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OCR for page 212
L
Accuracy of Prediction Models
Stephen D. Got~fredson and Don M. Got~fredson
Any decision made uncler uncertainty
with respect to future events, behaviors,
activities, resources, trends, demands, or
outcomes is a predictive one. If the goal
of the decision being made is utilitarian,
prediction certainly is critical to the deci-
sion-making process. Accordingly, the
concept of prediction is central to tradi-
tional crime-reduction or crime-preven-
tive concerns of the criminal justice sys-
tem, such as deterrence, incapacitation,
and rehabilitation (S. D. Gottfredson ant]
D. M. Gottfredson, 19851. Prediction is
implicit in the decisions made but rarely
is that explicitly recognized. It is quite
possible, however, to characterize the
American criminal justice system as a
network of interrelated decision points
(M. R. Gottfredson and D. M. Gottired-
son, 1980b); when this is done, the ubiq-
uity of prediction to most of the decisions
encountered is made clear.
This paper concerns the accuracy of
Stephen D. GottEredson is executive director,
Maryland Criminal Justice Coordinating Council,
Baltimore, Md., and Don M. Gottiredson is profes-
sor, School of Criminal Justice, Rutgers University.
2~2
prediction in criminal justice settings and
the utility of statistically (leveloped deci-
sion-making tools intended for practical
implementation. We have been forced to
limit our review in several ways. First,
our principal focus is the prediction of
criminal or delinquent behavior. Thus,
we do not address a variety of important
criminal justice prediction problems in-
volving resource allocation, criminal pop-
ulation projections, estimation of rates of
offending and the length of criminal ca-
reers, and many others, except as they are
relevant to assessing the impacts of some
proposed decision-making devices (e.g.,
those proposed for selective incapacita-
tion strategies).
Second, we omit detailed discussion of
work concerning the psychological or
psychiatric as se s sment of offenders, even
though much of this clearly is of a predic-
tive nature. We also give less attention to
predicting the behavior of criminal jus-
tice system functionaries (e.g., judges,
prosecutors, parole board members) than
to predicting the behavior of offenders.
Since the accuracy of prediction models
cannot responsibly be assessed in a vac
OCR for page 213
ACCURACY OF PREDICTION MODELS
uum, however, some attention to the be-
havior of functionaries is necessary.
Detailed critical reviews concerning
several distinct and important issues have
been published recently. Given the ready
availability of this information, we clo not
give detailed attention to the prediction
of violence (reviewed by Monahan, 1978,
1981; Monahan and Klassen, 1982), to
longitudinal studies bearing on predic-
tion issues Reviewed by Farrington,
1979, 1982), or to the prediction of sen-
tencing decisions (reviews are available
in Hagan, 1974; L. Cohen and Kluegel,
1978; Garber, Klepper, and Nagin, 1983;
Hagan and Bumiller, 1983; Klepper,
Nagin, and Tierney, 19831.
Because insufficient information is
available to allow reliable generaTiza-
tions, we ignore the areas of policing and
corrections, although the nature of cleci-
sions macle in these settings often clearly
is predictive. Our focus is on bait and
pretrial release decision studies and on
Collisions involving prosecution, sentenc-
ing (although as noted above, we do not
provide a detailed review of these). ant]
parole. We give attention to efforts de-
signed to provide acivice, based on scien-
tific principles of assessment and predic-
tion, to those confronted daily with the
variety of decision-making tasks consid-
ered.
In the first section of this paper we
discuss the nature of decisions generally,
and in criminal justice settings in partic-
ular. Because the accuracy of predictive
decision making is of concern, we discuss
some of the issues involved in such as-
sessments. In the next section we discuss
both descriptive and (where appropriate)
normative prediction studies for each of
the decision arenas under consideration.
Special attention is given to items of in-
formation commonly observed to be pre-
dictive, the general level of accuracy of
these (both in the bivariate case and
when considered in conjunction with
213
other predictors), and the general level of
predictive accuracy achieved in equa-
tions or models of the decisions under
consideration. Then, we summarize the
preceding discussion by focusing on pre-
dictors commonly observed across the de-
cision arenas studied. We provide a sum-
mary of those variables found to predict
the decisions of functionaries and those
fount! to predict the behavior of offenders
and show how they slider. Next, for each
of the decision arenas considered, we
examine the efficacy of statistically clevel-
oped decision-making tools that are in
use, or have been proposed for use, in a
number of jurisdictions. Finally, we cTis-
cuss ways to improve the accuracy and
hence the utility of prediction tools cle-
signecI for application in criminal justice
settings.
