established five categories of offenses: Violence, Robbery, Burglary, Other. Property, and ... Other Property offenses include grand theft, auto theft, possession.
Journal of Quantitative Criminology, Vol. I0, No. 4, 1994
Specialization in Juvenile Careers: Markov Results for a California Cohort 1 Pamela K. Lattimore, 2 Christy A. Visher, 2 and Richard L. Linster 3
In this paper, we examine the arrest careers through September 1985 of a highly active cohort of youth paroled by the California Youth Authority in the early 1980s. Our results are in some ways similar to and in other ways different from those reported by other researchers. We find that while adjacent transition matrices appear constant, the same cannot be said for nonadjacent matrices. We reject ~the first-order Markov hypothesis and find support for specialization in the statistical significance of the forward specialization coefficients. Our results also suggest that, in addition to transitions to the same type of offense, an oscillating pattern of offendingis common for our subjects. We also compare the transition matrices of three racial/ethnic and four regional,groups. These results indicate differences in the patterns of offending by the racial/ethnic groups in our sample and similar offense-transition behavior in three of the four regions that differs significantlyfrom that of the fourth region. KEY WORDS: offense specialization; juvenile careers; Markov processes; stationarity.
I. I N T R O D U C T I O N U n d e r s t a n d i n g the offense p a t t e r n s o f youthful offenders can provide valuable i n f o r m a t i o n a b o u t the course of criminal careers. In fact, this topic has been a recurrent theme in studies o f juvenile offenders and, more recently, o f adults. Researchers have e x a m i n e d whether offenders specialize in offense types or c o m m i t a variety o f offenses interchangeably, whether offense patterns show escalation from m i n o r offenses to more serious types, a n d whether arrests or other officially recorded events provide useful knowledge a b o u t 1Points of view are those of the authors and do not necessarilyrepresent the official policy of the National Institute of Justice, U.S. Department of Justice, or U.S. General Accounting Office. 2National Institute of Justice, 633 Indiana Avenue, NW, Washington, DC 20531. 3General Accounting Office, 441 G Street, NW, Washington, DC 20548. 291 0748-4518/94/1200-0291507.00/0 ,.~ 1994 Plenum Publishing Corporation
292
Lattimore, Visher, and Linster
the likelihood of future criminal activity. But despite a great deal of attention to these issues, there is no clear consensus about the nature of offense patterns among juvenile offenders, especially among persistent offenders with lengthy offense histories. Research on offending patterns among youth have examined many different types of juvenile offenders, including minor offenders, courtreferred delinquents, adjudicated cases, and incarcerated offenders. Offense involvement is variously measured by police contacts, arrests, court referrals, or convictions. In addition, offense types are collapsed into categories that often differ across studies, making comparisons difficult. A careful examination of existing studies reveals that the inconsistent results can be explained, in large part, by sample characteristics and various methodological complications that occur in studying offense patterns. 4 These studies of the nature of criminal careers are motivated by a desire to understand offending patterns among persons who engage in criminal behavior. Specialized patterns might require different juvenile and criminal justice system responses than those appropriate for more versatile offending patterns. Fo r example, specialized offending patterns might suggest that crime-specific incarceration policies--such as those directed at repeat violent offenders--would have large impacts on the incidence of specific crime types--such as violent crime. In the absence of criminal specialization, such policies could have only small impacts. Thus, the identification of specialized offending patterns would be useful in formulating targeted law enforcement strategies and assisting criminal justice decisions for individual offenders. Also, Farrington et al. (1988) have pointed out that studying changes in the nature of offending patterns during the course of a criminal career may help identify the role of causal influences such as individual, peer, family, or school factors in criminal behavior. Hence, studies of offense patterns have important implications for theories of criminal behavior and policy responses to crime. 1.1. Prior Research
In the landmark study of a Philadelphia birth cohort, Wolfgang et al. (1972) reported that juvenile offense patterns could be characterized as a first-order Markov process. That is, they found that "knowledge of the immediately prior offense type ( k - lst) does aid in the prediction of the kth type in that there is some tendency to repeat the same type of offense" (p. 4A comprehensivereviewof juvenile and adult criminal careers (Blumsteinet al., 1986)examined the available evidence on patterns of offense seriousness--particularly specialization, offenseclustering, and escalation. Much of the followingdiscussionis taken from the excellent analysis of these issuesby Cohen (1986).
