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OCR for page 292
Appendix B
Research on Criminal Careers:
Individual Frequency Rates
and Offense Seriousness
Jacqueline Cohen
INTRODUCTION
The level of crime experienced in a soci-
ety varies with both the participation by
individuals (b or d) in that society and the
frequency of offending by active offenders
(A). Increases in crime may be clue to in-
creases in either the participation rate or the
frequency of offending. Distinguishing
among the different dimensions of criminal
career's has implications both for our under-
stancling ofthe factors contributing to crime
and for efforts to control crime.
The characterization of criminal careers
invoked here assumes that offending is not
pervasive throughout a population, but
rather is generally restricted to a subset of
individuals who are actively committing
crimes cluring some period oftime. It is also
assumed that the constituents of the subset
of active offenders vary with time as some
inclividuals become criminally active (onset
of careers) and others terminate their crim-
inal activity. Uncler this characterization,
The author would like to thank Arnold Barnett,
Alfred Blumstein, David Farrington, and Jeffrey
Roth for their helpful comments on an earlier ver-
sion of this paper.
292
the defining attribute of offenders is com-
mission of at least one crime.
Participation, the subject of Appendix A,
refers to the size of the criminally active
offender subset cluring some observation pe-
riod. This subset of active offenders includes
both new offenders (first offense occurs dur-
ing the observation period) and persisting
offenders (criminal activity began in an ear-
lier period and continues into the current
observation period). Participation rates dur-
ing any observation period will thus depend
on the number of individuals who become
offenders and how long they remain crimi-
nally active. The longer criminal careers are,
the greater will be the contribution of persist-
ers to participation in any observation period.
The subset of active offenders in any
observation period is distinguished by hav-
ing a positive frequency of committing
crimes (e.g., five crimes per year per active
offender). Beyond the requirement of at
least one offense for active offenders, fre-
quency rates may vary substantially across
active offenders, with some offenders hav-
ing very high rates and others low rates of
offending. Frequencies may also vary over
time for an individual. Individual offenders
who have the highest frequencies will con-
tribute most to total crimes.
OCR for page 293
APPENDIX B: RESEARCH ON CRIMINAL CAREERS
Many different offense types may contrib-
ute to an individual's frequency. Individual
offenders, for example, may vary in the
scope of their offending, from "specialists"
(who engage predominantly in only one
type of offense or one group of closely
related offenses) to "generalists" (who en-
gage in a wide variety of offense types). The
degree of specialization may also vary
across offense types; some offense types
may be committed exclusively by special-
ists, while others are routinely committed
as part of an offender's varied mixture of
offense types. The mix of offenses commit-
ted by any offender may also vary as of-
fending continues individual offenders
may become either more or less special-
ized, or increase or decrease the serious-
ness of their offending. If there are consis-
tent patterns of change in the mix of
offenses, then commission of serious of-
fenses may be characteristic of certain peri-
ods during criminal careers (e.g., later ca-
reers may be periods of more serious
criminal activity).
The various aspects of individual crimi-
nality participation, career length, fre-
quency, and crime mix will affect the con-
tribution of individual offenders to the total
volume of crime experienced at any time.
Offending may be widespread, with many
offenders each committing crimes at rela-
tively low rates; in this event, individual
offenders contribute very little to the total
volume of crime. Altematively, individual
293
same individuals commit crimes over
longer periods of time, and these persisters
are major contributors to total crime.
This appendix provides a critical review
of the emerging body of research that em-
pirically characterizes various dimensions
of individual offending. Because of its scope
and volume, the full range of the literature
is beyond the reach of a single paper. Nar-
rowing the focus of this review builds on a
natural partition of the various dimensions
of criminal careers. Participation delimits
the subset of active offenders in a popula-
tion; this dimension of criminal careers is
addressed in Appendix A. This appendix
focuses on the progress, or course, of indi-
vidual offending during criminal careers, as
measured by frequency rates and offense
seriousness.
Frequency rates are addressed first, fol-
lowed by offense seriousness. In reviewing
the research findings, special attention is
given to their validity in light of various
methodological concerns. In many in-
stances, frequencies or offense seriousness
are not addressed directly in the reported
results, and whenever possible, available
data have been reanalyzed in order to pre-
sent results on frequency rates and offense
seriousness in comparable terms.
INDIVIDUAL OFFENDING
FREQUENCIES FOR ACTIVE
OFFENDERS
, ,
frequencies may be high and participationIndividual offending frequencies, A, are a
low; individual offenders would then befundamental feature of individual criminal
responsible for a larger portion of total
crimes.
Career lengths may be short or lone. If
careers are characteristically short, then
there is likely to be a large turnover of
active offenders as individuals quickly ter
minate careers and new individuals be
come criminally active. In this event, new
offenders would be major contributors to
crime. Also, with short careers, current par
ticipation levels may be relatively low,
while cumulative participation (all individ
uals who were ever criminally active) is
more widespread in the population. If crim
inal careers are characteristically long, the
careers. Despite the importance of A in
estimating the magnitude of offending dur-
ing~criminal careers, research that statisti-
cally characterizes the intensity of offend-
ing for large numbers of ordinary offenders
is relatively recent. Much of the early re-
search on individual criminal careers con-
sisted of biographical or autobiographical
studies. While such case studies provided
interesting and often insightful reports on
the individuals studied, there was little in
~Some of the classics among these studies are
Booth (1929), Shaw (1930, 1931), Sutherland (1937),
and Martin (19521.
OCR for page 294
294
dication that the individuals were represen-
~tive of a larger group of offenders. Indeed,
We subjects were more likely chosen for
Weir fascinating uniqueness than for Weir
representativeness.
More recently, a large body of research
has examined the attributes of large sam-
ples of offenders. This research includes
both studies of self-reported delinquency
and studies using official records, such as
arrest histones.2 Because this research has
been largely motivated by interest in the
causes and prevention of crime, it has fo-
cused on identifying the correlates social,
economic, psychological, and o~erwise-
of offending. This research has typically
developed estimates of participation (i.e.,
We prevalence of offenders) or of continued
offending in different population subgroups.
Estimates of the intensity of offending by
identified offenders, A, are rarely provided.
A related body of literature attempts to de-
velop topologies of offenders win similar
social or psychological at~ibutes.3
2The self-report literature is extensive and in-
cludes over 100 studies. A partial bibliography is
available in the review of the National Council on
Crime and Delinquency (1970~. A critical review of
much of this research is found in Reiss (1973) and
Hindelang, Hirschi, and Weis (19791. The following
represent only a small sample of the available re-
search in this area: Reiss and Rhodes (1959), Hirschi
(1969), Gold (1970), Waldo and Chiricos (1972),
Williams and Gold (1972), Elliott and Voss (1974),
Elliott and Ageton (1980), Hindelang, Hirschi, and
Weis (1981), Elliott et al. (1983~. A recent review of
participation measures, including those based on
self-reports, is available in Visher and Roth (Appen-
dix A).