PREDICTIVE DECISION MAKING
The Logic of Prediction
Any decision has three components: a
goal, the existence of alternatives, and
information upon which the decision may
be based (M. R. Gottfredson and D. M.
Gottiredson, 1980b). Decisions cannot ra-
tionally be macle (or stuclied) if decision-
making goals are unstated or unclear. Un-
fortunately, goals for criminal justice
decisions rarely are explicitly stated, and
often they are complex. Rarely is a single
goal for a (recision given.) Without alter-
natives, there can be no decision prob-
lem; and without information on which to
base the clecision, the "problem" reduces
to reliance on chance. As we shall see,
decision makers often are not sufficiently
attentive to the relation of information
used to the goal clesired, which results in
decisions being macle that would have
been better left to chance.
iSee D. M. Gottiredson and Stecher (1979) for an
example within the context of sentencing.
OCR for page 214
214
It is in the relation of information used
to the goal desired that prediction studies
are of most value to the criminal justice
decision maker. If decision makers desire
to minimize errors in the decision proc-
ess, prediction studies also are to be de-
sirect, for it is this that they are clesignecI
to accomplish. In brief, prediction simply
refers to the utilization of informational
items, singly or in combination, to esti-
mate the probable future occurrence of
some event or behavior (known as the
criterion). Methods of using the informa-
tional items (known as independent or
predictor variables) may be intuitive,
clinical, or subjective, or they may be
statistical or "actuarial." If of the latter
type, any of a wide variety of approaches
may be used. The specification of these is
beyond the scope of this paper, but we
assume the reader has some familiarity
with the more common methocis.2
The Nature of Decisions
Decisions involve choice, because of
the requirement that alternatives be
available. Much of psychology, econom-
ics, and philosophy concerns the stucly of
choices that people make. What deter-
mines the amount of money one will pay
this fall for a house? What is responsible
for the selection of a Labrador retriever
over a Chihuahua as a family pet? Why
does one (generally) obey the law? What
is the role of unconscious motivation, of
altruism, of superstition, of morality, or of
value in the choices macle? Clearly, de-
tailed discussion of the nature of human
choice behavior is beyond the scope of
this paper. We do, however, briefly con-
sider decision-making study that has as a
premise the notion that human decision
makers value rationality (for a delightful
2For general discussions of the logic of predic-
tion, see Sarbin (l943), Gough (1~362), and D. M.
GottEredson (1967~.
CRIMINAL CAREERS AND CAREER CRIMINALS
discussion of rationality in decision mak-
ing, see Lee, 1971~. Following Lee, deci-
sion theory considers the rational person
to be one who, when confronted with
choice, makes the (recision that is "best";
this decision is the optimal or rational
one. This decision (1) must be one of
those available, (2) will depend on the
decision principles uncler study (thus, dif-
ferent studies, proceeding from different
bases, may identify different optimal
choices), (3) may differ among persons
(e.g., due to differing utilities assigned to
alternatives, differing subjective proba-
bility estimates), but (4) must depend on
the information available to the decision
maker.
Behavioral decision theory (Edwards,
1954. 1961; Becker and McCTintock.
, ,
1967; Rapoport and WalIsten, 1972;
SIovic, Fischoff, and Lichtenstein, 1977;
R. M. Hogarth, 1980; Einhorn and
Hogarth, 1981; Pitz and Sachs, 1984),
"cognitive algebra" (Anderson, 1968,
1974, 1979), utility theories (Lee,
1971:Chapter 5), and "game theories"
and their assessments of strategies (e.g.,
minimax and maximin principles) (von
Neumann and Morgenstern, 1947; Luce
and Raiffa, 1957; Lee, 1971) are examples
of general considerations of ways in
which one may mode} the choice or deci-
sion behavior of the rational person (Lee,
1971, and R. M. Hogarth, 1980, review
much of this vast literature).
we note tins literature to make two
points. First, there is a distinction to be
drawn between normative and descrip-
tive decision studies (Lee, 19711. Norma-
tive studies concern the decisions that
people should make in a choice situation,
regardless of the decisions that they actu-
ally make. Descriptive studies concern
the decisions actually made, regardless of
those that should be made. This distinc-
tion, although clear, may become blurrecl
in practice, particularly when the goal is
to improve rational decision making. We
~? . .1 · 1 -. .
OCR for page 215
ACCURACY OF PREDICTION MODELS
believe that studies of both sorts may be
of considerable value and, accordingly,
we report on both in the sections that
follow.
