

cf 7

343

2

W 0

2

-! 0

in L 0 0) >.

r! 0

N 0

T-

o

2

344 VISHER ET AL.

categories of crime, and several other measures of prior criminal involvement. ARRESTS was strongly correlated with GENDELQ (r = 0.68), INCRIME (r = 0.66), AGEFIRST (r = -0.62). PRCOMMIT (r = 0.41), BUR- GLARY and OTHPROP (r = 0.37). These variables, which influence risk throughout the modeling period (see Table 2), are perhaps better measures of the underlying criminal history so that ARRESTS can offer little additional information. Such a simple explanation for the lack of predictive power for the measure of prior violent behavior (VIOLENCE), and family pathology (FAMVIOL and PARCRIM) is not readily apparent. Individuals with violent criminal histories did tend, on average, to have shorter histories. We can only speculate that the variables that have been shown to predict early delinquency, such as abusive or violent home lives and parental criminal involvement (e.g., Loeber and Stouthamer-Loeber, 1986), are less useful in predicting continuing criminal activity.

The likelihood-ratio test results presented at the bottom of Table 2 suggest that the model provides considerable explanatory power over that offered by a naive model. These results do not necessarily imply that the model is in fact a good one. Conceivably, it is simply much better than a very bad, naive model. In the following section, we turn to this issue by examining the predictive accuracy of the model.

CLASSIFICATION FOR RISK: PREDICTIVE ACCURACY AND RIOC

In this section, some simple tests are applied to assess in a more concrete way how accurate and how useful a model such as ours might be as a risk- classification instrument. It is important to emphasize that outputs of any model like the one analyzed in this paper will be probabilities: A given subject is asserted to have a specified probability of failing within Y years, or of surviving for M months, or of failing in week W, given that he has survived through week W - 1. Such probabilities are not directly observable. Rather, they form the basis for estimating expected numbers of failures or successes, which are observable. We, therefore, define the concept of accuracy in terms of agreement between expected and observed values.

But in many prediction studies “accuracy” is given a very different mean- ing. Each subject is assigned unambiguously either to the class of future failures or the class of future successes and accuracy is determined by some measure of the observed errors of class assignment. If recidivistic failure is thought to involve some element of pure chance (a likely scenario), this definition seems to reflect a chimerical view of prediction since perfect accuracy could only arise if the failure process was completely deterministic.

Still, individual dispositional decisions often involve only two options.


Hence, the practical application of a risk-assessment instrument must fre- quently ignore the probabilistic nature of its statements and act as if it was answering yes or no to the question of a subject’s future failure. The issue then is one of utility-a calculation of the benefits and costs associated with expected numbers of correct and incorrect class assignments. In this sense, a prediction instrument could be perfectly accurate but virtually useless for classification if, for example, it assigns the intrinsically correct (but unobserv- able) failure probability to each individual in the population, but all the probabilities lie within a narrow range. Obviously, any failure model being considered for adoption as a risk-assessment scheme (and a basis for treatment policy) must be able to demonstrate acceptable levels of accuracy and utility. 16

We begin with an analysis of the accuracy of the model developed in this paper. Figure 2 shows the number of observed first rearrests in each four- week interval and the number of expected failures among the population surviving to the beginning of the interval. A chi-squared statistic comparing observed with expected failures has a value of 34.74.17 With 40 degrees of freedom, the probability under the null hypothesis is 0.706.18 This result may be interpreted somewhat loosely as saying that the average four-week failure probability that the model assigns to survivors is, us ufunction of time, in reasonably good agreement with what is observed.

A statistical evaluation of how accurately the model estimates individual probabilities of failure within some given period after release can be obtained by dividing the probability range into nonoverlapping intervals and using those intervals for “classifying” subjects. In Figure 3, this classification is based on the probability of failure within three years. The intervals are of

16. Before a model is adopted for risk classification, analyses of accuracy and utility would presumably be camed out with data other than that used for model construction. Similar checks should also be made periodically to ensure that the current population is not somehow systematically different from the original.

17. For each subject, the intervals represent a sequence of Bernoulli trials, terminating with the interval in which he fails or with interval 40 if he is not rearrested within 160 weeks. Let P, (TbZ,) be the probability that subject i will fail during the kIh four-week interval, conditioned on his having survived to the beginning of that interval. The expected number of failures is in each case the sum of P, over all subjects who have not yet been rearrested and, thus, are still at risk at the beginning of interval k. The standard deviation of the expected failures is the square root of the sum of P,(1 - Pc). From these definitions it follows that the quantities

xk = [(expected rearrests)k - (observed reorrests)k/S.D.k are independent for different k and, under the null hypothesis, are asymptotically distrib- uted N(O.1). Consequently, the sum of their squares is asymptotically chi-square distrib- uted with degrees of freedom equal to the number of intervals.