Analyses of official records typically involve lon-
gitudinal analysis of large samples of criminal rec-
ords. Among such studies are Glueck and Glueck
(1937, 1940), McCord and McCord (1959), Robins
(1966), Wolfgang, Figlio, and Sellin (1972), West
and Farrington (1973, 1977), Robins, West, and
Heganic (1975), Robins and Wish (1977), McCord
(1978), Farrington and West (1981), Hindelang,
Hirschi, and Weis (1981), Famngton (1983b, 1984~.
3See Warren (1971) and Gibbon,s (1975) for re-
views of the topology literature. Examples of typol-
ogy research are found in Kinch (1962), Gibbons
(1965), Hurwitz (1965), Roebuck and Quinney
(1967), and Davies (1969~.
CRIMINAL CAREERS AND CAREER CRIMINALS
Recent interest in the crime control ef-
fects of incapacitation has underscored the
importance of developing estimates of A.
Recognizing the impact of variability in A
on estimates of incapacitative effects, the
National Research Council Panel on Deter-
rent and Incapacitative Effects (Blumstein,
Cohen, and Nagin, 1978:80) made the fol-
lowing recommendation:
Empirical investigation should also be directed
at estimating the parameters measuring the level
of individual criminal activity, especially the
indivicI~al grime rates ... and career lengths....
Furthermore since estimates of the incapacita-
tive effect are sensitive to variations in these
parameters, these estimates should not be re-
stricted to highly aggregated population aver-
ages. They should be disaggregated by crime
type and demographic group and should reflect
the statistical distribution of the parameters.
Recent studies in two research pro-
grams~ne at the Rand Corporation and
the other at Carnegie-Mellon University
have begun to provide explicit, disaggre-
gated estimates of A. That research is re-
viewed in this section, in particular the very
different approaches used and the resulting
estimates of A. A number of other studies
provide estimates of participation rates and
aggregate incidence rates for a study popu-
lation. These data provide a basis for devel-
oping estimates of A for the studied popula-
tions. The results of these new analyses are
also reported below.
Throughout this review of estimates of A,
various methodological issues in the mea-
surement of A are discussed and suggestions
are made for further research in this area.
The section begins with a discussion of the
distinction between A, the main interest
here, and more commonly available esti-
mates of aggregate incidence rates.
Distinguishing Individual Frequency
Rates from Aggregate Incidence Rates
Individual frequency rates, A, apply only
to active offenders. This restriction distin-
guishes A from the more commonly avail-
able measure of aggregate incidence rates,
which reflect the frequency of offenses, or
arrests, in the general population. Aggre
OCR for page 295
APPENDIX B.: RESEARCH ON CRIMINAL CA0ERS
gate incidence rates are exemplified by the
annual crime rates and arrest rates reported
by the Federal Bureau of Investigation. The
key feature distinguishing A from aggregate
incidence rates is the population base on
which the estimates are calculated.
In calculating A, only individuals with at
least one offense, or arrest, are included in
the population base. Estimates of A thus
reflect the average frequency of offending
for individuals who are actively committing
crimes. Aggregate incidence rates, by con-
trast, apply to a total population. The popu-
lation at risk includes offenders and nonof-
fenders alike.
Aggregate incidence rates reflect the com-
bined contribution of participation rates for
offenders in a population, ~ or b, and individ-
ual frequency rates, A or A, for active of-
fenders. Consider, for example, estimates of
aggregate arrest rates for some population i:
Aggregate
=
Number of arrests
of persons
arrest in population i
rate for
population i Number of persons
in population i
This aggregate measure can be partitioned
between the participation rate for offenders
(~) and the frequency rate for those of-
fenders (,u):
Aggregate Number of persons
arrest arrested in population i
rate for Number of persons in
population i population i
Number of arrests of
persons in population i
Number of persons
arrested in population i
=
Participation rated
x Frequency rated
(1)
The conceptual distinction between par-
ticipation rates and individual frequency
rates has important implications for the
evaluation of incapacitative effects. The
crime control potential of incapacitation
hinges on the magnitude of an individual's
offending frequency, A. This is the expected
295
number of crimes averted by incapacitating
an offender. Aggregate incidence rates in-
clude rates of zero for nonoffenders, who
are not vulnerable to incarceration, except
in the rare cases of wrongful conviction.
Aggregate incidence rates, therefore, would
seriously underestimate the crime reduc-
tion achieved by incapacitation. Likewise,
the impact of incapacitation policies on
prison populations depends on the partici-
pation rates of offenders in a population.
The more widespread that offenders are in a
population, the greater will be the potential
increases in prison populations as a result of
incapacitation strategies. To the extent that
A exceeds one offense per offender, aggre-
gate incidence rates will overstate the prev-
alence of offenders. In this event, use of
aggregate incidence rates in place of partic-
ipation rates would lead to overestimates of
the potential impact of increased incapaci-
tation on prison populations. Accurate esti-
mates of the tradeoffs between increases in
prison population and reductions in crime
through alternative incapacitation policies
depend critically on having separate esti-
mates of participation and frequency rates.
The partition of aggregate incidence rates
into participation rates, on the one hand,
and individual frequency rates for active
offenders, on the other, may also be useful
in evaluating the effectiveness of other
crime conko1 policies. To date, evaluations
of deterrent and rehabilitative effects have
relied almost exclusively on aggregate out-
come measures.4 To the extent that partici
4Recidivism rates are a special variant of aggre-
~ate incidence rates. While restricted to a popula-
tion of identified offenders, the prospective per-
foll~ance of this population is the combined result
of the level of continued participation by active
offenders and the magnitude of individual fre-
quency rates for those who remain criminally active.
In particular, failure to recidivate during a follow-up
period may occur because some offenders end their
criminal careers altogether, or because some offend-
ers who do remain criminally active do so at low
frequency rates. In the latter case, extending the
length ofthe follow-up period increases the likelihood
of observing eventual recidivism; in the former case,
recidivism will never occur no matter how long the
follow-up period.