The second point to be raised is that
very often human decision makers do not
appear to behave optimally, regardless of
the particular strategies under study. We
elaborate on this point later; here, we
simply suggest that for this reason we
believe the provision of decision-making
tools for criminal justice applications is
necessary and desirable.3
Francis Bacon observed: "We do ill to
exalt the powers of the human minc3,
when we shouIc! seek out its proper
helps" Quoted in R. M. Hogarth, 1980~.
Indeed, in most clecision-making situa-
tions, it has been found that actuarially
clevelopecT predictions outperform hu-
man judgments. This is true with respect
to psychiatric judgments (e.g., MeehI,
1954; Gough, 1962; Ennis and Litwack,
19741; graduate school admissions (e.g.,
Dawes ant! Corrigan, 1974; Dawes,
1979~; and in other areas (GoIc3berg,
1970~. Later, we review results of these
ant] other studies and suggest how human
judgments and actuarial preclictions can
profitably be used together; here, suffice
it to say that normative decision studies
appear to have the potential to improve
decisions made in criminal justice set-
tings significantly. Although we JO "exalt
the powers of the human minc3," we also
believe in attempts to provide it with
`` ,,
proper ae ps.
Problems of Measuring "Accuracy"
An obvious question to be asked when
considering predictive information is
"how good is it?" The answer is "it de
3There are other reasons also, such as the desir-
ability of making the decision process explicit. See
M. R. Gottfredson and D. M. Gottiredson (1980b) for
discussion of these.
275
pen(ls." The predictive accuracy of infor-
mation is a function of many things:
among the more salient are the reli-
abilities of the items of information used,
the methoc3(s) used to combine items of
information, the reliability ofthe criterion
variable chosen, the kinds of measure-
ments usecI, the base rate, the selection
ratio used, and the representativeness
of samples employed. Two questions
should be acIdressec3: one considers the
accuracy of inclivi(lual items of informa-
tion; the other refers to the accuracy of
items in combination with one another.
Our discussion requires that we first out-
line the nature of the issues aIreacly
raised.
Reliability
Reliability refers essentially to the sta-
bility with which measurements may be
made, and statistical validity-here im-
precisely considered as "accuracy"-is
constrained by the reliability win which
both criterion and predictor measure-
ments are made. No prediction device
can be better than the data from which it
is constructed. Often, attention is given to
the reliabilities of the predictor items but
the reliability of the criterion is ne-
glected.4
Methods of Combining Information
Many statistical methods have been
used in criminological prediction studies,
including the simple inspection of cross-
cIassification tables (e.g., Wamer, 1923),
multiple regression (e.g., D. M. Gottfred-
son and Bonds, 1961; D. M. Gottfredson,
Wilkins, and Hohinan, 1978), multiple dis-
criminant-function analysis (e.g., Brown,
40ne would be wise to view measurements of a
table with skepticism if the yardstick used is made
of rubber elastic. The careful investigator would
want to ensure as well that the table is not elastic.
OCR for page 216
216
1978),5 multidimensional contingency-
table analysis (e.g., Solomon, 1976; van
Alstyne and Gottfredson, 1978), tobit
analysis (e.g., Palmer and Carlson, 1976),
and a variety of clustering approaches
(e.g., Ballard and GottEredson, 1963;
D. M. Gottiredson, Ballard, and Lane,
1963; Fildes and Gottirec3son, 19681.6 For
a variety of statistical and practical rea-
sons, one or another approach may be
preferred, and the technique used theo-
retically could have dramatic conse-
quences for the accuracy of resultant pre-
diction devices. In criminal justice
applications this potential unfortunately
remains largely theoretical. Several re-
searchers have attempted to demonstrate
the relative utility of different statistical
approaches to criminal justice prediction
problems (e.g., D. M. Gotttrecison and
Ballard, 1964a; Babst, Gottiredson, and
Ballard, 1968; Simon, 1971, 1972;
Wilbanks and Hinclelang, 1972; Far-
rington, 1978), and the potential advan-
tages of different approaches have been
discussed by Wilkins and Mac-
Naughton-Smith (1964; see also Simon,
1971; S. D. Gottfredson and D. M. Gott-
frecison, 1979, 19801. S. D. GottErectson
and D. M. Got~redson (1979, 1980) com-
parecT the relative utility of six ofthe more
commonly used or promising methods,
concluding (as did the other studies cited)
that "no clear-cut empirical advantage in
prediction is provided by one or another
method (1979:631. Reasons for this dis-
appointing observation have been sug-
gested by Farrington ~ 1978), S. D.