18. That is, if one chooses to accept the model as a valid representation of rearrest as a stochastic process, overall deviations of the order of those shown in Figure 2 should be expected in about 70% of all applications to similar populations.

346 VISHER ET AL.

!

............

0 : a . ........................

........................

1

..........

/ >.’ ,-

/ / . .’ I

. I 7 ....... ...; ............. ; .......... , ; / I

- 2 - - w- - _ . - - . - A

.........

...........

.........

..........

d

1

.... d. ....

f l .... ..d..

/ ,

..........

-

f ; ‘ I

..............

i S aJ rl I ! O j

3 0 r

3 * r

0 N c

0 0 0 . - m

0

W LY

-

O L m z

4. m Y W

g$l

0 d-

0 hl

0


width 0.05. Thus, the points on the graph at x = 0.625, for example, correspond to subjects whose assigned three-year failure probability is greater than 0.60 and less than or equal to 0.65. To simplify the interpretation of the graph, expected and observed failures were normalized by dividing by the number of subjects assigned to the interval. Thus, the expected failure “rate” is by definition virtually a straight line through the origin with slope 1.

The distribution of the population over the intervals increases monotonically. Only one subject falls into the interval (0.45, 0.50); only nine fall into the interval (0.50, 0.55). Almost 28% of the 1,949 subjects are classified as having a three-year failure probability greater than 0.95. When forecast over three years, the agreement between the distributions of expected and observed failures is clearly not very good. If the 10 subjects in the two lowest probability intervals are combined, there are 10 degrees of freedom and the value of chi-square is 20.9. The associated probability under the null hypothesis is 0.02. Of even more significance, however, are the overestimation of failure probabilities among lower risk subjects and the somewhat less obvious underestimation among higher risk subjects. This is apparently a reflection of systematic errors in the assignment of three-year failure probabilities at the low and high ends of the distribution.

Instead of trying to predict failure within three years, we can restrict attention to the early period after release, comparing expected and observed failure rates during the first 36 weeks. The results are shown in Figure 4. The systematic errors now seem much less severe. Further, combining the lowest two intervals, the value of chi-square is 15.65. With 17 degrees of freedom, the null hypothesis probability is a satisfactory 0.55.

If such a model was being considered for actual use in risk classification, other classification schemes could also be considered and tested for accuracy. If shortcomings in accuracy were uncovered, they might be taken into account by cautions about uncertainties in probability values over specified ranges.

We turn now to a consideration of the model’s utility for risk classification, assuming that a contemplated policy requires that every subject be assigned either to a high-risk or low-risk class. The concept of utility involves definitions and choices dictated by an agency’s policies and practices and its purpose in establishing a risk-classification system. For example, an agency might want to assess risk of failure (here rearrest) within some fixed time after release (perhaps three years). Or it might only be interested in failure while a subject is still under its jurisdiction-an interval that could vary considerably over the population. A hazard model could do both. But the model might turn out to have a potential utility under one definition that is greater than under the other. Other obvious policy concerns are (1) a differential tolerance for the two types of classification errors (false positives and false negatives), (2) resource or political constraints limiting the size of the population that

348 VISHER ET AL.

RECIDIVISM OF YOUTHFUL OFFENDERS

I I I

349

9 c

a! 0

c9 0

2

2 ,-. ln Y

o w M

9 3 v a

t 0

2

: .-- 0

9 0

350 VISHER ET AL.

could be treated as high (or low) risk, and (3) the costs of establishing and maintaining the system relative to the program benefits expected from the classification.

We anchor the analytic discussion of utility in the relative improvement over chance (RIOC) statistic (Farrington and Loeber, 1989; Loeber and Dishion, 1983). We choose to focus attention on reductions in error rates rather than improvements in correct predictions. To this end, a bit of alge- braic manipulation allows the RIOC to be written

RIOC = (4)

where E is the number of observations designated high risk, F is the number of observed failures, Aobs is the number of correct predictions, and N is the sample size. Note that (E - &bs)/E is the false positive rate and (F - Aobs)/ F is the false negative rate.

In this form, the RIOC has a straightforward interpretation in terms of the choice of the selection ratio, E/N, and the implied objectives of the 2 X 2 classification. A relatively low value might be chosen for the selection ratio (E < F) if it is important to ensure that the high-risk group contains only those subjects about whose failure the model purports to be most certain. The RIOC, then, is a direct measure of the power of the model’s classification over that of pure chance in terms of the fractional reduction of false positives. A RIOC of 0.60, for instance, means an expected 60% reduction in the false positive rate.19 A parallel argument obviously holds if the dominating concern is for public safety and the model is used to make a conservative determination of subjects to be classified as low risk (E > F). The RIOC is then a measure of the model’s expected power to reduce the false negative r a t e 9

The results obtained in predicting rearrest during the first 36 weeks, the period for which the model achieves a satisfactory level of accuracy, are shown in Figure 5. Subjects were rank-ordered from highest to lowest risk by their model-assigned probability of rearrest.21 The high-risk group is defined

19.