Specialization in Juvenile Careers
293
206). They rejected, however, the hypothesis that knowledge of offenses prior to the k - I st contributed to prediction of the kth offense. Thus, they found weak evidence that juvenile offenders specialize in particular offense types, most particularly for theft, and this conclusion was supported in an extension of the original work into early adulthood (Wolfgang et al., 1987). However, two reanalyses of the Philadelphia data (Cohen, 1986, pp. 405406; Stander et al., 1989) found the original tests of the Markov model to be in error. Specialization is actually greater than originally thought in those data and the accumulated offense history is helpful in predicting the next offense type for the Philadelphia sample. Weak evidence of offense specialization has also been found in several other studies, particularly among samples of persistent juvenile offenders (see Cohen, 1986; Farrington et al., 1988; Rojek and Erickson, 1982; Smith and Smith, 1984; Tracy et al., 1985). Generally, specialization is weakest for injury offenses and strongest for property offenses, including burglary and theft, but differences emerge by race and across studies. For example, while Wolfgang et al. (1972) and Bursik (1980) reported evidence of racial/ethnic differences, Rojek and Erickson (1982) did not find significant differences among the white, black, and Hispanic members of their juvenile sample; they note, however, that their sample was 74% white, 20% Mexican-American, and only 6% black and suggest that their sample may have been too small for reliable results on tests of racial differences. Another type of specialization is revealed through patterns of "offense clustering" (Cohen, 1986, p. 395). The traditional partition among.property, violent/personal, and delinquency (status) offenses may be useful in describing offenses committed by juveniles. Offense clusters exist when there is a significantly greater preference to switch among offense types within a cluster (say, theft and burglary) and a decreased preference to switch to offenses outside the cluster (assault and weapons). The property-versus-violent offense cluster pattern appeared in one study of incarcerated juveniles (Smith and Smith, 1984), but this type of analysis has not been done with other persistent juvenile offenders. This partition is not as sharp among juveniles generally (Cohen, 1986, p. 397). Stander et al. (1989) investigated the extent to which the convictions of a sample of prison releases could be modeled by a stationary, first-order Markov chain; specialization was also investigated using the forward specialization coefficient (FSC). Briefly summarizing, they found for their sample and using convictions as states that successive transition matrices were stationary, i.e., "that the probability of switching from one offense to another remained constant over successive convictions" (p. 317) and that nonadjacent transition matrices were also stationary--suggesting that the transitions could be modeled using a single generating matrix. However,
294
Lattimore, Visher, and Linster
they rejected the first-order hypothesis, finding instead that past criminal history (specifically the k - 2 n d offense) contributed significantly to the prediction of the kth offense. Rejection of the first-order hypothesis was due largely to the contributions of offense triples to the overall test statistic--in every case for these iii triples the observed values were higher than the expected. They went on to note that observed being greater than expected frequencies for repeat offenses of the same types suggested some degree of specialization, which they investigated further through the calculation of FSCs. In almost all cases, these FSCs were significantly greater than zero. A study of recidivism among a large sample of young parolees also found that offense history was related to later arrest patterns (Bureau of Justice Statistics, 1987). Parolees were often rearrested for the same crime type for which they were incarcerated; this pattern was especially evident for robbery, fraud, assault, and drug offenses. Also, property offenders with a prior arrest for a violent offense were rearrested more often for a violent offense (43%) than those without prior violent arrests (29%). 1.2. Present Study
The current study builds on the past research by using data on the extensive arrest careers of a cohort of youthful parolees. The lengthy official records of these youth permit a reliable, detailed analysis of offense patterns using up to 42 successive arrests. The data also enable separate analyses of offense specialization for very frequent offenders (defined here as those with 10 or more arrests), as well as comparisons of offending patterns of three racial/ethnic groups and groups from four regions. The data include both juvenile and adult arrests and span at least one incarceration. These data permit replication of analyses based on smaller, less detailed studies and exploration of additional questions about offense specialization. 2. DATA The subjects of the current analysis are a random sample of 1998 male youth released from the California Youth Authority (CYA) between July 1, 1981, and June 30, 1982. Some characteristics of these subjects are shown in Table I. As a group, these individuals began crime at an early age (14.2 years at first arrest) and have been fairly active since (an average of 7.6 arrests). Additional description of the subject characteristics is given by Linster et al. (1990) and Visher et aL (1991). Of the 1998 subjects in the original sample, the focus of these analyses is the 1942 who had two or more arrests. The data characterizing these subjects include all arrests committed prior to the instant incarceration and
Specialization in Juvenile Careers
295
Table 1. Subject Characteristics Variable Criminal history Age at first arrest (years) Time between first arrest & instant commitment (yearv) Number of previous arrests Previous parole violations Previous commitments (number >10 days) Violence criminal history score Robbery criminal history score Burglary criminal history score Serious property offense score General delinquency offense score
N
Mean (SD)
1998 1997 1998 1998 1975 1997 1997 1997 1997 1997
14.19 (2.81) 4.14 (2.58) 7.58 (4.67) 1.03 (I.43) 1.16 (I.20) 1.22 (I .44) 0.58 (0.87) 1.65 (1.70) 1.34 (I.55) 3.24 (2.84)
Current commitment Offense type (I, misdemeanor; 2, "wobbler"; 3, felony) Aggressive acts/threats during commitment (0, none; l, minor act or threat; 2, minor act and threat; 3, major act or threat; 4, major act and threat) Infraction rate (No. #~'actions/years incarcerated) Length of confinement (years) Age at release O'ears) .