Gottfredson and D. M. Gottfredson
(1979), and Loeber and Dishion (1983~.
In acIdition to serious problems of crite
~It should be noted, however, that when the
criterion measure is dichotomous, as in the example
cited, Fisher's discriminant function is equivalent
(within a transformation) to the multiple regression
approach; see Porebski (19661.
6For discussions of clinical methods of combin-
ing items of information, see Gough (1962) or
Monahan (1981~.
CRIMINAL CAREERS AND CAREER CRIMINALS
rion measurement, problems of the reli-
ability of predictor information and the
consequences of this for certain of the
methods (particularly least-squares meth-
ocls; see Wainer, 1976) especially are (le-
serving of mention.
Meehl (1954) and Gough (1962) pro-
vicle good reviews of specific actuarial
methods that have been used widely in
the behavioral sciences generally, often
with reference to problems and applica-
tion in criminal justice system settings.
Mannheim and Wilkins (1955), Simon
(1971, 1972), and S. D. Gottfrectson and
D. M. Gottfredson (1979) have provided
reviews of methods typically used in
. .
cr1m1no ogy.
The Base Rate
The base rate for any given event is
clefinec3 as the relative frequency of oc-
currence ofthat event in the population of
interest.7 Typically, base rates are ex-
pressed as proportions or percentages. In
many criminal justice applications, which
traditionally have treater] criterion mea-
sures as dichotomous, the base rate is
found simply through inspection of the
appropriate marginal distribution of the
expectancy table.
The ctifflculty of predicting events of
interest increases as the base rate clingers
from .50 (Meehl and Rosen, 1955~. Thus,
the more frequent or infrequent an event,
the greater the likelihood of inaccurate
prediction. (While this seems intuitively
true for rare events, it must be remem-
berecl that the occurrence of very fre-
quent events requires the simultaneous
occurrence of very rare events unless
the probability of an event is precisely O
or 1.) As an example of the difficulty of
such prediction, suppose that the base
rate for failure on parole is .20. Given this
information alone, one would make cor
7This discussion is adapted from S. D. GottEred-
son and D. M. Gottfredson (19791.
OCR for page 217
ACCURACY OF PREDICTION MODELS
rect predictions 80 percent of the time if
one simply predicted that no one will fail
on parole. One would also, of course, be
wrong 20 percent of the time. (Note that
given only the base rate as a guide, there
is no way of estimating which 20 percent
will fail.)
Now assume that a predictive crevice
has been developer] that allows one to
predict parole outcomes with 78 percent
accuracy. Even given this apparently
powerful device, one would still be better
off in expecting that no one will fail on
parole that is, in "predicting" perform-
ance on the basis of the base rate alone.
Although the predictive device floes beat
a naive chance rate (50 percent), the true
chance rate is considerably higher, and in
fact is greater than the power of the pre-
clictive device.
Those concerned with the clevelop-
ment of predictive tools for use in crimi-
nal justice applications (and in other ar-
eas) often have failed to consider base
rates in the development process ancI,
consequently, have made classifications
or predictions based on criteria that pro-
cluce larger errors than would the simple
use of the base rate. In 1955 Meehl and
Rosen summarized the consequences of
failure to consider base rates and con-
cludect that then-contemporary research
reporting neglected the base rate, making
evaluation of utility cli~cult, if not impos-
sible. Although Reiss (1951c) clearly and
dramatically illustrated this point more
than 30 years ago in a classic review of
Glueck and Glueck's Unravelingluvenile
Delinquency (1950; see also Hirschi and
Selvin, 1967), failure to consider base
rates remains an unfortunately common
practice (but such studies are now found
rarely in the published literature).
Selection Ratios
2~7
as belonging to the criterion classification
of interest. In delinquency studies, for
example, the selection ratio is the propor
tion of persons studied and selected as
expecter] delinquents by means of some
prediction instrument (see Loeber and
Dishion, 1983, for a discussion). Thus, the
base rate provides one marginal clistribu
tion for an expectancy table, and the se
lection ratio (essentially) provides the
other; together, the marginal clistribu
tions determine the chance expectancies
for the table. Selection ratios may be
altered through manipulation of the cut
ting score, which has obvious but some
times unrecognized consequences for
prediction (Cronbach, 19601. These may
be particularly dramatic if the bivariate
distribution is heteroskerlastic (J. Fisher,
1959~.