20.

We emphasize again that this reduction is a percentage of the false positive rate anticipated under a random assignment with a given number E to be ranked high risk.

Any reduction in the expected number of false positives is always matched by an identical reduction in false negatives: (< B > - B ) = (< C > - C). This is not true for reductions in error rates.

Since the classifications considered here depend only on a rank-ordering of probabilities, a number of reasonable choices might be made of the particular model- assigned probability to use. One could, for example, use three-year failure probabilities throughout, whether or not the classification is for risk of failure within three years. We

21.

RECIDIVISM OF YOUTHFUL OFFENDERS 35 1

to be the population fraction shown along the x axis, with the selection starting from the top of the ordered risk listing. Each increment of 0.05 represents the inclusion in the high-risk category of the next 97 subjects in the list.22 Thus, each x value may be thought of as representing a different classification policy.

The population’s 36-week failure rate is 0.502, which is the failure rate one should expect a priori in any randomly chosen subgroup. The observed failure rate among the high-risk group starts at 0.85 and decreases monotonically to 0.52 at x = 0.95.23 The mirror image of the high-risk failure rate, the high-risk survival rate, is also shown since it is the false positive rate. With 5% of the population rated high risk, the failure rate for the low-risk group, the false negative rate, is 0.48. This decreases monotonically to 0.18 with only 5% of the population considered low risk.

The RIOC curve initially expresses, as a fraction of the population survival rate (0.48), the difference between the high-risk survival rate (false positive rate) expected under random assignment and the rate actually observed. The RIOC is initially 0.71 and only 5% of the population is classified as high risk; the RIOC decreases monotonically to 0.3, when 50% of the population is classified as high risk. Thereafter, the RIOC increases again, now expressing the fractional decrease in the false negative rate (since the number of high- risk subjects is greater than the total number of failures in the population).

If the principal concern is to avoid false positives, the RIOC values suggest that the model classification could produce reasonably acceptable results (RIOC > 0.5) as long as the high-risk fraction is kept fairly small-say 10 or 15%. However, this entails a false negative rate on the order of 0.45. But policy based on this classification might still be defensible in terms of its improvement over a policy that implicity assumes that all subjects pose the same risk. At the other extreme, if the concern is for public safety and the avoidance of false negatives, a relatively safe 10 or 15% of the population might be classified as low risk over the short term, but this again means accepting an error rate of about 0.45 in the designation of short-term high risks (false positives).

It might also be noted that the shapes of the curves in Figure 5 offer some assurance that the model-based ordering of individual risks is in general agreement with the observed group outcomes. In particular, if the model’s

generally found, however, that better results were obtained (as measured by comparison of RIOCs) when the probability corresponded to the event for which risk was being assessed-failure within 36 weeks, perhaps, or failure within three years conditioned on some period of survival. Incidentally, this also shows that as time goes on not all subjects’ risks maintain constant rank-order positions relative to one another.

22. 23.

7/389.

Or 98 if Nx is an integer. For the first points, the fractions of high-risk survivors are 0/97, 5/194, 7/292, and

I

I I

I I

I

I I

I

Ris

k F

ail

Rat

e

Low

Ris

k Fa

il pa

I I

I I

I I

I I

I

0.0

0

.1

0.2

0.

3 0.4

0.5

0.6

0.7

0

.8

0.9

1

.0

0

Fra

ctio

n P

op

ula

tio

n H

igh

Ris

k

4


rank ordering of rearrest risk is indeed valid, the RIOC must pass through a minimum when the number of observed failures is equal to the number of subjects designated high risk--consistent with the result shown in Figure 5.24

CLASSIFICATION FOR RISK: MODEL APPLICATIONS We now turn to another aspect of the practical utility of the model for risk

classification. How might parole officers and administrators make use of such a model as, for example, a case management tool?

We selected four subjects from the sample for purposes of illustration. Their values on the variables are given in Table 3. Subjects 1,235 and 64 were chosen because they had, respectively, the highest (0.52) and lowest (< lo-’*) modeled probabilities of surviving for three years after release. Subject 61 5 was taken from the middle of the probability distribution and represents a three-year risk level that is typical of much of the sample-a three-year survival probability of 0.09. Finally, subject 292 (S[3 years] = 0.04) was selected because, among three-year survivors, his hazard function showed the greatest variation over time.

Two kinds of model-generated output are shown in Figures 6 and 7. Fig- ure 6 reflects the model’s changing assessment of the rearrest risk each of these subjects poses. Each point on the curve specifies the probability that the subject will be rearrested during the next six months, given that he has not yet been rearrested.

The median-risk case, 615, was 14 years old when first arrested. He seems to have been seriously delinquent with a record of drug and alcohol abuse, gang involvement, and school problems. The six-month prediction of his risk of rearrest is quite flat, rising from an initial rearrest probability of 0.30 to about 0.37 at 36 weeks and then slowly declining to 0.24 at 2.5 years. He survived arrest-free for almost a year but was picked up on day 349 and charged with a serious property crime.

