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The Latent Structure of Sexual Violence Risk: A Taxometric Analysis of Widely Used Sex Offender Actuarial Risk Measures Glenn D. Walters, Raymond A. Knight and David Thornton Criminal Justice and Behavior 2009; 36; 290 DOI: 10.1177/0093854808330341 The online version of this article can be found at: http://cjb.sagepub.com/cgi/content/abstract/36/3/290

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THE LATENT STRUCTURE OF SEXUAL VIOLENCE RISK A Taxometric Analysis of Widely Used Sex Offender Actuarial Risk Measures GLENN D. WALTERS Federal Correctional Institution, Schuylkill

RAYMOND A. KNIGHT Brandeis University

DAVID THORNTON Sand Ridge Secure Treatment Center University of Birmingham

Actuarial scores from widely used sex offender risk instruments (Minnesota Sex Offender Screening Tool–Revised, Risk Matrix 2000, Static–99, Sex Offender Risk Appraisal Guide, Sexual Violent Risk–20, and Structured Risk Assessment) as well as the Psychopathy Checklist–Revised were subjected to taxometric analysis in a sample of 503 sex offending males using the following three procedures: mean above minus below a cut, maximum eigenvalue, and latent mode factor analysis. Results showed consistent support for a dimensional interpretation of the latent structure of sexual violence risk and psychopathic sexuality. The theoretical implications of these findings are discussed with respect to the etiology of sexual violence risk. Clinical implications are discussed with respect to future development of sex offender risk assessment procedures and cutoff scores. Keywords:  taxometric; latent structure; Risk Matrix 2000; Static–99; Sex Offender Risk Appraisal Guide; Sexual Violent Risk–20

T

he most successful approach to predicting future sexual aggression has been the use of empirically derived, mechanical actuarial risk assessment instruments (e.g., Barbaree, Seto, Langton, & Peacock, 2001; Hanson & Morton-Bourgon, 2004). Actuarials developed from this approach have consistently yielded higher hit rates than clinical judgment (Hanson & Bussière, 1996; Hanson & Morton-Bourgon, 2004; Hood, Shute, Feilzer, & Wilcox, 2002), and the Static–99 (Hanson & Thornton, 2000), Rapid Risk Assessment for Sexual Offense Recidivism (RRASOR; Hanson, 1997), Minnesota Sex Offender Screening Tool–Revised (MnSOST-R; Epperson et al., 1998), and Sex Offender Risk Appraisal Guide (SORAG; Quinsey, Rice, & Harris, 1995) are among the most popular sex offender actuarial

AUTHORS’ NOTE: Data for this study were collected under a research grant from the National Institute of Justice (2003WGBX1002). The assertions and opinions contained herein are the private views of the authors and should not be construed as official or as reflecting the views of the Federal Bureau of Prisons or the U.S. Department of Justice. Address all correspondence, including requests for taxometric graphs not included in this article, to Glenn D. Walters, Psychology Services, FCI-Schuylkill, P.O. Box 700, Minersville, PA 17954-0700; e-mail: [email protected]. CRIMINAL JUSTICE AND BEHAVIOR, Vol. 36 No. 3, March 2009 290-306 DOI: 10.1177/0093854808330341 © 2009 International Association for Correctional and Forensic Psychology