Representativeness of Samples
If accuracy of prediction is desired,
samples used in constructing selection
devices must be representative of the
population on which the crevice is in
tended to be used.8 This ensures that the
appropriate base rate is considerecl and
minimizes subsequent shrinkage of
power from the construction to the oper
ational samples.
The adage that no two people are ex
actly alike properly is extended to groups:
no two groups of people are i(lentical.9 If,
however, the groups have been selected
by some appropriate mechanism (such as
random sampling), they can be expecter]
to have a great deal in common in terms of
both their overall characteristics and the
interrelations of various individual char
acteristics. It is this similarity of relations
within different groups of people on
8Note that this is not the same as saying that the
sample must be representative of the population as
The selection ratio is simply the pro- a whole
portion of tncl~v~cluals or events studied 9Portions of this discussion are adapted from
and identified by the prediction method s. D. GottEredson and D. M. GottEredson (1979).
OCR for page 218
218
which all statistical predictions ultimately
rely. If in one group of subjects the young
c30 better in relation to some outcome, it
can be assumed that in a similar group of
subjects the young again will do better.
Prediction methods are intended to esti-
mate, on the basis of some group of peo-
ple available for study, how members of
other similar groups will behave. There is
a danger, however, of overestimating the
extent to which relations founct in one
sample can be used to explain relations in
a similar sample. Within the original sam-
ple alone, there is no adequate way to
distinguish how much of the observed
relation is due to characteristics and un-
derlying associations that wit! be shared
by new samples and how much is due to
unique characteristics of the first sample.
This is because the apparent power of a
prediction device clevelopec3 on a sample
of observations derives from two sources:
the detection and estimation of unclerly-
ing relations likely to be observed in any
similar sample of subjects and the pecu-
liar or indiviclual properties ofthe specific
sample on which the device has been cre-
ated. Cross-vaTiclation is important in esti-
mating the relative importance ofthese two
sources of predictive power. This is partic-
ularly advisable when the prediction study
is intended for practical application in new
samples. If not clone, the utility of the in-
strument as a predictor in new samples is
likely to be overestimated.
Cross-Va~iciation
Cross-vaTidation is simply an empirical
approach to the problem of obtaining an
unbiased! estimate of the accuracy of pre-
diction (whether based on a single item of
information or on some combination of
items). Typically, this is accomplished by
dividing the sample at hand in two, con-
structing the device on one, and using the
other to estimate predictive accuracy.
Horst (1966) refers to this general proce-
dure as the "sample fractionation" ap-
proach and argues, quite correctly, that
CRIMINAL CAREERS AND CAREER CRIMINALS
there are serious clisadvantages to it.
First, the stability of estimates is depen-
dent on the number of cases on which
they are ma(le. Thus, divicling the sample
reduces the reliability of the device con-
structec3, which, as aIrearly noterl, may
reduce validity. Second, the approach
gives only one estimate (from a poten-
tially large universe of estimates). In ef-
fect, one regards coefficients that result
from cross-vaTidation as an estimate of the
average expected validity in independent
samples and expects those vaTiclities to be
normally distributed. Accordingly, one is
as likely to underestimate as overestimate
ton validity but a single sample offers
weak empirical evidence of shrinkage
(Horst, 19661.
There appears to be no "best" answer
to the cross-vaTiclation problem; rather, a
tracle-off of concerns is raised. Sample
fractionation procedures do constrain va-
lidity (unIess the sample obtained is very
large, which is unusual in cr~m~na~Just~ce
research). A single estimate of shrinkage
is not optimal, is unlikely to represent the
actual mean validity, and is as likely to
underestimate as overestimate that value.
As noted by Horst, one can obtain two
estimates by examining expected valicli-
ties from each sample on the other (in the
traditional fractionation approach), but
one is then left with deciding which of
the crevices actually to use. Similarly, one
could furler fractionate the sample and
develop several empirical estimates.
Again, however, one encounters prob-
lems of reliability as the sample size de-
creases. To meliorate this, one could re-
combine the subsamples and create a
device on the full sample, relying on the
subsample estimators to provide an index
of shrinkage (see Horst, 1966:3801. It
seems likely, however, that the validity of
the device developed in this fashion will
be underestimatecl (perhaps seriously)
given that the samples from which valid-
ity is estimated are much smaller than is
the sample on which the final device is
constructed.