Subject 292 began his arrest career much earlier than did subject 615 and subsequently had more frequent encounters with the criminal justice system. He seemed to be primarily involved in burglary and other serious property crimes, along with assorted, more minor offenses, but gave no evidence of serious drug abuse or school problems. His initial six-month failure

24. As the high-risk group is expanded, it acquires subjects ranked lower on the risk scale, taking them from the top-ranked of the low-risk subjects. An increase in the fraction classified as high risk thus represents, according to the model, a continual decrease in the high-risk group’s homogeneity with respect to the probability of rearrest but an increased homogeneity of the low-risk group. As the size of the high-risk group passes through the point at which E = F, the RIOC by definition shifts its target from the high-risk to the low- risk group-that is from false positives to false negatives. Thus, one should expect the RIOC, which is in effect a measure of outcome homogeneity of the target group, to behave much as it does in Figure 5.

354 VISHER ET AL.

Table 3. Characteristics of Selected Subjects

Case Number Variable 1,235

AGEFIRST 19.5 INCRIME 0.8 ARRESTS 1 PPARVIOL 0 PRCOMMIT 0 Criminal History Scores VIOLENCE 1 ROBBERY 0 BURGLARY 0 OTHPROP 0

MWF 3 CYAVIOL 1 INFRRATE 0.8 TIMEIN 1.2 AGEOUT 21.4 ALCOHOL 2 DRUGS 2 GANG 0 DROPOUT 1 SCHDISC 0 FAMSIZE 0 FAMVIOL 2 PARALCH 1 PARCRIM 0 SIBCRIM 2 WEAKMOM 0 PCLRATE 0.16 PCRATE 58.9 VCLRATE 0.56 VCRATE 9.7 Region SONOTLA Outcome No Arrest

GENDELQ 0

615

14.6 6.7 4 1 1

0.7 1.4 0 0 1 2 1 0 0.2

21.5 2 2 1 1 2 1 0 0 0 0 1 0.19

65.8 0.62

13.9 SONOTLA

Arrested

292

8.5 8.9

16 0 2

3 0 5.6 4.6 3.7 2 0 2.2 2.3

19.6 0 1 0 0 0 1 0 0 0 2 3 0.14

65.3 0.45

17.3 LA

No Arrest

64

12.7 5.1

21 8 0

1 0 0 2.7

15.1 2 4 0 0.8

18.6 2 2 2 1 2 1 0 1 0 2 2 0.22

49.4 0.47

11.7 NORCNTRL

Arrested Days After Release 1,322 349 1,547 314


r-

I

,

......................

...................... ...........

............

...........

.. ............... ~i ....................................

. ......._........ .... ...

11

II

I

I

356 VISHER ET AL.

probability is quite high (0.64), but drops off quite rapidly to 0.35 by week 36. After that, the rearrest risk the model assigns to 292 is virtually the same as that for 615. Despite 292’s more extensive arrest history, he had no record of previous parole violations, unlike 615. This variable is a strong indicator of current risk among those subjects who survived for an extended period of time (see Linster et al., 1990). For over four years after release, subject 292 had no record of an arrest.

The model gives almost no hope of postrelease success to a subject like 64. He was almost 13 when first arrested and in the next five years accumulated an astonishing record of an arrest about every three months. Although these arrests did not result in a commitment prior to the current one, he often violated the conditions of prior supervisions. He also had a serious record of juvenile delinquency (substance abuse, gang involvement, and school problems). His conditional probability of rearrest within the next six months begins at 0.84 and increases to 0.999 at 2.5 years. He was rearrested on day 314 for a general delinquency offense.

In contrast, for subject 1,235, the model’s six-month forecast begins with the low value of 0.16 and decreases monotonically thereafter to practically zero (0.03) after 2.5 years. This subject had no criminal record prior to his arrest on a violent felony charge when he was 19 years old. His record indicated some serious family, school, and substance abuse problems, but he was convicted in a Southern California county with very low rates of both property and violent crime. There is no record of any rearrest for this subject during more than 3.5 years of follow-up.

The six-month forecast period was arbitrarily chosen. Graphs like these could be generated for each subject with the forecast period being any given interval of interest. Similar results could be used by correctional administrators to estimate staff and resource needs. For example, the conditional probabilities could be used to estimate the expected fraction of the surviving population that will fail during the next interval.

Figure 7 is intended to convey somewhat different information. Here, we suppose that the interest is the probability that a subject, having gone arrest- free for any given length of time, will now survive for some predefined period after release-for example, an individual’s term on parole. The illustration here examines these probabilities for a three-year period for all four subjects. These predictions are statistical prognoses based on the experience of several thousand individuals. They could serve as a basis for policy guidelines, for example, suggesting the assignment of different levels of intensity of parole supervision for different ranges of rearrest risk. Like medical prognoses, they cannot predict the outcome of specific cases; they leave considerable discre- tion to the “clinician,” in this case, the parole officer.