1998
2.38 (0.52)
1998 1991 1998 1998
0.85 (I.30) 0.82 (I.18) 1.12 (0.61) 19.45 (1.85)
Substance abuse and school problems Alcohol abuse (0 if none, 1 if minor, 2 if major) Drug abuse (0 if none, 1 if minor, 2 if major) Gang involvement (0 if none, 1 if minor, 2 if major) School dropout (0 if no, I if yes) School discipline problems (0 if none, 1 if minor, 2 if major)
1998 1998 1998 1993 1997
0.84 (0.81 ) 1.02 (0.80) 0.47 (0.79) 0.54 (0.50) 0.81 (0.82)
1998
0.48 (0.50)
1998
0.40 (0.79)
1998 1997 1998
0.46 (0.80) 0.32 (0.68) 0.65 (0.86)
1998
1.05 (1.oo)
Family background Number of siblings (0/f 4) lntrafamily violenceor abuse (0, none; 1, minor violence or abuse; 2, major violence or abuse; 3, major violence and abuse) Parental alcohol/drug dep. (0, none; 1, minor; 2, major) Parental criminality (0, none; I, minor; 2, major) Sibling criminality (0, none; 1, minor; 2, major) Parental neglect/poor supervision (0, none; 1, minor neglect or supervision; 2, major neglect or supervision; 3, major neglect and s,lpervision)
all follow-up arrests that occurred through September 1985. By c o n c a t e n a t ing what would usually be called " p r i o r arrests" and all arrests occurring in the 3 years following release, we avoid the bias problem C o h e n (1986) identified with some earlier studies that looked at incarcerated offenders a n d included as the final offense for each subject the arrest/charge that led to incarceration. As n o t e d by C o h e n , such charges are usually serious ones so the final transition is to a serious offense, which can bias studies o f offense
296
Lattimore, Visher, and Linster
seriousness. The average age at release was 19.45 years; thus, the arrest data include both juvenile and adult arrests. The maximum number of arrests for the sample was 42. As the interest here is the arrest transitions of these subjects, we discuss these arrests in some detail. F o r the purposes of these analyses, we have established five categories of offenses: Violence, Robbery, Burglary, Other Property, and Delinquency. Violence includes homicide, assault, rape, weapons, and kidnapping. Robbery and Burglary include these charges and attempts. Other Property offenses include grand theft, auto theft, possession and sale o f drugs, and arson. 5 Delinquency offenses, our "other" category, 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. Up to three offenses per arrest were recorded for each subject. The most serious charge for each arrest was used in our analyses. Previous studies o f offense specialization have also used the most serious arrest charge in analyses (e.g., see Stander et al., 1989). In the CYA data, more than one charge per arrest was relatively rare. 6 However, the reader should be aware that since a single criminal event often includes several types of illegal activities, the " m o s t serious charge" measure m a y mask information about diversity or specialization in offending. Table II shows the distribution of most serious charge by arrest number. More than half of the sample (1087 subjects ) had 10 or more arrests and 25% of the sample had 15 or more. As is usually the case with these types of categorizations, the most c o m m o n charge, regardless of arrest number, was for an offense in the "other category," i.e., for a Delinquency offense. However, the most serious charge for most arrests was for something other than a Delinquency charge (e.g., 1205 of the 1941, or 62% of, second arrests). 7 A charge of Robbery was the least common. 5possession and sale of drugs were included in the Other Property category because of the relatively low incidence of these offensesin our sample. The time period of our study generally was prior to the escalation of use and sale of crack cocaine. 61n our data, simultaneous charges for different events were relativelyrare. For example, if we were to look at the first arrest followingrelease, 85% of the subjects had (at least) one charge, but only 300/oof the subjects had two charges and only 13% had three charges. Of those with two charges, 40% of the multiple charges were of the same type. For our analyses, therefore, we ignore multiple charges and focus on most serious charge. 7Note that 1942 subjects had two or more arrests. The charge for the second arrest could not be determined for one subject. Of the 21,878 arrests for all subjects, the charge associated with .the arrest could not be identified for 14 arrests. These values were treated as missing in the transition matrices.
N"
.-I
.~'=
~.~-
~aa
~
~'~
0
~Q
~Z
8
o
o
>
z
~r
.~
o
~_.