OCR for page 219
ACCURACY OF PREDICTION MODELS
Some argue for a "IongitucTinal" vaTida-
tion approach (e.g., Horst, 1963, 1966) in
which one develops a device on the larg-
est sample available and applies the de-
vice in operational use. Validity is as-
sessed over time, and research is
integrates! into the administrative proc-
ess. It seems to us that the central issue
has to do with (1) the types of decisions to
be made on the basis of a predictive
crevice and (2) the expected validities of
the crevices used. For certain relatively
benign applications, when expected va-
lidities may be relatively high, we would
not object to such a procedure. When the
decisions to be macle involve conse-
quences of liberty, however, ant] when
expected valiclities are Tow (as commonly
is the case in criminal justice applica-
tions), we wouIc! object. Wright, Clear,
and Dickson (1984) recently illustrated
that the consequences (in terms of re-
duced vaTiclities) of the wholesale aclop-
tion in several jurisdictions of crevices
developecI in one locale can be dramatic.
Measures of Predictive Accuracy
The issues considered so far can affect
the accuracy of a predictive crevice, but
. _
0
>
I
UJ
m
6 i,'
219
we have not yet consiclerecl how best to
assess that accuracy. This section focuses
on such a consideration.
In selection applications, predictive
crevices reduce to a dichotomy resulting
in a decision situation, with actual out-
comes considered, that can be repre-
sentec3 by a 2 x 2 contingency table
(Figure 1~. The cutting score clecicled on
determines the selection ratio ant! the
marginal distribution of the columns in
Figure 1. The base rate determines the
marginal distribution of the rows. To-
gether, these determine the distribution
of cases within the table, subject to one
degree of freedom. They also determine
the distribution of cases within the table
to be expected by chance. Although
statistics such as x2 are useful in assessing
inclepenclence in tables such as this, the
value of x2 is a function of the dimension-
aTity of the table and the number of cases
considered, as well as of the relation be-
yond that expected by chance. Further, y2
is used to assess statistical significance;
directly, it tells the investigator nothing
about the magnitude of the effect discov-
erec3. It gives an assessment of"accuracy"
to the extent that the investigator may be
confident of the reliability of the elect
False | Positive l
Negatives Hits
_. ,
Negative Fa Ise
l Hits I Positives
Succeed
Fail
PREDICTED BEHAVIOR
FIGURE 1 The selection decision problem.
OCR for page 220
220
ctiscoverecT, but it floes not depict the
degree of relation associated with that
elect. A variety of statistics are available
to help in this assessment (e.g., the con-
tingency coefficient or Cramer's V; see
Hays, 1963:60~606), but none com-
pletely overcomes the climensionality
problem.
The use of ~ (phi coefficient) (Hays,
1963:604) is meliorative when used for
tables with one degree of freedom. Since
the practical application of predictive
tools for selection purposes often recluces
to such a table, ¢, (which is simply \/X2/N)
would appear to be an attractive choice
for an index of predictive efficiency. The
marginal distributions of a table with only
one degree of freedom, however, con-
strain ~ by imposing an upper limit on the
possible relation observed in the table
(Guilford, 19651.~° Moreover, ¢, is subject
to a limitation common to correlational
measures: it is sensitive to the base rate.
As noted by Richardson ~ 1950), the
standard error of prediction provides an
immediate, but incomplete and poten-
tially misleading, answer to the question
of the predictive value of a selection cle-
vice. This statistic is given by:
cry Hi,
where of is the standard deviation of the
criterion measure. As we have noted,
most selection applications of predictive
crevices use some cutting score, essen-
tially reducing the predictor scale to a
dichotomy. As commonly used, however,
the standard error of prediction assesses
the predictive device and the criterion
measured continuously and may, in fact,
result in an underestimation of the power
of the selection crevice, since the device
as used simply is predictive of success or
failure. The standard error of prediction,
however, is a function also of degrees of
i°This does not appear to be true for the point-
biser~al, as commonly applied to 2 x k tables (B. F.
Green, Jr., personal communication, 1979).
CRIMINAL CAREERS AND CAREER CRIMINALS
success or failure; that is, it requires an
assessment of just how good a success, or
how bad a failure, an incliviclual is
(Richarclson, 19501. Further, the standarcl
error of precliction also is sensitive to
variations in the base rate and, hence,
may be of little value in assessing the
relative merits of crevices used on dif-
ferent populations.
A number of indices are intencled to
provide an estimate of the "proportionate
reduction in error" resulting from use of
some selection or predictive crevice. In
general, these inclices are designed to
offer an evaluation of predictive power
above that afforded by simple use of the
chance rate. OhTin and Duncan (1949),
among the first to give practical attention
to the problem in the criminal justice
fielcl, suggested an "index of predictive
efficiency" (see also Horst, 1941; Reiss,
1951a; Goodman, 1953a, b; McCord,
1980; Loeber and Dishion, 1983), which
is defined simply as the percentage re-
(luction in error gained by use of a pre-
dictive device over that achieved by
knowledge of the base rate alone.