OCR for page 296
296
pation rates and frequency rates are dif-
ferentially affected by deterrence or reha-
bilitation policies, important effects on
these component parts may be obscured in
the aggregate measures. Analyses of effects
on the partitioned measures may provide
valuable insights for improving the crime
control effectiveness of deterrence and re-
habilitation policies. It may be, for example,
that different strategies will be more effec-
tive if they are targeted on selected popula-
tion subgroups.
Review of Estimates of Individual
Frequency Rates
The main interest in this subsection is
empirically based estimates of A. Relatively
few studies provide explicit estimates of A,
and they are limited to samples of serious
adult offenders. Three such studies are re-
viewed in this section. Indirect estimates of
A, derived expressly for the panel from
other published data on current participa-
tion rates and aggregate incidence rates, are
also reviewed. The indirect estimates have
been developed for a wider variety of study
populations.
The studies that provide explicit esti-
mates of A are summarized in Table 1.
Separate rates are generally estimated for
individual offense types, and total rates are
presented for larger offense classes. Of-
fense-specific frequencies reflect the aver-
age number of offenses committed when
that offender is active in that offense type.
Active offenders are distinguished by hav-
ing at least one offense (or one arrest) for a
crime type. Individuals with no offenses of
a particular type during the observation
period are excluded in the computation of
rates for that offense type.
By this criterion, the earliest self-report
survey, the Rand survey of 49 prison in-
mates (Petersilia, Greenwood, and Lavin,
1977), is properly excluded from consider-
ation. The offending rates reported in that
study apply to the total sample of 49 of-
fenders; rates of zero for inmates who re-
ported no offenses of a given type are in-
cluded in the reported rates. As the di-
rect precursor of the two later Rand inmate
CRIMINAL CAREERS AND CAREER CRIMINALS
surveys, however, the study is included
here.
All of the studies summarized in Table 1
are based on samples of adult offenders.
The samples are also generally restricted to
more serious, or more criminally active,
subsets of adult offenders. The three self-
report surveys, all by the Rand Corporation,
are based on surveys of inmates serving
sentences in state prisons and, in one study,
inmates in local jails. These inmate samples
are thus restricted to offenders whose cur-
rent offense or prior criminal record was
serious enough to have warranted a sen-
tence of incarceration.
The two studies using official arrest rec-
ords are based on samples of adult ar-
restees. While potentially including a
broader range of offenders, these studies
also focus on offending by a more serious
subset of offenders. To enter the sample, an
offender must have had at least one arrest
for a serious index offense (murder, rape,
robbery, aggravated assault, burglary, or
auto theft) during the sampling period. This
criterion excluded offenders who engaged
exclusively in minor offenses or who were
never arrested for a serious index offense.
By focusing on subsets of offenders who
are active in serious offense types, studies of
frequency rates can develop estimates of A
in those serious offense types. Because they
are generally quite rare, these more serious
offense types have often been excluded
from surveys of general population samples.
The studies that provide estimates of A for
serious offenders are in direct contrast to the
much larger body of research on participa-
tion in offending, which is typically based
on self- or official reports of offending and
deviance for juveniles sampled from a gen-
eral population, and which is therefore
dominated by the more common minor of-
fenses, such as vandalism or simple assault.
This difference in design reflects the dif-
ferent focus of the studies, in the first in-
stance, the intensity of serious offending by
more continuously active offenders, and in
the second, the scope of deviance found in a
broad population.
In addition to focusing on active offend-
ers, the studies in Table 1 also restrict the
OCR for page 297
297
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OCR for page 302
302
calculation of frequency rates to periods
when the offenders were at risk of commit-
ting offenses in the community. Time when
the offender was incapacitated through in-
carceration or long-term hospitalization
(e.g., more than a 1-month stay) was ex-
cluded from the time at risk. The resulting
frequencies reflect the intensity of offend-
ing while an offender is criminally active in
the community, A, the rate of offending that
would be expected ' if the offender were
never incarcerated. The estimates of A are to
be distinguished from the effective rates for
offenders, A*. In estimating the reduction in
crime associated with different periods of
incarceration, the appropriate quantity is
the individual's active offending frequency.
This is the rate at which crimes would be
committed if the offender were not incarcer-
ated. Any time spent incarcerated will re-
duce the annual active rate to yield the
effective rate for offenders. For example, an
offender may commit crimes at a rate of 10
per year while he is free in the community.
If this offender is incarcerated for 6 months,
however, he can only commit crimes at rate
10 for the 6 months he is free. His active rate
is 10 offenses per year, but his effective rate
during the entire year is only 5, since he
was only actively committing crimes in the
community for half of the year.
The effective offending rate reflects the
reduction in the potential level of crime as a
result of current incapacitation policies. Be-
cause effective rates are already discounted
by current incapacitation levels, using the
effective rate instead of the active rate
would lead to underestimates of the total
crime reduction associated with increases
in incapacitation. When the effective annual
offending rate is used, incarceration during
all of the following year would be incor-
rectly estimated to avert only five offenses.
This fails to include the additional five of-
fenses that would have occurred had the
offender not been incarcerated for one-half
year. On the basis of the offender's offend-
ing frequency while free, incarceration for a
full year can be expected to avert 10 of-
fenses.
CRIMINAL CAREERS AND CAREER CRIMINALS
Estimating A from Self-Reports: The
Rand Inmate Surveys
Survey of Habitual Offenders. The
study of 49 habitual offenders by Petersilia,
Greenwood, and Lavin (1977) laid the
groundwork for later Rand surveys of larger
samples of inmates. The original 49 inmates
were chosen as exemplars of serious, recid-
ivistic offenders. To be included in the
sample, an inmate had to be currently serv-
ing a sentence for at least one armed rob-
bery conviction and have at least one prior
sentence of incarceration. Through per-
sonal interviews, the inmates were asked
about their frequency of offending and prior
criminal record (arrests, convictions, and
incarcerations) for nine offense types, as
juveniles, as young adults (before their first
incarceration as adults), and prior to the
start of the current sentence. In addition,
they were asked about other aspects oftheir
personal histories, including family circum-
stances, school and employment experi-
ences, drug and alcohol use, personal moti-
vations for crime, and styles of committing
crimes (e.g., the amount of planning and
preparation, use of accomplices).
The findings on average levels of offend-
ing over time for the 49 offenders, including
offenders who were active in an offense and
those who were not, are summarized in
Table 2. As one reads down the table, the
offense classes become more inclusive; the
total rate includes offending in any of the
nine offense types surveyed. Except for vi-
olent offenses, the reported monthly rates
declined markedly as offenders got older.
The anomalous slight increase in monthly
rates with age for violent offenses is attrib-
uted by the authors to the sampling crite-
rion that required an atoned robbery prior to
the current incarceration, which marks the
end of the adult period (Petersilia, Green-
wood, and Lavin:27~.