298
Lattimore, Visher, and Linster
record is likely affected by victim reporting, law enforcement practices, and charging policies. However, if studying offense patterns with official record data reveals patterns that are significantly different from chance expectations, then those results can provide important knowledge and hypotheses about the nature and progression of criminal careers. Further validation of such findings could include different data sources or methods. Finally, because studies of offense specialization require data on large numbers of successive events, results are usually more representative of the offense patterns of serious, frequent offenders; the results of our analyses are no exception. 3. MARKOV ANALYSES AND R E S U L T S The analyses reported in this section examine the arrest careers (through September 1985) of a highly active and seriously criminal cohort of CYA parolees. We consider two groups of subjects--those with 2 or more arrests and a persistent group classified as those with 10 or more arrests. We also examine and compare the transition matrices of three racial groups and four regional groups. 3.1. Testing Transition Matrices for Stationarity
The first-order, arrest transition matrices are constructed to show the frequency of ( t - 1, t) offense pairs. We have five offense categories. Thus, the matrices are 5 x 5, with each row representing the offense charge for the t - 1st arrest and each column representing the charge for the tth arrest. For example, the first row of each matrix contains the subjects charged with Violence on the t - 1st arrest distributed over their tth offense--either Violence, Robbery, Burglary, Other Property, and Delinquency. The first transition matrix (T= 1), which shows the first and second arrests, is shown in Table III. As can be seen, the first arrests of the 261 subjects with two or Table ill. First and Second Arrest Transitions"
Second arrest charge First arrest charge
Violence
Violence Robbery Burglary Other property Delinquency Total
51 20 63 27 91 252
~
are numbers of subjects.
Other Robbery Burglary Property Delinquency Total 17 !9 26 25 35 122
52 25 207 59 173 516
42 14 83 83 93 315
99 39 201 80 317 736
261 117 580 274 709 1941
Specialization in Juvenile Careers
299
more arrests were for violent offenses (sum of row 1 in Table III). For this group, the next arrest was for a violent offense in 51 cases. Similar matrices can be constructed for each transition T = 1, 2 . . . . ,41. The offense transition process is stationary if the probability of moving from one charge to another is the same for all arrests. A stationary transition process would argue against, for example, an escalation in the seriousness of offenses for persistent offenders. The method of Goodman (1962) was used to compare adjacent transition matrices. In this method, a row from one matrix (e.g., that containing the offense transitions between the first and the second arrests such as shown in Table III) is compared with the same row from the next transition (e.g., that containing the transitions between the second and the third arrests). The Z 2 values are calculated in the usual way for each cell of these 2 x c tables, where c is the number of columns (equal to the number of offense types, or five for our analyses). The procedure is repeated for each of the c rows. The ;(2 values are summed, yielding a test statistic that is distributed ;(2 with c. ( c - 1) degrees of freedom (df). Results of 20 such comparisons are shown in Table IV for two g r o u p s - all subjects with two or more arrests (2+) and the group consisting of those with 10 or more arrests (10+). In no case was the test statistic significant (with 20 df, ;(2= 31.41 is statistically significant at the 0.05 level), suggesting that all of the transition matrices for the two groups could have been generated by the same process. This finding is consistent with those reported by Stander et al. (1989) and other researchers (e.g., Bursik, 1980; Rojek and Erickson, 1982). Although the hypotheses that the adjacent matrices for these two groups appear to be constant were not rejected, the question arises as to whether the same can be said for nonadjacent matrices. Two tests (Goodman, 1962; Anderson and Goodman, 1957) were applied to the data to investigate this question. The Goodman (1962) test is an extension of the test that compares adjacent matrices. Tables are constructed of dimension T x c, where T is the number of transitions. A separate table is constructed for each offense type by extracting the same rows from each of the T transition matrices (e.g., the first row from each of 20 transition matrices); thus, c tables are constructed. The test statistic consists of the sum of cell ;(2 values calculated in the usual way; this statistic isdistributed Z 2 with c- ( c - I) 9 ( T - 1) df. We again examined the first 20 transitions for the groups composed of all subjects with 2+ and 10+ arrests. The total numbers of arrest transitionpairs were 19,279 and 14,939 for the 2+ and 10+ groups, respectively. The resulting values of the test statistics were 426.50 and 489.93, for the 2+ and 10+ groups, respectively. Both values are significant at the 0.05 level (380 df)--suggesting, for each group, a rejection of the null hypothesis that
300
Lattimore, Visher, and Linster Table IV. Comparison of Adjacent Transition Matricesu
2+ arrests
10+ arrests
Matrices compared
,Z2
N
Z2
N
1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10 10 to II 11 to 12 12 to 13 13 to 14 14to 15 15 to 16 16 to 17 17 to 18 9 18 to 19 19 to 20 20 to 21
26.68 19.63 18.29 12.25 15.92 17.65 15.68 11.11 14.64 10.67 19.27 18.34 21.28 28.26 27.95 24.04 18.15 26.57 14.74 12.16
1941 1880 1797 1719 1615 1485 1362 1221 1086 959 830 713 594 493 413 338 273 229 180 147
17.82 17.15 24.05 22.96 19.79 13.86 14.72 12.57 14.64 10.67 19.27 18.34 21.28 28.26 27.95 24.04 18.15 26.57 14.74 12.16
1086 1083 1083 1085 1086 1086 1086 1086 1086 959 830 713 594 493 413 338 273 229 180 147
*With 20 dr, X2=31.41 is significant at the 0.05 level. N is the number of subjects in the t - 1 matrix. all transition matrices could have been generated by the same process. 8 The Z 2 statistics that were significant at the 0.05 level were also f o u n d for the D e l i n q u e n c y tables for b o t h g r o u p s a n d for the Violence table for the 10+ group. The Z 2 test statistic for the Violence table for the 2 + group had a p value o f 0.0543. F o r the 2 + .group, nearly 25% of the total test statistic (100.51 o f 426.5) was a t t r i b u t a b l e to the Z 2 c o n t r i b u t i o n s o f only 15 o f the 500 cells. These values are shown in T a b l e V. These results differ from those reported by S t a n d e r et al. (1989) a n d others (e.g., Bursik, 1980; Rojek a n d Erickson, 1982), who did n o t reject the stationarity a s s u m p t i o n a n d were able to conclude that "the p r o b a b i l i t y o f one offense type being followed by a n y other offense type was n o different o n the tenth conviction (for example) t h a n on the first c o n v i c t i o n " (Stander et aL, 1989, p. 323). O u r results suggest otherwise for o u r sample. In other words, for o u r subjects, there are differences as the n u m b e r o f the arrests SA heuristic for the validity of a •' statistic is that no more than 20% of the cells have expected values less than 5. This condition was met for both groups. The total number of cells for each group was 500 (5 x 20 x 5). The 2+ group had 54 cells with expected counts less than 5, while the 10+ group had 60 cells with expected counts less than 5.