_
. . .
The index of predictive efficiency also
has the limitation of sensitivity to the base
rate. Thus, it has little utility for the ex-
amination of accuracy across different
situations.
Considering specifically cases such as
that diagrammecI in Figure 1 (in which
one essentially wishes to predict mem-
bership in one or the other of two mutu-
ally exclusive categories), Berkson (1947)
noted that there are utilities, definer] as
true positives ant] negatives, as well as
costs, defined as false positives and neg-
atives, associated with the decision macle.
Arguing that predictive devices shouIcI
be evaluated with respect to a compari-
son of costs and utilities, he developecI an
index of effectiveness (which may be
used at any utility) called "mean cost"
anti clefinecT the "mean cost rating"
(MCR) to allow the index to vary from 0 to
1. The MCR is less sensitive to the base
OCR for page 221
ACCURACY OF PREDICTION MODELS
rate than is ~ or the point-biserial coeffi-
cients. The index was introclucec] to crim-
inologists by Duncan et al. (1952), and it
has seen widespread use since as a mea-
sure of the predictive efficiency of a se-
lection device. It recently was shown that
the MCR is related to Kendall's tan, pro-
vicling a method of testing the statistical
significance of the index (Lancucki ant]
TarTing, 19781; and Fergusson, Fifield,
and Slater (1977) have shown the relation
between the MCR and the familiar pro-
portion of area under a receiver operating
characteristic (ROC) curve, which pro-
vides a grounding for the inclex in the
framework of signal detection theory
(Green ant] Swets, 1966~.
For the two-by-two decision case (which
represents the "fairest" test of a predictive
device as user] in selection decisions),
Loeber and Dishion (1983) cleveloped an
index called the RIOC (relative improve-
ment over chance), which considers chance
occurrence within the table as well as the
maximum correct value that prediction
could achieve given applicable selection-
ratio ant! base-rate conditions. Since this
statistic is more recent than others de-
scribec3 and less common in the criminal
justice literature, we describe it further.
The RIOC is cleaned as
%IOC
RIOC= 100
%MC- ARC
where the numerator represents the per-
centage improvement over chance (IOC)
and the denominator is the difference
between the maximum percentage cor-
rect (MC) that couIct be achiever! and the
percentage required by chance (RC),
both given the joint marginals observed.
Although not inclependent of either the
base rate or the selection ratio, the RIOC
correlates much less highly with either
than does the simple index of predictive
efficiency (Loeber and Dishion, 19831.
None of the inclices yet developed,
however, can answer completely the
227
question of how accurate a predictive
device is. Correlational indices and indi-
ces such as the RIOC and the index of
predictive efficiency suffer because they
are affected by variations in the base rate.
Thus, they do not reacliTy allow a compar-
ison of crevices (or items) across base-rate
conditions. The MCR floes allow this, but
it is not often that one wishes to evaluate
a specific predictive crevice regarcIless of
base-rate conclitions, although this is the
most common application of this index
(S. D. Gottfredson and D. M. Gottfredson,
1979; Hoffman, 19831.
Measures that are sensitive to base
rates and those that are not can leacl to
dramatically different conclusions con-
cerning the value of predictive crevices
(Fergusson, Fifielc3, and STater, 19771.
The former (e.g., correlation measures)
describe the performance of the instru-
ment in application with given popula-
tions and decision rules; the latter (such
as the MCR) essentially give an inclica-
tion of the general power of the device
without respect to constraints of base
rates and selection ratios.
Which to use depends on the question
at hand. If one seeks to evaluate the
relative power of different crevices devel-
ope<1 on different populations (for which
the base rates may well be different),
indices that are less sensitive to base rates
would seem preferable. If, however, one
wishes to estimate the power of a partic-
ular crevice, aclministerec3 with particular
decision rules on a particular population,
base-rate-clepenclent indices will be more
informative.
Other Problems Concerning
"Accuracy"
The practical application of predictive
tools in criminal justice raises other prob-
lems relatecl to the "accuracy" question.
One almost always is attempting to con-
struct, validate, ant] assess the accuracy of
crevices uncler circumstances that already
OCR for page 222
222
have required some selection: thus, true
base rates often cannot be known, nor
"accuracy" assessed relative to them.
