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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

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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.

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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 -. .

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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.

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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.

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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).

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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.

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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.

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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 iThis 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

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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

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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

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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. REFERENCES Adams, K. 1983 The effect of evidentiary factors on charge reduction. Journal of Criminal Justice 11:525-537. American Bar Association 1968 Standards Relating to Pretrial Release. New York: Institute for Judicial Administration. Anderson, N. 1968 A simple model for information integration. Pp. 731-743 in R. P. Abelson, Elliot Aronson, CRIMINAL CAREERS AND CAREER CRIMINALS William J. McGuire, Theodore M. Newcomb, Milton J. Rosenberg, Percy H. Tannenbaurn, eds., Theories of Cognitive Consistency: A Sourcebook. Chicago, Ill.: Rand McNally. 1974 Cognitive algebra: integration theory ap- plied to social attribution. Pp. 1-101 in L. Berkowitz, ea., Advances in Experimental Social Psychology. New York: Academic Press. 1979 Algebraic rules in psychological measure- ment. American Scientist 67:555-563. Angel, A., Green, E., Kaufman, H., and Van Loon, E. 1971 Preventive detention: an empirical analysis. Harvard Civil Rights Civil Liberties Lau; Review 6:301-396. Babst, D. V., GottEredson, D. M., and Ballard, K. B. 1968 Comparison of multiple regression and con- figural analysis techniques for developing base expectancy tables. Journal of Research in Crime and Delinquency 5(11:72~80. Babst, D. V., Inciardi, J. A., and Jaman, D. R. 1971 The uses of configural analysis in parole prediction research. Canadian Journal of Criminology and Corrections 13(31:20(~ 208. Babst, D. V., Koval, M., and Neithercutt, M.G. 1972 Relationship of time served to parole out- come for different classifications of burglars based on males paroled in fifty jurisdictions in 1968 and 1969. Journal of Research in Crime and Delinquency 9:9~116. Baldwin, J. 1979 Ecological and areal studies in Great Britain and the United States. Pp. 2~66 in N. Morris and M. Tonry, eds., Crime andJus- tice: An Annual Review of Research. Chi- cago, Ill.: University of Chicago Press. Ballard, K. B., Jr., and GottEredson, D. M. 1963 Predictive Attribute Analysis in a Prison Sample and Prediction of Parole Perforrn- ance. Institute for the Study of Crime and Delinquency. Vacaville, Calif. Becker, G., and McClintock, C. 1967 Value: behavioral decision theory. Annual Review of Psychology 18:23~286. Berkson, J. 1947 Cost utility as a measure of efficiency of a test. Journal of the American Statistical As- sociation 42:246-255. Bernstein, I., Kelly, W., and Doyle, P. 1977 Societal reaction to deviants: the case of criminal defendants. American Sociological Review 42~0ctober):743-755. Bernstein, I., Kick, E., Leung, J., and Schulz, B. 1977 Charge reduction: an intermediary stage in the process of labelling criminal defendants. Social Forces 56(2~:362-384.

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ACCURACY OF PREDICTION MODELS Feeley, M., and McNaughton, J. 1974 The Pretrial Process in the Sixth Circuit. Unpublished manuscript, University of Cal- ifornia, School of Law, Berkeley. Fergusson, D. M., Fifield, J. K., and Slater, 9. W. 1977 Signal detectability theory and the evalua- tion of prediction tables.Journal of Research in Crime and Delinquency 14(21:237-246. Fildes, R., and Gottfredson, D. M. 1968 Cluster analysis in a parolee sample.Journal of Research in Crime and Delinquency 5(1):2~11. Fischer, D. R. 1981 Offender Risk Assessment: Implications for Sentencing and Parole Policy. Statistical Analysis Center, Iowa Office for Planning and Programming. 523 E. 12th St., Des oines, Iowa. 1983 Better public protection with fewer inmates? Corrections Today (December):1~20. 1984 Risk Assessment: Sentencing Based on Probabilities. Statistical Analysis Center, Iowa Office for Planning and Programming, 523 E. 12th St., Des Moines, Iowa. No Selective Incapacitation of Potentially Vio date lent Adult Offenders. Statistical Analysis Cen- ter, Iowa Office for Planning and Program- ming, 523 E. 12th St., Des Moines, Iowa. Fisher, F. M., and Kadane, J. B. 1983 Empirically based sentencing guidelines and ethical considerations. Pp. 18~193 in A. Blumstein, J. Cohen, S. Martin, and M. Tonry, eds., Research on Sentencing: The Search for Reform, Vol. II. Washington, D. C.: National Academy of Sciences. Fisher, J. 1959 The twisted pear and the prediction of be- havior. Journal of Consulting Psychology 23:400~05. Forst, B. 1976 Participation in illegitimate activities: fur- ther empirical findings. Policy Analysis 243~:477~92. 1983 Selective incapacitation: an idea whose time has come? Federal Probation 46: 1~23. Forst, B., and Brosi, K. 1977 A theoretical and empirical analysis of the prosecutor. Journal of Legal Studies 6: 177-191. Forst, B., Lucianovic, J., and Cox, S. 1977 What Happens After Arrest? Washington, D.C.: INSLAW. Fowler, L. 1983 Classification and prediction: improving on chance. Corrections Today (December): 41 17. Freed, D., and Wald, P. 1964 Bail in the United States: 1964. Washington, 283 D.C.: U.S. Department of Justice and the Vera Institute of Justice. Frey, E. 1951 Der frnhEriminelle Ruckfallsverbrecher. Criminalite precoce et recividisme, Schweizerische Criminalistische Stud., 4. Basel: Berlag fur Recht und Gesellschaft. Galegher, J., and Carroll, J. S. 1983 Voluntary sentencing guidelines: prescrip- tion for justice or patent medicine? Law and Human Behavior 7(4):361~00. Galton, F. 1895 (Nature, June). Cited in E. Banks, 1964, Reconviction of young offenders. Curren~t Legal Problems 17:61-79. Garberj S., Klepper, S., and Nagin, D. 1983 The role of extralegal factors in determin- ing criminal case dispositions. Pp. 129- 183 in A. Blumstein; J. Cohen, S. Martin, and M. Tonry, eds., Research on Sen- tencing: The Search for Reform, Vol. II. Washington, D.C-.: National Academy Press. Gaudet, F., Harris, G., and St. John, C. 1933 Individual differences in the sentencing of judges. Journal of Criminal Law and Crim- inology 23:811. Gerecke 1939 Zur Frage der Ruckfallsprognose. Monats- schriftfurKriminalbiologie und Strafrechts- reform 30:35 38. Glaser, D. 1954 A reconsideration of some parole prediction factors. American Sociological Review 19: 335 341. 1955 The efficacy of alternative approaches to pa- role prediction. American Sociological Re- view 20:28~287. 1962 Prediction tables as accounting devices for judges and parole boards. Crime and Delin- quency 8(3):239-258. 1964 The E:ffectivenes of a Prison and Parole Sys- tem. New York. Bobbs-Merrill. Glaser, D., and O Leary, V. 1966 Personal Characteristics and Parole Out- come. National Parole Institutes. Office of Juvenile Deiinquency and You~ Develop- ment, Washington, D.C:.: U.S. Department of Heal~, Education, and Welfare. Glass, G. V. 1976 Primary, secondary, and meta-analysis of re- search. Educational Research 5:~8. Glass, G. V., McGaw, B., and Smith, M. 1981 Meta-analysis in Social Research. Beverly Hills, Calif.: Sage. Glueck, S., and Glueck, E. 1950 Unraveling Juvenile Delinquency. New York: Commonweal~ Fund.

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