Specialization in Juvenile Careers
301
Table V. Largest Cell Z2 Values for Nonadjacent Comparisons: 2+ Arrest Group
~
Arrest Charge*
Cell value
Transition No.
t- 1
t
Z2
Observed
Expected
1 2 18 16 12 14 1 9 6 18 2 17 2 1 14
D D B R D D V V V D D D V V R
B V R V B V B B OP V R V R V V
11.2946 8.1147 7.2787 7.1987 6.8873 6.8429 6.4031 6.2957 6.2883 6.1027 5.8738 5.7153 5.6243 5.4694 5.1163
173 74 7 10 32 42 52 I1 20 20 59 22 29 51 1
134.1 102.9 2.6 4.4 50.7 28.1 36.7 23.0 34.8 11.6 43.1 :3.3 18.7 70.7 7.0
Burglary; D, Delinquency; OP, Other Property; R, Robbery; V, Violence.
increase during a career in the probability o f the charge on one arrest being followed by any other charge on the next arrest. These results m a y be due either to changes in individual offender behavior as criminal experience increases (e.g., escalation in offense seriousness) or to changes in the c o m p o sition o f the sample over successive transitions (e.g., only 147 subjects have 21 arrests and, thus, contribute offense transitions to the T = 2 0 matrix). We investigated the stationarity issue further using the maximum-likelih o o d m e t h o d o f Anderson and G o o d m a n (1957). The maximum-likelihood estimator under the null hypothesis that p#(t) =pg is
Ln~J
which is the observed transition probability matrix calculated from the sum o f T transitions. F o r o u r data and T = 2 0 , the maximum-likelihood estimators for the 2 + arrests and I 0 + arrests groups, were as follows:
V ~z§
= '
R
B
OP
D
V ['0.2707
0.0808
0.1405
0.1626
0.3454
R ]0.1992 B 0.1219
0.1558 0.0559
0.1442 0.3271
0.1806 0.1535
0.3202 0.3415
OP 0.1325
0.0738
0.1737
0.2842
0.3359
D I.0.1413
0.0592
0.189t
0.1534
0.4569
(2)
Lattimore, Visher, and Linster
302
V
~,0+T=2o = '
V ['0.2511 R [ 0.1876 B 0.1105 OP 0.1294 D .0.1330
R
B
OP
D
0.0713 0.1401 0.0502 0.0662 0.0520
0.1391 0.1412 0.3222 0.1728 0.1838
0.1749 0.1955 0.1560 0.2809 0.1554
0.3636 0.3356 0.3610 0.3508 0.4758
(3)
where the order of offenses (down the rows and across the .columns) is Violence, Robbery, Burglary, Other Property, and Delinquency. (Rows may not sum to 1 due to rounding.) As can be seen, the most likely transition regardless of the t - I st arrest charge is to an arrest at t for a relatively minor charge, those we have denoted as Delinquency (column 5). However, the next most likely transition is to the same offense for each category except Robbery. If the charge at arrest t - 1 is for Robbery, the next most likely charge at arrest t is a Violence charge for the 2+ group and for an Other Property offense for the 10+ group. It can also be noted that for the 10+ group, a Robbery charge on the tth arrest is least likely to follow a Robbery charge on the t - 1st arrest. Those with 10+ arrests also appear to be slightly more likely than those with 2+ arrests to transition to a Delinquency charge from any previous charge [compare the values of the last columns in Eqs. (2) and (3)]. Conversely, the 10+ group is slightly less likely than those with 2+ arrests to transition from any offense to either a Violence or a Robbery charge. (Note these two groups/matrices are not independent.) The differences are small however. The likelihood ratio comparing observed transition matrices with the maximum-likelihood estimator is calculated as # , j T ~'('' ~'=~~ IL~J
(4)
The test statistic [ - 2 - ln(~,)] is distributed X 2 with ( T - I) 9 c. ( c - 1) df. As Stander et al. (1989) note, this statistic is approximately equal to the Z 2 statistic already reported. And, indeed, for T = 20, we find the test statistic to equal 433.8169 and 496.1763 for the 2+ and 10+ groups~ respectively. We then compared successive numbers of transition matrices, i.e., the first and second ; the first, second, and third; etc. Our purpose was to identify the transition at which we could no longer accept the stationarity hypothesis. For the 2+ group, the likelihood-ratio test statistic for T = 2 was 26.8287, not significant at usually accepted probability levels and very similar, as would be expected, to the X 2 test statistic reported for the comparison of the first two matrices reported in Table IV. At the 0.05 level of significance,
303
Specialization in Juvenile Careers
the null hypothesis of stationarity could not be rejected for T < 16. At T = 16, the test statistic was 333.5822, which, with 300 dr, has a probability value of 0.0885. At T = 17, the test statistic (calculated over 18,719 arrest transition pairs) was 365.0709, which, with 320 df, has a probability value of 0.0418. Examination of the 20 transition matrices and the maximum-likelihood estimators generated for T = 2, 3, 4 . . . . . 20 reveals that transitions to Violence from any previous offense increases with T. This is seen by comparing Eq. (2) above with the maximum-likelihood estimator for T - 2 : V R B OP D