One cannot, for example, know the true
base rate for parole violation for all of-
fenclers considered for parole. Since not
all are in fact parolecl, one can at best
identify the base rate for known viola-
tions by paroled inmates.
Problems exist also in the area of as-
sessing the relative contributions of spe-
cific predictor variables to the overall ac-
curacy of a predictive or selection crevice.
Items that may be highly predictive un-
der some base-rate conditions may be
much less so uncler other base-rate condi-
tions (this is most likely to be the case
when the distribution of the predictor
variable itself is skewed). Items that may
prove predictive for some clefinecl popu-
lations may be less (or more) predictive
when the composition of the population
is different (e.g., the item "race" may be
predictive of criminal convictions in
some large urban populations and not at
all predictive in suburban or rural popu-
lations). Items that are predictive during
some age ranges may not be predictive if
other age ranges are considered. As we
have pointed out elsewhere (S. D.
Gottfrecison and D. M. Gottfredson,
1979), such issues are meliorated if one
remembers that the greatest limitation of
prediction methods [is] that the devices
. . . are developed and validated win respect
to specific criteria, using available data, in a
specific jurisdiction, during a specific time
period. Thus, any generalizations to over out-
comes of interest, or after modifications of the
item definitions used, or to over jurisdictions
or populations, or to over time periods, are to
be questioned.
Still, the question of the "best" predic-
tors is an important one, both for pro-
viding guidance for those who wish to
construct predictive devices and for the-
oretical (levelopment. Several criteria of
CRIMINAL CAREERS AND CAREER CRIMINALS
"best" could be consi~lerecl: (1) most
powerful (in unique contribution to pre-
cliction), (2) most stable (e.g., from popu-
lation to population), (3) most reacliTy
available (e.g., age, sex), or (4) most ethi-
cally or legally defensible. In the cTiscus-
sion that follows, each of these will be
consiclerecI. The "most powerful" crite-
rion, however, is clifficult to apply for
several reasons. First, few authors have
provided sufficient information to allow a
comparison ofthe predictive efficiency of
items across an adequate variety of situa-
tions. Ideally, one would like to calculate
RIOCs or MCRs to assist in this evaTua-
tion; the data provi-cled usually are insuf-
ficient for this. Second, devices con-
structed following a simple unweightec3
linear mode! (and there are many of
these) provide no assessment of the rela-
tive value of in(lividual items of informa-
tion. Third, although devices constructed]
using multiple regression methods do
provide information for such an assess-
ment, studies on which these are based
almost always have used a dichotomous
criterion. Uncler such circumstances, beta
weights are quite unstable (Palmer and
CarIson, 1976) and cannot be relied on to
provide unbiased estimates of the unique
contributions ofthe variables considered.
Other regression methods that would be
meliorative (e.g., the logistic moclel) are
not used often.
Two kinds of errors will be macle in any
predictive ciecision-making situation:
some persons preclictec! to belong to cri-
terion classification A in fact will not
(false positives), and some persons pre-
clicted to belong to criterion classification
B in fact will not (false negatives) (Figure
1~. Each of the various indices discussed
above considers that the two types of
errors are equivalent. In practice, of
course, they may not be, whether mea-
surecl in monetary, social, or ethical
terms. In most practical (recision-making
situations, and particularly those in crim
OCR for page 280
280
question is stated this way, the answer
can only be "yes and no." Prediction in
criminal justice settings clearly is not suf-
ficiently accurate to form the basis of
social policy. Proposals for dramatic
changes in policy and practice that rely
on the accuracy of prediction are prema-
ture at best. Once social policy has been
set, however, prediction clearly is suffi-
ciently accurate to be useful, and deci-
sions made will be made more accurately
if statistically based prediction tools are
used. Even when validity is very low, it
has been clemonstratec3 that selection cle-
vices provide significant improvements
in accuracy (Dunnette, 19661.
We freely admit the judgmental nature
of our preference for the selective clein-
stitutionaTization proposal over the selec-
tive incapacitation proposal and note that
the choice largely is an ethical one. It
floes appear, however, that consequences
of the proposal we advocate are more
benign than are consequences arising
from a selective incapacitation proposal.
Ant] we believe that predictive accuracy,
while in need of much improvement, is
sufficient for the former but insufficient
for the latter. If society should clecide that
selective incapacitation is the appropriate
strategy for sentencing criminal offend-
ers, it is clear that prediction tools should
be used in the decision-making process.
To decide the policy question on the
basis of current predictive accuracy, how-
ever, would be foolish.
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Representative terms from entire chapter:
base rate