Parole officers could take this kind of information into consideration when deciding how best to distribute their energies and available resources among


0

...._...._....

358 VISHER ET AL.

the cases for which they are responsible. For example, one parole officer might decide that supervision intensity should be proportional to risk level: higher risk cases in the early period after release (subjects 64, 292, and 615) would get more supervision. Another officer might decide on a triage approach, in which cases like subjects 64 and 1,235 are least likely to benefit from his or her efforts (for different reasons) and the greatest chance of making a difference lies with the more uncertain, middle-risk group. Officers could monitor the results of their own tactics by comparing the number of cases surviving arrest-free for one year, for example, with the number expected on the basis of the risk assessment.25

Correctional administrators also could use this type of risk information to establish uniform guidelines for the intensity and kind of supervision and services to be assigned to parolees based on an examination of the distribution of rearrest risk over the paroled population. In addition, statistical results derivable from a model like the one presented would allow the administrator to monitor the impact of policy changes on recidivism and could form an important part of the basis for requests for increased resources.

But as with any statistical predictor, it would be very important to maintain a realization among all users that such prognoses cannot see into the future. Although developed for each subject on the basis of his characterization by the model’s independent variables, they can “forecast” only what should be expected, on average, among a large number of similar cases.

CONCLUSIONS In this paper, we have developed a multivariate survival model that charac-

terizes the rearrest patterns of a cohort of serious youthful offenders. The model results suggest that a variety of variables theoretically linked to criminal behavior are important predictors of the timing of rearrest for these young parolees. Further, the model assigns statistically reasonable risk functions to individuals, which suggests that hazard models may provide a useful approach for establishing treatment protocols or supervision requirements for paroled youths.

For example, suppose there exists within the population a set of offenders that might loosely be described as chronic recidivists-subjects who can be relied on to fail and to do so relatively early (here, 36 weeks) in the period after release. The 36-week results shown in Figure 4 might be interpreted as indicating that the model’s covariates appear to be doing a reasonable job of assigning to each subject a probability of membership in this chronic group.

2 5 . Any such analysis would have to take care to ensure that the outcome was not a self-fulfilling prophecy. For example, if more intensive parole supervision was assigned to high-risk cases, the opportunity for detecting technical violations and, perhaps new crimes as well, would increase.


Figure 5 demonstrates that assignment of individuals to high- and low-risk groups on the basis of their individual risk functions improves the ability to predict failures over that provided by random assignment.

The practical utility of these model results lies in their ability to assist decision makers in allocating scarce treatment and supervision resources. If an intensive level of supervision can be provided to only a small percentage of parolees (e.g., 10 or 15%), the model does an acceptable job of identifying the highest risk individuals and minimizing the resources that would be expended on false positives. Similarly, 10 or 15% might be classified as relatively low risk and assigned to a lower level of supervision.

Similar analyses might be performed to address other policy options. For example, an agency might be interested in a reclassification of subjects who have actually survived for some time T, after release, basing the analysis on conditional probabilities of survival to TI. As time goes on, the nature of the surviving population should be changing through a differential loss of high- risk subjects, and the model could be useful in identifying subjects originally classified as high risk who might now reasonably be shifted to a low-risk sta- tus. Or, perhaps an agency would like to explore a triage policy of distinctly different treatments for the high and low extremes of a risk distribution, shift- ing resources from one group to the other and leaving unchanged the policy with regard to the handling of the middle group.

Used as a basis for risk classification, a reliable hazard model would seem to have the potential for preliminary examination of a wide class of policy options. We would also point out that, because of the ease with which alter- native periods of interest can be handled, hazard models offer a versatility in application that is unique among statistical models of recidivism.

REFERENCES

Ashford, J.B. and C.W. LeCroy 1990 Juvenile recidivism: A comparison of three prediction instruments. Adoles-

cence 25:441-450.

Baird, S.C., G.M. Storrs, and H. Connelly 1984 Classification of Juveniles in Corrections: A Model Systems Approach.

Final report to the Office of Juvenile Justice and Delinquency Prevention. Washington, D.C.: Arthur D. Little.

Prosecutorial waiver: Case study of a questionable reform. Crime and Delinquency 35: 179-201.

Bishop, D.M., C.E. Frazier, and J.C. Henretta 1989

Blumstein, A., J. Cohen, J.A. Roth, and C.A. Visher (eds.) 1986 Criminal Careers and “Career Criminals.’’ Vol. I. Washington, D.C.:

National Academy Press.

VISHER ET AL.

Bureau of Justice Statistics 1987

1988

Recidivism of Young Parolees. Special Report. Washington, D.C.: U.S. Department of Justice. Report to the Nation on Crime and Justice. 2d ed. washington, D.C.: U.S. Department of Justice.