As indicated above, all 49 offenders are
included in a rate, whether or not they were
active in that offense type. The opposite
trends across age observed for violent of-
fenses and all other offense types illustrate
OCR for page 408
408
her of prior arrests for that same type found
in a career, or using some weighted statistic
for that offense type that gives greater
weight to more recent occurrences of the
offense type.
Reliance on Official Records
All of the studies ot ottense switching
reviewed here relied on official-record data
on sequences of police contacts or arrests
for samples of offenders. This dependence
on official-recorc! data arises from the re-
quirement for data that document the exact
sequences of offense types over time" in-
formation that is readily available in official
records.
The picture of offense switching that
emerges from analyses of official-record
data, however, confounds patterns of of-
fense switching by offenders with patterns
of law enforcement, especially by the po-
lice. As noted earlier, the offense types
observed on successive police contacts or
successive arrests will vary with the levels
of police effectiveness in apprehending of-
fenders for different offense types. Offense
types with higher detection and apprehen-
sion rates will be overrepresented among
official contacts compared with their repre-
sentation in successive crimes committed.
If enforcement rates vary substantially for
different offense types, the patterns of
switching observed in official-record data
will provide a distorted view of offense
switching between actual crimes commit-
ted. This confounding effect is recognized
in virtually all studies of offense switching,
and the studies are careful to note that the
reported results apply to successive official
contacts for offenders.
The variability in arrest risk for different
offense types is illustrated in Table 53.
Based on data for the United States, the
ratio of arrests to reported crimes (in column
3) varies from a low of .12 for auto theft to a
high of.42 for aggravated assault. The ratio
of arrests to reported crimes alone, how-
ever, is an inadequate estimate of the
chance of arrest for a crime for an indi-
vidual. Crimes committed but not reported
to the police are not included, and arrests
CRIMINAL CAREERS AND CAREER CRIMINALS
sometimes include arrests of more than one
individual for the same crime incident.
The number of reported crimes can be
adjusted for nonreporting by using the re-
porting rates for various offense types avail-
able from national surveys of criminal vic-
timization. A further adjustment for
multiple offenders per crime incident is
also available in these national surveys.36
The adjusted estimates of the probability
that any individual offender is arrested for a
crime committed, whether reported to the
police or not, are shown in the last column
in Table 53. The risk of arrest is highest for
offenses involving direct contact between
offenders and victims (robbery and aggra-
vated assault) and lowest for property of-
fenses without contact.
The final arrest risk for the various offense
types is generally low, averaging only 1
arrest for every 20 crimes committed. De-
snite the reduction in arrest risk after the
adjustments, there is still a threefold differ-
ence between the highest risk (aggravated
assault) and the lowest risk (larceny and
auto theft). Variability in arrest risk for dip
ferent offense types is thus a very real con-
cern in analyses of offense switching that
rely on official contacts only.
Two strategies are available for dealing
with distortions in offense-switching pat-
terns that arise from use of official-record
data. The first is to expand the scope of
self-reports of offenses committed to in-
clude data on the actual sequence of dif-
ferent offense types. To date, such data on
sequences of crimes actually committed
have been unavailable. It is only recently
Mat self-report studies have begun to col-
lect data on frequency of offending during a
reporting period. Collecting data on the
sequence of offense types will require
36The adjusted arrest risk for a crime of offense
type k, qk, is given by
Arrests of Type k rk
qk = X-
Reported Offenses of Type k °k
where rk is the rate of reporting offenses to the
police by crime victims and °k is the average
number of offenders per crime incident.
OCR for page 409
APPENDIX B.: RESEARCH ON CRIMINAL CAREERS
409
TABLE B-53 Probability of Arrest for a Crime, Adjusted for Nonreporting
to the Police and Multiple Offenders per Crime
Proportion
Offense
Type
Reported
Offenses
in U.S.,
1980a
Arrests
in UPS.,
1980
Ratio of of Total
Arrests to Offenses
Probability
Number of of Arrest for
Offenders a Crime, A,
Reported Reported per Crimg for Individual
Offenses to Police- Incident- Offenders
Robbery548,809146,270
Aggravated
assault654,957277,470
Burglary3,759,193513,300
Larceny7,112,6571,191,900
Auto theft1,114,651138,300
.27
.42
.14
.17
.12
.57
.54
.51
.27
.69
2.3
2.6
1.6
1.6
1.8
.07
.09
.04
.03
.03
federal Bureau of Investigation (1981:Table 1).
bFederal Bureau of Investigation (1981:Table 24).
bureau of Justice Statistics (1982a:Table 89).
dReiss (1980b:Table 2).
panel designs that include data collection
from the same sample of offenders at fre-
quent intervals. Depending on the antici-
pated rates of individual offending, monthly
or perhaps even weekly reports may be
required.
Given that the focus of the research is
offense seriousness, the strategy of repeated
and frequent self-reports is best limited to
samples of known ollenders. Those offend-
ers might be identified from self-reported
offenses in a more widely used screening
instrument, or through arrest or police con-
tact associated with an offense. As noted
earlier, self-report studies involving re-
peated and frequent reporting will be
costly, will require a reasonably long-term
commitment-of at least several years- to
data collection, and will involve difficult
logistics in order to maintain contact
throughout the study with samples whose
members are likely to be uncooperative and
mobile. While the self-report approach is
certainly possible, the various implementa-
tion problems in addition to the large sam-
ple sizes required to estimate switching
patterns make pursuit of this research
strategy all the more difficult. The data re-
quirements are somewhat less demanding
if repeated self-reports are used to estimate
changes in offense mix during successive
reporting periods. Such analyses would not
require data on the exact sequence of of-
fense types and smaller samples of offend-
ers would be adequate.
An alternative strategy for analyzing the
actual sequence of crimes committed builds
on the current reliance on official-record
data, extending it to address offense switch-
ing between crimes actually committed. As
we learn more about the links between
individual offending and the criminal jus-
tice selection process, we will be better
able to model the selection process. By
incorporating models of the selection proc-
ess with readily available official-record
data, we can begin to draw inferences about
the switching process for undetected crimes
that intervene between official-record
events. This inferential strategy has begun
to be employed with some success in stud-
ies of individual crime rates based on offi-
cial-record data.