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risk measures currently in use (McGrath, Cummings, & Burchard, 2003). The consensus of investigators conducting research on sexual offender actuarial risk measures is that these procedures possess consistent, albeit modest to moderate, efficacy (Sjöstedt & Grann, 2002) in predicting both general and sexual recidivism (e.g., Beech, Fisher, & Thornton, 2003; Craig, Browne, Stringer, & Beech, 2005; Fabian, 2006; Langton et al., 2007). Despite their documented improvement over clinical judgment in predicting recidivism, sex offender actuarial risk measures are not without their limitations. First, risk assessment in general and sex offender actuarial risk measures in particular have been criticized for being atheoretical (Craig, Browne, Beech, & Stringer, 2004; Litwack, 2001). In his presidential address before the American Psychology–Law Society, Ogloff (2000) argued that if psychology is to have a meaningful impact on the law then it must effectively blend psychological theory with empirical findings to explain important causal relationships. Such meaning is currently lacking in sex offender risk assessment. Second, the base rate of sexual recidivism varies according to offense type (child molestation vs. rape), recidivism definition (arrest vs. conviction vs. reincarceration), and length of follow-up. Recidivism rates for 12- to 25-year follow-ups vary widely (14% to 52%), with the highest recidivism rates being recorded by offenders who were committed as sexually dangerous and followed for 25 years (Hanson, 2000; Hanson & MortonBourgon, 2005; Janus & Meehl, 1997; Prentky, Lee, Knight, & Cerce, 1997). Third, the meaningfulness and applicability of items and cutting scores across samples are currently unknown. The SORAG, for instance, was developed on a sample of forensic psychiatric patients and inmates referred for psychological evaluation, whereas the Static–99 and RRASOR were derived from a meta-analysis of four mixed samples of sex offenders, thereby treating child molesters, rapists, and noncontact sex offenders as more alike than different (Fabian, 2006). Finally, most sex offender actuarial risk assessment measures include few, if any, dynamic or changeable items, even though available research indicates that the best dynamic predictors of recidivism (e.g., participating in sex offender treatment while incarcerated or on release) might outperform the best static or unchangeable predictors (e.g., prior convictions for contact sexual offenses) (Brown, 2002; Hanson & Harris, 2000). Actuarial risk assessment procedures have assumed a place of importance in civil commitment proceedings for sexual offenders (Doren, 2002), but concerns have been raised about basing such consequential decisions on these measures. Such procedures rarely account for more than 20% of the variance in sexual recidivism, and they are prone to both false positive and false negative classification errors (Campbell, 2003). Moreover, their ability to exceed the overall hit rates and utility of simply using base rates has been challenged (Knight, 2003). Nevertheless, actuarial risk procedures continue to play an integral role in civil commitment proceedings, and controversies about how different actuarials interface and about what cutoffs should be applied continue to be debated (Knight & Thornton, 2007). Understanding the latent structure of the psychological construct that underpins these procedures, a construct we refer to as sexual violence risk, might help clinicians and administrators make more effective use of these procedures in risk assessment. Meehl’s taxometric method (Meehl, 1995, 2004; Meehl & Yonce, 1994, 1996; Ruscio, Haslam, & Ruscio, 2006; Waller & Meehl, 1998) is one way of investigating the latent structure of psychological constructs such as sexual violence risk and psychopathy. Taxometric research recently conducted on the construct of psychopathy, using the four facet scores of the Psychopathy Checklist–Revised (PCL-R: Hare, 2003) or Psychopathy Checklist: Screening Version (PCL:SV: Hart, Cox, & Hare, 1995) as indicators, has shown that the latent structure of Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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psychopathy is dimensional rather than categorical in nature (Edens, Marcus, Lilienfeld, & Poythress, 2006; Guay, Ruscio, Knight, & Hare, 2007; Walters, Duncan, & Mitchell-Perez, 2007; Walters, Gray, et al., 2007). These studies have corrected most of the methodological errors that plagued earlier research that had mistakenly identified a taxonic latent structure for psychopathy (e.g., G. T. Harris, Rice, & Quinsey, 1994; Skilling, Harris, Rice, & Quinsey, 2002; Skilling, Quinsey, & Craig, 2001; Vasey, Kotov, Frick, & Loney, 2005). Accordingly, there are quantitative rather than qualitative differences between those who score high and those who score low on measures of psychopathy. Although G. T. Harris, Rice, Hilton, Lalumière, and Quinsey (2007) have recently attempted to provide a theoretical model for a psychopathic sexual violence taxon, their supporting taxometric analyses suffer from some of the same methodological limitations found in their earlier work (e.g., see Edens et al., 2006). It is the purpose of this study to examine the latent structure of sexual violence that underlies the most popular of the actuarials currently in use. Lenzenweger (2004) argued that it is essential that researchers who undertake taxometric analysis provide adequate theoretical justification for their search, lest false taxa be generated simply from blind application of taxometrics to samples of convenience. Taxonicity implies both a nonarbitrary latent category and a particular causal structure. The most widely accepted theoretical understanding of taxonicity and the strongest justification for taxometric analysis have focused on hypotheses that particular entities represent the conjunction of a distinct pathology and etiology (Meehl, 1973, 1992). Despite the efforts of G. T. Harris et al. (2007), the justification for the examination of the taxonicity of repeated sexual violence lies not in etiological theory but in the core assumptions about the latent structure of what we call sexual violence risk and in practical concerns about the implementation of particular statistical prediction rules to identify high-risk offenders. Taxometric research could be helpful in laying the groundwork for a working theory of sexual violence risk by establishing whether the latent structure of this construct is taxonic or dimensional. Taxometric analysis of the sexual violence risk construct could also have important practical implications. If, on one hand, sexual violence risk is taxonic, then base rates and cutting scores would be nonarbitrary and it would be possible to locate the taxonic boundary between high- and low-risk sexual offenders. If, on the other hand, violence risk is dimensional, then base rates should vary across samples, and cutting scores would be pragmatic and situational rather than nonarbitrary and fixed. Furthermore, if violence risk is dimensional, this would strengthen the argument that a range of predictors should be included in sexual offender actuarial risk assessment because such measures could provide increased differentiation along the continuum from low to high risk. Based on previous taxometric research on psychopathy, it is hypothesized that sexual violence risk, as measured by popular sex offender actuarial risk measures, will yield dimensional rather than taxonic results on three commonly used taxometric procedures: mean above minus below a cut (MAMBAC), maximum eigenvalue (MAXEIG), and latent mode factor analysis (L-Mode). METHOD PARTICIPANTS