California Department of Youth Authority and National Council on Crime and Delinquency 1987 Classification for Risk: The Development of Risk Prediction Scales for the

Youth Offender Parole Board. Sacramento: California Department of Youth Authority.

The (surprising) stability of youth crime rates. Journal of Quantitative Criminology 2:265-278.

Prediction equations, statistical analysis and shrinkage. In David Famngton and Roger Tarling (eds.), Prediction in Criminology. Albany: State University of New York Press.

Some methodological issues in making predictions. In A. Blumstein, J. Cohen, J.A. Roth, and C.A. Visher (eds.), Criminal Careers and “Career Criminals.” Vol. 11. Washington, D.C.: National Academy Press.

Evaluation of the Habitual Serious and Violent Juvenile Mender Program: Executive Summary. N U 105230. Washington, D.C.: Office of Juvenile Justice and Delinquency Prevention.

Survival Models and Data Analysis. New York: John Wiley & Sons.

Delinquency and Drug Use. Beverly Hills, Calif.: Sage.

Relative improvement over chance (RIOC) and phi as measures of predictive efficiency and strength of association in 2 X 2 tables. Journal of Quantitative Criminology 5:201-214.

Farrington, D. and R. Tarling (eds.) Prediction in Criminology. Albany: State University of New York Press.

Federal Bureau of Investigation Crime in the United States, 1989. Washington, D.C.: U.S. Department of Justice.

Gottfredson, D., and M. Tonry

Cook, P. and J. h u b 1986

Copas, 1. 1985

Copas, J. and R. Tarling 1986

Cronin, R.C., B.B. Bourque, J.M. Mill, F.E. Gragg, and A.A. McGrady 1988

Elandt-Johnson, R.C. and N.L. Johnson 1980

Elliott, D., D. Huizinga, and S. Ageton

Farrington, D. and R. Loeber

1985

1989

1985

1990

1987 Prediction and Classification. Vol. 9 of Crime and Justice. Chicago: University of Chicago Press.

Predictors of chronic criminal behavior. In P. Greenwood (ed.), Interven- tion Strategies for Chronic Juvenile Offenders. New York: Greenwood Press.

Greenwood, P. 1986


Gruenewald, P.J. and B.R. West 1989 Survival models of recidivism among juvenile delinquents. Journal of

Quantitative Criminology 5(3):2 15-229

Developing a model of stuctured decision making in juvenile corrections: The Massachusetts experience. Crime and Delinquency 35:270-302.

The Statistical Analysis of Failure Time Data. New York: John Wiley & Sons.

Guarino-Ghezzi, S., and J.M. Byrne 1989

Kalbfleisch, J.G. and R.L. Prentice 1980

Krisberg, B., I.M. Schwartz, P. Litsky, and J. Austin

Larimore, W.E. and R.K. Mehra

Linster, R.L., P.K. Lattimore, and C.A. Visher

1986 The watershed of juvenile justice reform. Crime and Delinquency 325-38,

1985 The problem of overlitting data. Byte, Oct.:156-180.

1990 Predicting the Recidivism of Serious Juvenile Menders: A Discussion Paper. Washington, D.C.: National Institute of Justice.

Early predictors of male delinquency: A review. Psychological Bulletin Loeber, R. and T. Dishion

1983 94:68-99.

Loeber, R. and M. Stouthamer-Loeber 1986 Family factors as correlates and predictors of juvenile conduct problems and

delinquency. In M. Tonry and N. Moms (eds.), Crime and Justice. Vol. 7. Chicago: University of Chicago Press.

Maltz, M.

National Advisory Committee for Juvenile Justice and Delinquency Prevention Serious Juvenile Crime: A Redirected Federal Effort. Washington, D.C.: Office of Juvenile Justice and Delinquency Prevention.

An operational definition of prior criminal record. Journal of Quantitative Criminology 5(4):333-352.

California’s juvenile probation camps: Findings and implications. Crime and Delinquency 35:234253.

A federal perspective on juvenile justice reform. Crime and Delinquency

1984 Recidivism. Orlando, Ha.: Academic Press.

1984

Nelson, J.F. 1989

Palmer, T. and R. Wedge 1989

Regnery, A.S. 1986

32:39-51.

Schmidt, P. and A. D. Witte

Sechrest, L., S.O. White, and E. Brown (eds.)

1988 Predicting Recidivism Using Survival Models. New York: Springer-Verlag.

1979 The Rehabilitation of Criminal Offenders: Problems and Prospects. Wash- ington, D.C.: National Academy Press.

Targeting serious juvenile offenders for prosecution can make a difference. NIJ Reports. No. 211. Washington, D.C.: National Institute of Justice.

Speirs, V.L. 1988

362 VISHER ET AL.

Visher, C.A. and R.L. Linster 1990 Survival model of pretrial failure. Journal of Quantitative Criminology

6: 153-184.