Biases Associated with Sample
Selection
The most obvious biases arising from the
sampling process are distortions introduced
by the sampling event itself. These are most
OCR for page 410
410
likely to arise when sampling is based on
some threshold of seriousness in offense
types. The analyses of criminal histories for
a sample of prison inmates by Frum (1958)
and incarcerated juveniles by Smith and
Smith (1984) are excellent illustrations of
this problem. The samples were drawn
from among inmates in state correctional
facilities. Since all sample members were
incarcerated for the last arrest in their rec-
ords, that last event was likely to be for a
serious offense type or to follow a record of
repeated convictions for serious offense
types. The sampling strategy of using incar-
cerated offenders, and the failure to exclude
the last offense type from the analysis, were
no doubt major factors contributing to the
findings of escalation toward more serious
offense types over the course of criminal
careers and of the tendency for some of-
fenders to specialize in serious offense
types.
When sample selection is based on a
seriousness threshold, it is essential that the
sampling event be excluded from analysis
of offense-switching patterns. Failure to ex-
clude the necessarily more serious sam-
pling event will bias estimates of offense
.. . .
switching patterns toward these more
serious events. It was precisely to avoid
such biases that the more serious sampling
event was excluded from analyses of adult
arrestees by Moitra (1981) and Blumstein,
Cohen, and Das (1985~.
Sample selection in Rojek and Erikson
(1982) and Bursik (1980) was based on ei-
ther processing by the juvenile court or an
adjudication as a delinquent in the juvenile
court. Given that the discretion to resolve
juvenile cases informally is available to
both the police and to intake officers at
juvenile court, the formal involvement of
the juvenile court likely increases the seri-
ousness of the sampling event in both sam-
ples. The sampling event was not excluded
from either analysis. The sampling event,
however, was not restricted to the last event
in the record; it could appear anywhere in
the record, depending on the age of the
offender during the sampling period. This
distribution of the sampling event over dif-
ferent points in a record limits the biasing
CRIMINAL CAREERS AND CAREER CRIMINALS
effect toward more serious events at the end
of the record. On the other hand, it may be
responsible for findings of stationarity over
transitions as intermittent escalations in se-
riousness associated with the sampling
event are randomly distributed over indi-
vidual arrest histories, obscuring any pat-
terns over time that may otherwise exist.
Two strategies are available to control for
distortions arising from the sampled event.
First, the sampled event can be excluded
from the analysis entirely. This strategy is
especially appropriate when the sampled
event falls at the end of arrest history data.
The alternative is to include the sampled
event in the analysis, but to limit the anal-
ysis to similar events. Thus, in the two
juvenile court samples, analysis of offense
switching would be limited to contacts
processed by juvenile court (in the case of
Rojok and Erikson, 1982) or to offenses that
were adjudicated delinquent (in Bursik,
1980~. In this way, the sampling event is
indistinguishable from other events in the
analysis. This strategy of only analyzing
events similar to the sampling event was
employed in the study of offense switching
by juveniles in the Philadelphia cohort
(Wolfgang, Figlio, and Sellin, 1972~. Like
the adult analyses, this study of juveniles is
free of biases associated with the sampling
event.
Aside from biases introduced into the
switching process by the sampling event,
the sampling process itself selectively lim-
its the population of offenders who are stud-
ied. All analyses of offense switching re-
quire at least one official-record event
(police contact, arrest, juvenile court proc-
essing, juvenile court adjudication, convic-
tion, or incarceration). Those that exclude
Resistance require at least two contacts for
each offender. The switching patterns ob-
served thus apply most accurately to sub-
sets of offenders with official records. Even
if the criminal justice selection process was
completely random, offenders with official
contacts would be a random sample of all
offenders only if all offenders are homoge-
neous in offending. Any variability in of-
fending (e.g., higher frequency rates for
some offenders compared with others, or
OCR for page 411
APPENDIX B.: RESEARCH ON CRIMINAL CAREERS
N
longer criminal careers) would increase the
representation of more active offenders in
the sample. Because their greater criminal
activity increases their exposure to risk, of-
fenders with higher frequencies and longer
criminal careers are more likely to experi-
ence an official contact and thus are more
likely to be found in samples.37 Most anal-
yses of offense-switching patterns, there-
fore, reflect offense switching for the more
active offenders who are found in the sam-
ple and may not apply to all offenders.
Role of Frequency Rates, Career
Length, and Incapacitation in
Switching Patterns
Frequency rates, career length, and time
spent incarcerated vary for different offense
types. As reported in the review of fre-
quency rates above, individual crime rates
are higher for property crimes and lower for
violent crimes. Analyses of the length of
criminal careers (Blumstein and Cohen,
1982) report an opposite relationship:
shorter average careers in property crimes
and longer average careers in violent
crimes. Time spent incarcerated is also
likely to be longer for violent crimes than
for property crimes. These differences can
affect the switching patterns observed, es-
pecially when observation periods are lim-
ited in length. In particular, offense types
that occur at high rates, and thus involve
short intervals between events and short
periods of incarceration, are likely to be
more prevalent as switching destinations.
Conversely, switching to offense types that
involve longer average intervals between
events and longer periods of incarceration
is likely to be underrepresented, especially
when observation periods are short.
The possible distorting effect of the dis
37This tendency to oversample more active of-
fenders holds under a variety of conditions. The
only exception is those instances in which selection
risk per offense committed is strongly inversely
related to individual offending patterns win high-
rate or long-career offenders having a much lower
risk of official contact per offense than low-rate or
short-career offenders.
4~]
tribution in the various offense types was
evident in the analysis of specialization for
adults. Without controlling for differences
in the distribution of offense types, burglary
and larceny have the largest diagonal
switching probabilities of all offense types
for adults, which suggests greater special-
ization in these offense types by adult of-
fenders. Examination of the column
marginals for these offense types, however,
reveals that switching to these offense types
is higher generally. Thus, the tendency to
specialize in burglary or larceny is not es-
pecially great relative to the generally
higher frequency of switching to burglary
and larceny as the next offense type. Con-
versely, even apparently small diagonal val-
ues may reflect significant specialization
when switching to an offense type is gener-
ally quite rare. The distribution in different
offense types is explicitly controlled in all
analyses in which the observed frequency
of switches is tested against a model of
complete independence in switching. Dif-
ferences in the distribution of the offense
types are reflected directly in the frequency
of switches expected in an independent
process.
Variations in the number of events in a
criminal history are one indication of dif-
ferent levels of offending and differences in
incapacitation experiences. Most directly,
differences in the number of events will
reflect variations in individual frequency
rates and in career length. High-rate of-
tenders are more likely to accumulate large
numbers of events, as are offenders who
remain criminally active for long periods of
time. Extended periods of incarceration
during careers. bv contrast. will limit the
c , , ,
number of events in a career. Because lev-
els of offending and incapacitation experi-
ences may also be associated with the of-
fense types found in a record, differences in
the number of events can affect analyses of
offense-switching patterns.