Participants for this study were 503 male sex offenders evaluated at the Massachusetts Treatment Center for Sexually Dangerous Persons (MTC) in Bridgewater, Massachusetts Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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(Knight & Thornton, 2007). These cases were taken from a larger pool of 602 men and were selected because they had been rated on all seven instruments included as indicators in this study. The major reason for exclusion was the poor quality and coverage of earlier historical records. Only those cases with sufficient information for adequate coding were included. In cases where two raters evaluated a participant, the mean rating between the two raters was employed. The average age of participants was 36.42 years (SD = 11.79), and the majority of participants were Caucasian (91.5%). Of these men, 175 (34.8%) could be classified as pure rapists, 211 (41.9%) could be classified as pure child molesters, and 117 (23.3%) were classified as indeterminate or mixed using criteria developed at the MTC (Knight, Carter, & Prentky, 1989; Knight & Prentky, 1990). MEASURES

In a factor analysis (with varimax rotation) of static items from sex offender actuarial risk measures, Knight and Thornton (2007) identified five factors: Criminal Persistence (rate and persistence of prior general criminal behavior), Sexual Persistence (rate and persistence of prior sexual offending), Youth (young age and single), Violent Stranger Assaults, and Male-Victim Choice. Each of the measures included in the present investigation loaded on one or more of these factors. MnSOST-R. The MnSOST-R (Epperson et al., 1998) is a 16-item rating scale composed of 12 historical items and 4 institutional adjustment items designed to assess extrafamilial sexual offending. Each item on the MnSOST-R is weighted by its relation to sexual reoffending in the normative sample. When these items are added together they form a total score with a range of –14 to +30. The static items on this measure load highest on Knight and Thornton’s (2007) Sexual Persistence, Violent Stranger Assaults, and Criminal Persistence factors and the total MnSOST-R score achieved a mean Cohen’s d effect size of .72 in a recent metaanalysis of sexual recidivism studies (Hanson & Morton-Bourgon, 2007). Risk Matrix 2000 (RM2000). The RM2000 (Thornton et al., 2003) was created to assist U.K. police, prison, and probation agencies in screening for sexual offender risk. The RM2000 consists of three scales: a sexual scale (S) designed to predict sexual recidivism, a violent scale (V) designed to predict violent recidivism, and a combined scale (C) designed to predict either sexual or violent recidivism. The C score, which can range from 0 to 6, was employed in the present investigation. The S scale loads heaviest on Knight and Thornton’s (2007) Criminal Persistence, Sexual Persistence, and Youth factors, whereas the V scale loads heaviest on the Criminal Persistence and Youth factors. In the Hanson and Morton-Bourgon (2007) meta-analysis, the S scale achieved a mean d of .82 and the V scale earned a mean d of .98. RRASOR. The RRASOR (Hanson, 1997) was one of the first actuarial measures developed for use in sexual offender risk assessment. Comprising four weighted items that correlated best with sexual recidivism in the original validation sample and loaded highest on Knight and Thornton’s (2007) Sexual Persistence and Male-Victim Choice factors, the RRASOR generates a total score with a range of 0 to 6. The RRASOR has been widely used clinically and achieved a mean d effect size of .59 in the Hanson and Morton-Bourgon (2007) meta-analysis. Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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Static–99. The Static–99 (Hanson & Thornton, 2000), which incorporates nonredundant items from the RRASOR and Thornton’s Structured Actuarial Clinical Judgment–Minimum (Grubin, 1998), is the sexual offender risk assessment instrument most often used in civil commitment hearings in the United States. Scores on the Static–99 range from 0 to 12, with individuals assigned to one of seven risk categories. Individuals with scores equal to or greater than 6 on the Static–99 are identified as high risk. All of the items on the Static–99 are static historical in nature, and the scale loads on Knight and Thornton’s (2007) Sexual Persistence, Criminal Persistence, and Violent Stranger Assaults factors. In the Hanson and Morton-Bourgon (2007) meta-analysis, the Static–99 earned a mean d of .70. Static–2002. The Static–2002 (Hanson & Thornton, 2003) is a research instrument that as of November 2008 had not yet been released for routine clinical use. Designed to increase the conceptual clarity and coherence of the Static–99, the Static–2002 is made up of 13 items that load on Knight and Thornton’s (2007) Sexual