Weiner, N.A. 1989 Violent criminal careers and “violent career criminals.” In N.A. Weiner and

M. Wolfgang (eds.), Violent Crime, Violent Criminals. Newbury Park, Calif.: Sage.

Wright, W.E. and M.C. Dixon 1977 Community treatment of juvenile delinquency: A review of evaluation

studies. Journal of Research in Crime and Delinquency 19:35-67.

Christy A. Visher is a Senior Research Associate at the National Institute of Justice in Washington, D.C. She received her Ph.D. in sociology from Indiana University in 1982. Her interests include ways in which social science research can inform criminal justice policy, especially in the areas of drugs and crime, violence, and criminal careers. Her recent research on pretrial rearrest and drug testing has appeared in the Journal of Quanti- tative Criminology and the Journal of Criminal Justice.

Pamela K. Lattimore is a Senior Research Associate at the National Institute of Justice in Washington, D.C. She received her Ph.D. in economics from the University of North Carolina (Chapel Hill) in 1987. Her research interests include applications of survival modeling to criminal justice problems, including recidivism, program evaluation, and prison population projection, and empirical examinations of decision making under conditions of uncertainty or risk. Recent research appears in the Journal of Economic Behavior and Organization and Evaluation Review.

Richard L. Linster has been on the staff of the National Institute of Justice and its prede- cessor organizations since 1971 and an Assistant Director since 1975. He graduated from the University of Illinois in 1962 with a Ph.D. in physics. His research interests focus mainly on the adaption of some of the more recently developed analytic methods to the study of criminal justice problems.


APPENDIX A CHARACTERISTICS OF EARLY FAILURES

AND LONG-TERM SURVIVORS As previously noted, the mean time to failure for the cohort was 306 days,

but the median of 204 days suggests that the time-to-failure distribution is highly skewed. In this appendix, the characteristics of two distinct subsamples of the cohort are compared. Specifically, the characteristics of those who failed early (within 36 weeks of release) are compared with those of subjects who survived the initial 36-week period.

Table A.l gives the means and standard deviations of the dependent van- ables for these two groups. For ease of comparison, the values for the com- plete sample (from Table 1) are also included. For the most part, the differences in means between the early failures and survivors are consistent with theory and prior research.

On average, the early failures were arrested for the first time at a younger age than the survivors. They tended to have significantly more extensive criminal histories in terms of length of careers, number of arrests, parole violations, prior commitments, and criminal history scores for prior arrest charges other than violence and robbery. They had worse records of threats, violent behavior, and rule breaking during their current commitment. They were also more likely to have had serious gang involvement and school disciplinary problems. Finally, the early failures were more likely to come from backgrounds of poor parenting and to have siblings with criminal records. More peculiar, perhaps, is the fact that in this cohort the 36-week survivors tended (on average) to have been committed for more serious offenses (MWF) than the early failures and to have served longer sentences. The survivors were also significantly older when released than the early failures.

The early failures had significantly higher scores on 5 of the 1 1 individual and family variables: GANG, DROPOUT, SCHDISC, SIBCRIM and WEAKMOM. Finally, the long-term survivors came from counties with a significantly higher property crime clearance rate. Otherwise, there were no statistically significant differences between the early failures and long-term survivors in the measures of mean crime and criminal justice environments.

364 VISHER ET AL.

Table A. 1. Comparison of Early Failures and Long-Term Survivors

Sample

Variable All

Criminal History AGEFIRST 14.19/(2.81) INCRIME 4.14/(2.56) ARRESTS 7.58/(4.64) PPARVIOL 1.034 1.43) PRCOMMIT 1.174 1.20)

Scores VIOLENCE 1.22/( 1.43) ROBBERY 0.58/(0.87) BURGLARY 1.664 1.7 1) OTHPROP 1.33/( 1.56) GENDELQ 3.24/(2.83)

MWF 2.39/(0.52) CYAVIOL 0.85/(1.30) INFRRATE 0.824 1.18) TIMEIN 1.13/(0.61) AGEOUT 19.45/( 1.84)

ALCOHOL 0.84/(0.8 1) DRUGS 1.02/(0.80) GANG 0.4740.79) DROPOUT 0.55/(0.50) SCHDISC 0.81/(0.82)

FAMSIZE 0.48/(0.50) FAMVIOL 0.40/(0.79) PARALCH 0.4640.80) PARCRIM 0.32/(0.68) SIBCRIM 0.65/(0.86)

Current Commitment

Substance Abuse and School Problems

Family Background

WEAKMOM 1.04/( 1 .oo) Environment PCLRATE 0.17/(0.03) PCRATE 65.244 10.66) VCLRATE 0.51/(0.09) VCRATE 14.95/(4.49) N 1.949

36-Week Failures

1 3.7642.7 1) 4.5742.50) 8.8044.84) 1.30/( 1.5 1) 1.37/( 1.26)