This potential source of bias in analyses
of switching was illustrated most dramati-
cally in the earlier examination of escalation
effects. Without controls for differences in
the number of arrests for different individ-
uals, average seriousness appeared to de
OCR for page 412
412
cline with each additional arrest for adults.
The analysis, however, was not based on
the same sample of individuals at each ar-
rest. Offenders with only a few arrests con-
tributed to the average seriousness of early
arrests, but seriousness on successive ar-
rests was increasingly based on offenders
with larger numbers of arrests. Thus, the
observed decline in seriousness could re-
flect differences among offenders, and not a
change as individual offending progresses.
The key role of population heterogeneity
was confirmed when controls for this sam-
ple-selection effect were introduced. Con-
trolling for the number of arrests in a his-
tory, average seriousness was generally
stable on successive arrests for adults. Av-
erage seriousness, however, was lower for
adult offenders who had larger numbers of
arrests.
Variations in record length among offend-
ers is a similar concern in estimating switch-
ing probabilities more generally. More ac-
tive offenders, with their larger numbers of
arrests, will contribute disproportionately to
estimates of a single, summary transition
matrix that combines all offense switches
together. To the extent that switching pat-
terns vary with record length among of-
fenders, the combined matrix estimate will
be biased to reflect the pattern of offenders
who have long records. This potential bias
is partially controlled by estimating sepa-
rate transition matrices for each offense
switch; variations in switching with record
length will be evident in the variability
(nonstationarity) across the separate matri-
ces. These separate matrices, however, are
subject to the same sample-selection biases
affecting average seriousness. Successive
matrices are based on an increasingly more
selected sample of offenders those with
larger numbers of arrests. Thus any trends
in switching observed over successive ma-
trices may reflect population heterogeneity
and not a progression in switching during
individual criminal careers.
The potential role of selection effects in
successive transition matrices was illus-
trated in the reanalysis above of the data on
juvenile offenders in Pima County. The
reanalysis found nonstationarity in switch-
ing probabilities from juvenile status of
CRIMINAL CAREERS AND CAREER CRIMINALS
tenses, with more Resistance on early tran-
sitions compared with later transitions, and
more switches to personal and "other"
crimes on later transitions compared with
early transitions. This pattern suggests an
escalation in seriousness for status offend-
ers.
The successive transition matrices, how-
ever, were not estimated using the same
sample of offenders on each transition. Of-
fenders with only a few police contacts
were selected out of the analysis through
early Resistance. Thus, the apparent trend
to more serious offending for status offend-
ers may reflect a selection effect in which
status offenders with a small number of
contacts were also less serious offenders.
These less serious offenders, however, only
entered the estimates of early transition
matrices. Later transition estimates were
based increasingly on status offenders who
had larger numbers of police contacts. If
these more active status offenders were also
more serious offenders generally, the trend
to more serious offending observed on suc-
cessive transitions would reflect this popu-
lation heterogeneity and not a tendency to
move to more serious offenses for individ-
ual status offenders.
As in the analysis of trends in average
seriousness, the effects of this form of pop-
ulation heterogeneity can be explored by
estimating successive transition matrices af-
ter controlling for the number of arrests in a
history. This, however, places increased de-
mands on the sample size necessary for
analysis.
Population heterogeneity, especially
with respect to record length, represents a
strong competing hypothesis in accounting
for differences in offense patterns observer!
in the studies reviewed here. In comparing
adult and juvenile offenders, for example,
greater specialization was observed for
adult offenders than for juvenile offenders.
In the juvenile years, offender samples may
consist of some casual offenders whose of-
fending is exploratory and ends quickly and
of other more committed offenders who are
specialized in their offending. As explor-
atory offenders leave offending in the juve-
nile years, adult samples would consist
more heavily of committed, specialized of
OCR for page 413
APPENDIX B: RESEARCH ON CRIMINAL CAREERS
fenders. In this event, the difference in
specialization for adults and juveniles
might arise from differences across offend-
ers and not from a developmental process
toward greater specialization as offenders
get older. Sorting out these rival hypotheses
requires analyses of offense-switching pat-
terns for a common sample of offenders who
begin offending as juveniles and persist into
adulthood.
Aside from the potential distortions asso-
ciated with variations in the number of
events in criminal histories, variations in
the length of observation periods may also
affect the switching pattern observed. Of-
fenders' frequency rates and career lengths,
as well as their incarceration experiences,
all affect the length of intervals between
events. Inter-arrest intervals, as notecl, will
be sho* when individual arrest rates are
high. When individual arrest rates are low,
by contrast, or when long periods of incar-
ceration are likely to substantially reduce
the time at risk for subsequent arrests, inter-
arrest intervals are more likely to be long,
and these intervals will only be observed in
longer careers. To the extent that frequency
rates, career length, and incarceration risk
vary across different offense types, the asso-
ciated differences in intervals between
events for different offense types can affect
the mix of offense types observed in switch-
ing data. In particular, offense types charac-
terizec] by short inter-event intervals are
more likely to be observed when observa-
tion periods are short.
~.
Correspondingly
longer observation periods are required if
offense types characterized by longer inter-
event intervals are to be adequately repre-
sented.
Variations in inter-arrest intervals for dif-
ferent offense types may affect the estimates
of transition matrices. All the analyses of
offense switching reviewed here have sup-
pressec] differences in the time intervals
between events. Switching events were de-
fined by the occurrence of a next arrest (or
police contact), and switching events were
aggregated regardless of the differences in
the time interval to that event. The pattern
of switching among offense types, however,
may vary with the length of inter-arrest
intervals.
4~3
Building on the differences in frequency
rates and career lengths observed for dif-
ferent offense types, for example, it might
be expected that switches to property of-
fenses-with their higher individual fre-
quencies and short careers would be more
likely when the intervals between events
are short. Conversely, when intervals are
long, greater switching to violent offenses-
with their lower frequencies ant] longer
careers- would be expected.
The data on offense switching between
arrests for adults in Washington, D.C., and
Michigan are user] here to explore these
potential differences. The estimated transi-
tion probabilities for selected offense types
for Washington, D.C., arrestees are pre-
sented in Table 54. The significance of
differences in switching was assessed using
the ASRs of Goodman's (1962, 1968) contin-
gency table approach. Taking one offense
type at a time, a test was made of whether
switching patterns from that offense were
independent of the length of the interval to
the next arrest. Although not presented
here, results similar to those for Washing-
ton, D.C., arrestees were also found for both
whites and blacks in the Detroit and south-
ern Michigan samples.