V "0.2191 0.1931 0.1076 0.1052 0.1148
R
B
OP
D
0.0933 0.1545 0.0492 0.0828 0.0654
0.1704 0.1931 0.3469 0.2052 0.2296
0.1623 0.1545 0.1438 0.2862 0.1371
0.3550 0.3047 0.3525 0.3207 0.4530
(5)
When only the transitions between the first and second and the second and third arrests are considered, the probability of a Violence charge being followed by another Violence charge on the subsequent arrest is about 0.22 [first cell in Eq. (5)]. The comparable probability when the first 20 transition matrices are considered [Eq. (2)] is 0.27. Comparison of the first columns of Eq. (2) and Eq. (5) reveals that the probability of a transition from any offense at t - 1 to a Violence offense at t is greater when the first 20---as opposed to the first 2--transition matrices are considered. One interpretation is that those who have accumulated many arrests become increasingly likely to be arrested for violent offenses, i.e., that these offenders are becoming more serious. At issue is the extent to which this is due to changes in the individual offenders and changes in the population of offenders over successive transitions. Cohen (1986, p. 383), for example, has noted that "nonstationarity might also arise from changes in the sample of offenders at successive transitions.., the later matrices are limited to offenders who have a sufficiently large number of arrests." If we look only at those offenders with 10 or more arrests, we find that the stationarity hypothesis cannot be rejected at the a = 0.05 level for T= 2, 3 . . . . . 9. In other words, as long as we are focusing on only those transitions made by the complete sample, the hypothesis of a single generating process cannot be rejected (at T = 9 , the test statistic equals 185.4372, p = 0.0823, 160 df). When the first 10 transition matrices are considered, however, the value of the test statistic is 214.5706, which has a p value of 0.0399 (180 df). As a group, these 10+ individuals are less likely than the 2+ group to be arrested for the most serious offenses (Violence, Robbery)early in their
Lattimore, Visher, and Linster
304
arrest careers. This can be seen by comparing the T= 2 maximum-likelihood estimator for this group (2169 offense transitions) with that for the complete sample [Eq. (5)]:
fJt~247
V V I'0.1290 R 0.1456 B 0.0832 OP10.1122 D 1.0.0951
R 0.0737 0.0777 0.0399 0.0609 0.0513
B OP D 0.1659 0.1843 0.4470 1 0.2330 0.1748 0.3689/ 0.3411 0.1331 0.4027/ 0.1731 0.2756 0.3782 / 0.2147 0.1346 0.5043J
(6)
As can be seen, the probability of any first arrest being followed by a Delinquency charge is higher for the 10+ group than the complete sample when only the first two transitions are considered. (For example, the probability of Violence-Delinquency is 0.45 for the 10+ group and 0.36 for the 2+ group.) The increasing likelihood over successive arrests that the 10+ group will be arrested for violent crimes is also apparent by comparing the first columns of Eqs. (6) and (5). The probability of a Violence-Violence transition is 0.1290 when only the first 2 transitions (three arrests) are considered, in comparison to 0.2511 when the first 20 transitions are considered. Moreover, when the first nine transitions are examined for the I0+ group (data not shown), the probability of a Violence-Violence transition is 0.2147 and the probability of a Robbery-Robbery transition is 0.1360. Thus, among the 10+ group, both escalation in crime seriousness and more specialization in violent offenses are occurring over time. 3.2. Testing the First-Order Markov Assumption
A Markov process is characterized as first-order if knowledge of the t - 2 n d (or earlier) state(s) does not improve our ability to predict the tth state beyond that realized by knowing the t - 1 s t state. As such, Markov processes are often called "memoryless" because transitions depend, at most, only on the current state. One method of testing whether a Markov process is first-order is to determine whether the probabilities pijk(t), the probability of being in state k at t conditioned on being in statesj at t - 1 and i at t - 2 , are significantly different from the probabilities pjk(t) (see, e.g., Stander et al., 1989). If the second-order Markov condition is assumed to hold, all T /jk transitions can be summed to produce c tables, each representing i-to-k transitions holding the j state constant. The H 2 test statistic compares observed values with expected values (under the null hypothesis) and is calculated in the usual way for a ;(2 statistic; H 2 is distributed ;(2 with c- ( c - l ) . ( c - 1) dr.