Persistence, Criminal Persistence, and Youth factors. The Hanson and Morton-Bourgon (2007) meta-analysis reported a mean d of .78 for the Static–2002. Adult Sex Offender Assessment Protocol (A-SOAP). The A-SOAP (Prentky & Righthand, 2003a) is the adult analogue of the Juvenile Sex Offender Protocol (Prentky & Righthand, 2003b). It comprises 11 static and 10 dynamic items, all of which are rated on a 3-point scale (0, 1, 2). Both the static and dynamic scales of the A-SOAP were used in the present investigation. The Knight and Thornton (2007) factor analysis indicated that the A-SOAP static scale loads mostly on the Sexual Persistence and Criminal Persistence factors and to a lesser extent on the Violent Stranger Assaults factor. The A-SOAP was not included in the Hanson and Morton-Bourgon (2007) meta-analysis. Knight and Thornton were the first to test this actuarial on adults. SORAG. The SORAG (Quinsey et al., 1995) was designed to assess risk for violent recidivism in sexual offenders. Composed of 14 weighted items, 10 of which come directly from the Violence Risk Appraisal Guide (Quinsey, Harris, Rice, & Cormier, 1998), the SORAG generates a total score that can range from –27 to +51. Besides static historical measures, this instrument also includes direct measures of psychopathic personality and sexual interest. In the Knight and Thornton (2007) factor analysis, the SORAG loaded best on the Criminal Persistence factor, and in the Hanson and Morton-Bourgon (2007) metaanalysis the SORAG achieved a mean d of .61. Sexual Violence Risk–20 (SVR-20). The SVR-20 (Boer, Hart, Kropp, & Webster, 1997) provides structured guidelines to assist evaluators in assessing factors deemed by professionals to be relevant to the management of sex offender risk. There are 20 items on the SVR-20, and each item is rated on a 3-point scale (0, 1, 2). SVR-20 items can be grouped into static historical factors, broader clinical traits, and specific risk management factors. The authors of the SVR-20 instruct evaluators to use clinical judgment in assigning offenders to risk categories, technically making it a nonactuarial procedure, although researchers normally sum the item scores to form a total score with a range of 0 to 40. The summed total (actuarial) score was employed in the present investigation. The SVR-20 obtained a mean d of .66 in the Hanson and Morton-Bourgon (2007) meta-analysis and loaded on the Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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Criminal Persistence factor and to a lesser extent on the Violent Stranger Assaults factor in the Knight and Thornton (2007) factor analysis. Structured Risk Assessment (SRA). The SRA (Thornton, 2002) adopts a multistep framework designed to assist evaluators in assessing sexual offenders. The second step organizes psychological factors associated with repeated sexual offending into four domains: sexual interests (sexual preoccupation combined with offense-related sexual interests), distorted attitudes (general beliefs that make it easier for offenders to offend), socioaffective functioning (insecure attachment styles), and self-management (lifestyle impulsiveness and poor coping skills). The three SRA indicators considered for inclusion in the present study were those that could be adequately rated with the information available in the archival records: sexual interests, socioaffective functioning, and self-management. The SRA earned a mean d effect size of .79 in the Hanson and Morton-Bourgon (2007) meta-analysis. PCL-R. The PCL-R (Hare, 2003) is a 20-item rating measure designed to assess psychopathy rather than predict sexual aggression risk. Nevertheless, it figured prominently in the previously reviewed G. T. Harris et al. (2007) taxometric study and is considered along with several coercive-precocious sexuality items. Each PCL-R item is rated on a 3-point scale (0 = does not apply, 1 = may apply or in some respects applies, 2 = does apply), which when added together yield a total score with a range of 0 to 40. Research has shown that the PCL-R possesses good reliability and validity (Hare, 2003). Five student research assistants provided ratings for this study, and in some cases two coders independently rated the same participant. It should be noted that these dually coded cases were assigned randomly. Using the single measures intraclass correlation coefficient (ICC) as an estimate of interrater reliability and the two coders with the largest number of overlapping ratings for that measure as raters, moderate agreement was obtained for the PCL-R total score (ICC = .79, n = 90), Factor 1 score (ICC = .66, n = 90), and Factor 2 score (ICC = .68, n = 91). Interrater reliability estimates for the other measures included as indicators in this study, along with the number of coder pairings on which the estimate was based, are listed in Table 1. PROCEDURE