1.244 1.45) 0.61/(0.93) 1.904 1.79) 1.54/(1.67) 3.74/( 2.96)

2.34/(0.51) 0.95/(1.35) 0.97/( 1.28) 1.1 O/(O. 5 8)

19.42/(1.80)

0.82/(0.82) 1.04/(0.80) 0.5440.83) 0.57/(0.50) 0.86/(0.84)

0.48/(0.50) 0.38/(0.78) 0.44/(0.79) 0.34/(0.69) 0.72/(0.88) 1.10/(0.99)

0.16/(0.03) 65.35/( 10.14) 0.5 140.08)

15.03/(4.29) 979

36-Week Survivors

14.62/(2.85)** 3.7 1/(2.56)* 6.34/(4.08)** 0.754 1.28)** 0.984 1.12)**

1.194 1.42) 0.56/(0.80) 1.424 1.59)**

2.73/(2.61)** 1.124 1.40)* *

2.44/(0.53)** 0.76/( 1.24)* * 0.68/( 1.05)** 1.16/(0.63)*

19.494 1.89)

0.86/(0.80) 0.99/(0.80) 0.40/(0.74)* * 0.52/(0.50)* 0.77/(0.80)*

0.49/(0.50) 0.42/(0.80) 0.48/(0.8 1) 0.31/(0.66) 0.58/(0.83)* * 0.984 1.00)**

0.17/(0.03)** 65.12/(11.16) 0.5 1/(0.09)

14.87/(4.68) 970 _ . - , ~ .~

NOTE: Entries are means/(standard deviations). Asterisks indicate significance of two-tailed r test for significance of difference in means of 36-week failures and 36-week survivors:

p ( r ) ~ 0 . 0 5 ** p ( t ) <0.01


APPENDIX B MATHEMATICAL MODEL AND ESTIMATION

PROCEDURE

The basic functional form used for the hazard functions in this paper is

where y, /3, and a are defined as linear functions of a vector of individual covariates Z

h(x) = eyxorePx, (B-1)

y = z’c /3 = Z’b (B-2) a = Z h .

This form allows for considerable flexibility in the individual hazard functions that can be represented (see Linster. et al., 1990; Visher and Linster, 1990). (1) If a is less than zero, the function is very large at small values of x .

Conversely, if a is greater than zero, the function increases from zero at x = &very rapidly if a is less than 1; slowly if a is greater than 1.

(2) If /3 is less than zero, the function decreases to zero exponentially for very large x . It is exponentially increasing if /3 is greater than zero.

(3) If a and /3 have the same sign, the function is monotonic. If they are of opposite sign, it is U-shaped for a < 0 and has a single maximum for a > 0. In either case, it passes through its extremum at x = b/pI.

(4) If /3 is less than zero, h(x) can always be transformed into a function proportional to a gamma density. In that case, its integral over all positive x converges to a finite limit. Thus, the model does not dictate a priori that all subjects will eventually be rearrested.

The model parameters were estimated by maximum likelihood. By definition, the likelihood function is the joint probability of occurrence assigned by the model to all observed outcomes-in this case either failure (arrest) or no failure during the follow-up period. These probabilities can be written in terms of the hazard functions yielding the following log-likelihood function:

F, N, ‘I

In L~ = c In h I ( t , , z , ) - c J h , ( x , ~ , ~ x il jt 0

03-3)

and

3 66 VISHER ET AL.

Fi In L2 = C l n h2(f , ,Z , ) - C N1 1 h ,(x, Z,)dx . (B-4)

11 j 1 36 w k r

In the first of these equations, the sum over i, is the sum over all subjects rearrested within 36 weeks after release; the sum overj, is over subjects either failing or censored during this period. (In our data no subject was censored in the early period so F, is equal to N , . ) The sum on j , is over all subjects surviving at least 36 weeks. In the second equation, the sum over i2 is over those subjects who survived at least 36 weeks but were subsequently observed to fail; the second sum here is over all subjects who survived at least 36 weeks.

One of the common problems encountered in developing prediction models with covariates is that the estimation process in a construction sample simply capitalizes on random variation within the data. In an effort to overcome this problem and achieve some degree of parsimony, we estimated the parameters separately on two randomly selected, nonoverlapping subsets of the data. We used an iterative process to drop parameters showing low validity or reliability (see Linster et al., 1990; Visher and Linster, 1990). A similar approach to model identification is discussed in Copas (1985), Copas and Tarling (1986), and Larimore and Mehra (1985).

The program to estimate the maximum-likelihood parameters is written in GAUSSm. Copies of the program are available from the authors for one year following the date of publication.

PREDICTING THE RECIDIVISM OF SERIOUS YOUTHFUL OFFENDERS USING SURVIVAL MODELS*

Documents

Transcript of PREDICTING THE RECIDIVISM OF SERIOUS YOUTHFUL OFFENDERS USING SURVIVAL MODELS*