Specialization in Juvenile Careers
305
For our analyses, five tables---one for each of the offense types--were constructed. Each 5 x 5 table compared the offense on arrest t - 2 to the offense on arrest t for t = 3, 4 . . . . . 42. (Analyses were also conducted limiting t to 20; the results did not differ from those reported here.) For the 2+ group and 10+ group, the H 2 statistics were 674.1144 and 573.8983 respectively. These values greatly exceed 101.6, the 0.05 critical value for a Z 2 statistic with 80 df. These results are consistent with those of Stander et al. (1989). Unlike Stander e t al., however, whose "analysis was limited by small expected values" (p. 324), we experienced no such difficulty. The smallest expected value in our analysis was 9.5 (which was for the RobberyBurglary-Robbery offense triple). The diagonal entries in each table represent/jk offense triples where i = k (e.g., Violence-Violence-Violence or Violence-Burglary-Violence). Two types of behavior are represented by these diagonal entries--a tendency to specialize and a tendency to oscillate between two different offense types. Stander et al. (1989) found that all iii offense triples--indicating specializat i o n - m a d e comparatively large contributions to the H 2 statistic and that, in each case, the observed value was greater than the expected value under the null hypothesis. For our data, the largest cell contributions to the H 2 statistic came from values along the diagonals (shown in Table VI). For each of these 25 triples, the observed values were greater than the expected values. Additionally, either the differences between observed and expected counts for off-diagonal entries were negligible (contribution to H 2 less than 1) or the observed counts were less than the expected counts. 9 Clearly repeat offenses of the same type suggest a tendency toward specialization. It is more difficult to interpret an oscillating pattern. This oscillating pattern may indicate changes in offenders' choices of criminal acts as offenders deliberately switch between more serious, risky behaviors and less serious behaviors. Alternatively, this pattern could reflect law enforcement practices as arrests for serious offenses increase the likelihood of detection and arrest for other, less serious offenses. Cohen (1986, p. 408) has pointed out that in specialization analyses relying on official data, transitions from rare events (such as robbery and violence) to frequent events (such as larceny) will appear more common than they actually are because of differences in law enforcement practices that result in differences in detection and apprehension rates. Another explanation for the oscillating pattern is the general tendency for serious, frequent offenders (which would describe 9TheonlyexceptionswereR - B - V(O = 28, E = 20.28), V - D - R (O = 68, E= 52.90), R - D - V ( 0 = 61, E=52.95), and R - B - O P (0=33, E=25.20). Stander et al. (1989) did not report all of their findings with respect to their first-order test, but of the 16 values they reported, none involved three different types of offense.
306
Lattimore, Visher, and Linster Table V1. Selected Offense Triple Contributions to H 2 Offense Type Expected
( 0 - E)"/E
228 27 95 75 375
171.03 17.83 62.00 63.07 328.56
18.97 4.72 17.56 2.26 6.57
Violence Robbery Burglary Other property Delinquency
44 35 46 61 143
39.04 26.71 29.64 42.96 126.98
0.63 2.57 9.04 7.57 2.02
Burglary Burglary Burglary Burglary Burglary
Violence Robbery Burglary Other property Delinquency
75 18 517 119 525
45.78 9.51 413.73 84.89 467.76
18.65 7.59 25.78 13.71 7.00
Violence Robbery Burglary Other properiy Delinquency
Other property Other property Other property Other property Other property
Violence Robbery Burglary Other property Delinquency
86 40 179 316 436
55.95 15.74 103.05 248.97 375.31
16.15 37.37 55.97 18.04 9.8 I
Violence Robbery Burglary Other property Delinquency
Delinquency Delinquency Delinquency Delinquency Delinquency
Violence Robbery Burglary Other property Delinquency
194 51 355 261 1730
127.50 22.00 248.90 169.05 1546.80
34.68 38.21 45.25 50.01 21.70
i
j
k
Violence Robbery Burglary Other property Delinquency
Violence Violence Violence Violence Violence
Violence Robbery Burglary Other property Delinquency
Violence Robbery Burglary Other property Delinquency
Robbery Robbery Robbery Robbery Robbery
Violence Robbery Burglary Other property Delinquency
Observed
the CYA cohort) to commit a wide range of offenses which vary considerably in seriousness (Chaiken and Chaiken, 1982). Rejection of the first-order hypothesis (in favor of the second-order hypothesis) suggests that the probabilities of interest are thep,yk probabilities rather than the Pjk probabilitiesJ ~ For same offense pairs and triples the maximum-likelihood estimator values are shown in Table VII. For four of the five offense types (all except Robbery), transition to the same offense given that the two previous offenses were of that same type is the most likely transition--i.e., piig>puk for j, k q:i. For Robbery, the most likely charges following two Robbery arrests were for Delinquency and then for Violence (PRRo = 0.2982 and PRRV= 0.2105). ~~ of the first-order hypothesis in favor of the second-order suggests that knowledge of the t - 2 n d offense in addition to the t - 1st offense will help us predict the tth offense. As noted by a reviewer, more distant offenses (e.g., t - 3rd) might also offer significant information. The data d e m a n d s to test a second-order hypothesis are quite extensive, as we would have to consider ijkl offense quadruples.