Systematic variations in switching were
found with differences in the length of in-
tervals between arrests. Consistent with the
lower frequency and longer careers in ag-
gravated assault, the most persistent differ-
ence was an increased tendency to switch to
aggravated assault as the length ofthe inter-
val between arrests increased (indicated by
a shift from negative to positive ASRs).
Switches to robbery, with its higher fre-
quency rate and shorter careers, were more
likely after short intervals (indicated by a
shift from positive to negative ASRs). A
decline in specialization as intervals in-
creased was also observed for robbery and
burglary (indicated by a shift from positive
to negative ASRs).
-
Alternatives to Simple Markov ModeZs
A simple Markov property was invoked
in several analyses of offense-switching pat-
terns. Under this Markov assumption, of-
Sense switching Lepers, at most, on the
OCR for page 414
414
CRIMINAL CAREERS AND CAREER CRIMINALS
TABLE B-54 Variations in Offense-Type Switching with Length of
Interval Between Arrests for Washington, D.C., Arrestees
Prevalence
Offense Length of Probability of of Offense
Type on Interval Offense Type on k + 1st Arrest Type on kth
kth Between Aggravated Arrest
Arrest Arrests Assault Robbery Burglary (percent)
Aggravated <1 year.300 .086.059 11.6
assault (NS)a (2.7)**(NS)
(x2 = >1 year and.269 .070.065 16.9
51.03,* <2 years(NS) (NS)(NS)
33 d.f.)
>2 years and.259 .026.043 18
<4 years(NS) (-2.1)*(NS)
>4 years.385 .049.045 19.3
(3.0)** (-1.8)(NS)
Robbery <1 year.109 .312.074 10.4
(-2.7)** (3.7)***(NS)
(x2 = >1 year and.133 .301.062 10
57.03,** <2 years (NS) (NS) (NS)
33 d.f.)
>2 years and .143 .214 .071 8
<4 years (NS) (NS) (NS)
>4 years .195 .134 .101 10
(3.0)** (-4.4)*** (NS)
Burglary <1 year .071 .083 .316 10
(-3.8)*** (NS) (4.8)***
(x2 =
. .
68.96,*** >1 year and .113 .056 .185 11.3
33 d.f.) <2 years (NS) (NS) (-2.6)**
>2 years and .067 .067 .225 14.2
<4 years (NS) (NS) (NS)
>4 years .180 .087 .174 12.5
(4.7)*** (NS) (-3.5)***
pOnly ASRs significant at the .10 level or better (two-tailed test using
standard normal distribution) are reported in parentheses. All other
nonsignificant values are indicated by NS.
*Significant at the .05 level.
**Significant at the .01 level.
***Significant at the .001 level.
OCR for page 415
APPENDIX B: RESEARCH ON CRIMINAL CAREERS
offense type of the current arrest. The lim-
ited tests available for assessing the ade-
quacy of the Markov assumption suggest
that offense switching is not adequately
modeled as a first-order Markov chain. De-
pendence on prior offense types appears to
extend beyond the current offense type and
results in greater specialization than would
be expected in this simple Markov model.
The tendency for observations to bunch
on the diagonals of transition matrices has
been observed in a variety of social pro-
cesses, most notably residential migration
and status mobility. Failure of simple
Markov models in these processes is often
attributed to population heterogeneity, and
a variety of alternative modeling strategies
have been proposed (see, for example,
Singer and Spilerman, 1978, for a discus-
sion of the various approaches). In its most
common form, the population is presumed
to vary in its tendency to stay in the same
state on successive transitions. In the case
of offense switching, offenders would vary
with respect to offense specialization. At
one extreme, some offenders might be
highly specialized and thereby have a high
likelihood of repeatedly engaging in the
same offense type. At the other extreme
would be generalists, whose offending
would vary randomly over many different
offense types.
Various alternative models have been
proposed to address population heterogene-
ity satisfactorily. Many ofthese models pre-
serve the Markov property for switching
within different population subgroups, but
specify different transition matrices for each
subgroup. The non-Markov aggregate tran-
sition matrix reflects the combined effect of
these separate Markov transition processes.
The simplest, and one of the earliest, ap-
proaches to population heterogeneity was
the "mover-stayer" model first introduced
by Blumen, Kogan, and McCarthy (1955~.38
If this model is applied to offense switch-
ing, the population of offenders would be
38Various later extensions and tests of the mover-
stayer model are available in the research literature;
see, for example, Goodman (1961), White (1970),
and Spilerman (1972b).
4~5
TABLE B-55 Distr ibution of
Youths with Over Half of
Their Police Contacts in a
Single Offense Category
White
(percent)
Nonwhite
(percent)
Personal injury
Personal property
Impersonal property
Other ~
No n specialization"
Total
1.5
1.5
34.3
28.4
34.3
100
(N = 134)
1.5
0.9
32.5
14.9
50.1
100
(N = 335)
NOTE: Cook County Juveni le Court s able
of youths with at least five police contacts.
SOURCE: Bursik (1980:Table 5).
divided into two groups-the "stayers,"
who would always repeat the same offense
type, and the "movers," who would switch
among offense types according to a common
Markov transition process. Switching by
both groups can easily be combined and
various predictions of expected future
switching patterns for the aggregate popu-
lation are available.
The finding of specialization in a variety
of offender samples suggests that this parti-
tion of offenders into specialists and gener-
alists may be a fruitful approach to model-
ing offense switching. While there is
evidence of specialization in all samples,
some offenders seem to be more likely to
specialize than others. As indicated in Ta-
ble 55, specialization within aggregate of-
fense categories was widespread among
Cook County juvenile offenders. For of-
fenders with at least five police contacts as
juveniles, one-half of the nonwhites and
two-thirds of the whites in the sample had
over 50 percent of all their contacts in a
single offense category. The distribution of
specialists in different offense categories
reflects the relative distribution over these
offense categories generally.
On the basis of data on adult arrestees in
Washington, D.C., the proportion of spe-
cialists varies considerably for different of-
fense types. As indicated in Table 56, spe
OCR for page 416
416
CRIMINAL CAREERS AND CAREER CRIMINALS
TABLE B-56 Proportion of Specialists Found Among Adult Arrestees
in Washington, D.C.