Specialization in Juvenile Careers
307
Table VII. Maximum-likelihood Estimates ofpi~ and Pt~
All subjects Offense i Violence Robbery Burglary Other Property Delinquency
10+ Arrests subjects
P~i
P,i
P,
Pii~
0.2701 0.1565 0.3252 0.2832 0.4589
0.3701 0.2047 0.4002 0.3571 0.5143
0.2512 0.1418 0.3197 0.2798 0.4774
0.3604 0.2054 0.3927 0.3572 0.5318
*Maximum-likelihood estimates are based on the maximum number of transitions, i.e., 41 transitions for Pii and 40 transitions for pi~.
Results were similar when we considered only those with 10+ arrests. Primary contributions to the H 2 test statistic derived from iji offense triples and observed values were much higher than expected. Nonnegligible differences between observed and expected values with observed values exceeding expected values for three different offenses occurred only for RobberyBurglary-Violence ( 0 = 2 0 , E = 13.76), Robbery-Burglary-Other Property (O=27, E = 19.31), and Violence-Delinquency-Robbery (O=53, E = 37.51). Again, with the exception of Robbery, transition to the same offense given that the two previous offenses were of the same type was the most likely transition. These P,i transition probabilities are included in Table VII. These results suggest some evidence of specialization.
3.3. Examining the Forward Specialization Coefficient Additional evidence of specialization was found in the examination of the forward specialization coefficient. The forward specialization coefficient [FSC (see Farrington, 1986; and Farrington et al., 1988)] has been proposed as a measure of specialization that corrects to some extent for the frequency of the offense. The FSC equals 1 if there is complete specialization and is calculated
FSC -
O-E R-E
(7)
where 0 indicates observed, E indicates expected (calculated in the normal way for a X2 test), and R is the row total. The statistical significance of the FSC is tested using the adjusted standardized residual (ASR), which is asymptotically distributed N(0, 1).
Lattimore, Visher, and Linster
308
The FSCs were calculated for the first 20 transitions for the 2+ arrests groups (see Table VIII). Most of the FSCs are statistically significant, indiTable VIII. Forward Specialization Coefficients: 2+ Arrests" Transition No.
Violence
Robbery
Burglary
Other property
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.0754 0.1337 0.0623 0.1501 0.1146 0.1731 0.1284 0.1441 0.1969 0.1605 0.1411 0.1386 0.1279 0.2106 0.0700" 0.2200 0.1376 0.0254" 0.1358 0.1624
0.1062 0.0699 0.1054 0.1236 0.0761 0.0897 0.0350"' 0.1140 0.1410 0.0601 0.1553 0.0409 "~ 0.1491 0.1120 0.0382 "s -0.0275" -0.0620" 0.0597"' 0.1429 0.3267
0.1240 0.1347 0.1341 0.1631 0.1849 0.1603 0.1082 0.1354 0.1861 0.1919 0.1122 0.1936 0.0514" 0.1604 0.1550 0.1355 0.3275 0.1886 0.0500"' 0.1658
0.1679 0.1223 0.0893 0.1130 0.1571 0.1644 0.1001 0.1344 0.1520 0.1366 0.0932 0.1177 0.1273 0.0717 0.0909 0.2207 0.1104 0.0285" 0.0595"' 0.1094"
0.1094 0.1175 0.1052 0.1364 0.1429 0.1148 0.0964 0.0917 0.1339 0.1173 0.1504 0.1905 0.0876 0.0478"' 0.1092 0.1669 0.0608"' -0.0098" 0.2216 0.0963"'
Mean(T=20)
0.1354
0.0928
0.1531
0.1183
0.1143
Delinquency
"FSCs are calculated for all subjects with 2+ arrests. Values identified as not significant (ns)are statistically insignificant at p