Offense Type
of Arrest Number of
in 1973 Arrestees
Percent
with Prior
Arrests for
Index
Offenses
Percent
Specialists
Among Those
with Prior
Index Arrests
Percent
Specialists
Among All
Arrestees
Murder277 65.0 - 21.1 13.7
Rape253 63.3 22.0 13.9
Robbery1,230 65.2 53.4 34.8
Aggravated
assault1,930 59.6 57.0 34.0
Burglary902 55.5 44.5 24.7
Auto theft496 52.4 35.7 18.7
NOTE: "Specialists" are arrestees with prior arrests for the same
charge as the sampled arrest in 1973. For arrestees with only one
prior arrest for an index offense, that one prior index arrest is for
the same charge as the sampled arrest. With two or more prior index
arrests, the preponderance of the prior arrests are for the same charge
as the 1973 arrest. Under the "predominance" criterion, about one-half
of all index arrests in a record--including the 1973 sampled arrest--
must be for the current charge. For a record with a total of 3, 4, or
5 index arrests, including the sampled arrest, at least 2 must be for
the current charge. For a total of 6 or 7 index arrests, at least 3
must be for the current charge. More generally, if n is equal to the
number of prior index arrests of any type, and m is equal to the number
of prior index arrests of the same type as the current arrest, a person
satisfies the "specialist" criterion if for n > 3, m > (n - 1)/2
for n odd or m > (n - 2)/2 for n even, and for n = 2, m > n/2 = 1.
SOURCE: Derived from data in Cohen (1982:Table 3-3).
cialists within an offense type were most
often found among offenders arrested for
robbery and aggravated assault. One-third
of all arrestees in these offense types had
prior records ant! a predominance of arrests
for the same offense type. Specialists in
robbery and aggravated assault represented
over one-half of those arrestees who had
any prior arrests for index offenses. Special-
ists were least prevalent in murder and
rape, accounting for only 14 percent of all
arrestees for these offense types. This lower
prevalence of specialists was not due to a
lower likelihood of any prior arrests. Two-
thircls of the arrestees for murder and rape
had prior arrests for index offenses, but less
than one-quarter of those recidivistic ar-
restees were specialists in those offense
types.
A similar mix of specialists and general-
ists was evident among respondents to the
second Ranc! inmate survey. As in~licatecl in
Table 57, diversity in offending was very
common; most inmates indicated that they
committed several different offense types
during the observation period. Never~e
OCR for page 417
APPENDIX B.: RESEARCH ON CRIMINAL CAREERS
less, more than one-quarter of all respon-
dents reported that they committed only
one offense type. Only robbery was rarely
committed as a sole offense type. Even
among the category of"Iow-level robbers,"
64 percent of the respondents (N = 153)
also reporter] that they committed burglary
and theft crimes during the 1- to 2-year
observation period.
The simple mover-stayer model and vari-
ations ofthe model that permit a continuous
distribution of differences among offenders
(see, for example, Spilerman, 1972b) rest on
an assumption of population heterogeneity.
4~7
The transition process varies across the
population, but within any subgroup the
transition process is invariant over time. An
alternative explanation offered for the ten-
dency of switching processes to bunch on
the diagonals explicitly incorporates vari-
ability in the process with time. This is most
often Lone by allowing for duration clepen-
dence in the switching process.
In analyses of residential migration and
status mobility, duration depenclence re-
flects a phenomenon of cumulative inertia
(McGinnis, 1968), whereby the probability
of remaining in the same state increases as
TABLE B-57 Combinations of Offense Types Committed by Respondents to the
Second Rand Inmate survey
Offenses Reported During Observation Period
Combinations
a b Drug
Robbery Assault- Burglary Theft- Deals
Number of
Respon- Per
dents cent
Violent predators
(robbery-assault
drug deals)
Robber-assaulters
Robber-dealers
Low-level robbers
Mere assaulters
Burglar-dealers
Low-level burglars
Property and drug
offenders 0
Low-level property
offenders
Drug dealers
Totals
+ +
+ + ?
?
? ? O
o o o
+ o
+ o
o +
?? +
o o
? + 306
? 0 160
? + 188
240
105
199
171
+ O O
?? O
128
0 0 0 + 0168
112
1,777
O O O
+
15.0
7.8
9.2
11.8
5.1
9.8
8.4
6.3
8.2
5.5
87.1
NOTE: + Respondents commit this crime by definition. 0 Respondents do
not commit this crime by definition. ? Respondents may or may not commit this
crime; analysis shows that nearly all in this category do. ?? Respondents may
or may not commit this crime; analysis shows that most in this category do not.
Assault includes homicide arising out of assault or robbery.
bTheft includes auto theft, fraud, forgery, and credit card crimes.
CThe remaining 12.9 percent did not report committing any of the offense
types surveyed. Respondents with missing data (150 out of 2,190) were
excluded in calculation of the percentages.
SOURCE: Chaiken and Chaiken (1982a:Table 2.5).
OCR for page 418
418
time already spent in that state increases.
Switches to a different state are more likely
the shorter the duration in any state. In
offense switching, duration dependence is
reflected in variations in switching patterns
with increases in the length of the intervals
between arrests. The preliminary analysis
of the role of different intervals (Table 54)
suggests that duration dependence may be
a factor in offense switching. Contrary to the
cumulative inertia observed in studies of
mobility, however, repeating the same of-
fense type seems to be more likely when
intervals between arrests are short. The
tendency to specialize appears to decrease
for longer intervals.
A variety of modeling strategies have
been proposed for incorporating duration
dependence. These include expanding the
state space to include duration explicitly
as a defining attribute (Cox and Miller,
1965; McGinnis, 1968), introducing inde-
pendent variables into Markov chain mod-
els (Coleman, 1964; Spilerman, 1972a), and
semi-Markov processes (Ginsberg, 1971~.
(See Hoem, 1972, for a review of various
models that incorporate duration depen
CRIMINAL CAREERS AND CAREER CRIMINALS
dence.) These approaches may be fruitfully
applied to analyses of offense switching as
well.
The analytic treatment of offense switch-
ing is currently in the earliest stages of
development. Only the simplest first-order
Markov models have been explored, and
then in very limited ways. Analysis in this
area may gain substantially from the many
developments in modeling already avail-
able in other fields, especially the treatment
of mobility processes in demography and
sociology. Attempts to model offense
switching may also benefit from expanding
the process to include consideration of the
role of intervening, but undetected, of-
fenses in the observed switching process
between arrests. Such models would char-
acterize switching between arrests in terms
of the basic switching process between of-
fenses committed and the selection process
that transforms some offenses into observed
arrests. Alternatives to Markov fo,,~ula-
tions, with their limited focus on successive
events, might also be fruitfully explored to
accommodate the role of prior history in
future offense seriousness.
Representative terms from entire chapter:
offense type