After determining which of the 12 actuarial measures to include as indicators in this study, we subjected the data to taxometric analysis using Ruscio’s (2008) taxometric program in the statistical language R. The three taxometric procedures employed in this study were MAMBAC (Meehl & Yonce, 1994), MAXEIG (Waller & Meehl, 1998), and L-Mode (Waller & Meehl, 1998). Operating from the premise that there should be an optimal cutting score or taxonic boundary that separates the taxon and complement groups in the case of a categorical construct, summed input MAMBAC makes a series of cuts along the axis of an input indicator composed of all variables except the output indicator. Fifty cuts were made along the axis of the summed input indicator, and comparisons were made between the mean scores for the single output indicator above and below each cut. Taxonic constructs frequently display a peak on the MAMBAC curve, denoting that scores above and below the cut are more divergent than surrounding cuts and identifying a discontinuity in the distribution. Dimensional constructs often peak at the upper and lower tails of the curve where Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

296   Criminal Justice and Behavior TABLE 1:   Descriptive Statistics and Validity Estimates for the Six Actuarial Risk Indicators

Validity

Variable

Range

M

SD

Skewa

(d)b

ICC

n

1. MnSOST-R 2. RM2000 3. Static–99 4. SORAG 5. SVR-20 6. SRA self

–11–18 0–6 0–10 –21–43 2–35 0–6

4.39 2.83 4.55 8.75 14.30 2.91

5.93 1.48 2.13 12.50 1.50 1.50

–0.11 –0.03 –0.14 0.09 0.32 0.29

1.50 1.41 2.11 1.82 1.61 1.37

.86 .85 .88 .89 .63 .68

70 68 47 45 52 87

Note. MnSOST-R = Minnesota Sex Offender Screening Tool–Revised; RM2000 = Risk Matrix 2000 combined scale; SORAG = Sex Offender Risk Appraisal Guide (SORAG); SVR-20 = Sexual Violence Risk–20; SRA self = Structured Risk Assessment self-management domain; range = range of lowest to highest scores; ICC = intraclass correlation coefficient (single measures); n = number of cases on which ICC is based. a. The standard error of measurement for skew was .11. b. Cohen’s d estimated with a summed sex offender actuarial risk score > 1.45 (base rate = 46.1%) representing the taxon group.

the most extreme scores can be found on the normal curve, giving the curve a concave or dish-shaped appearance (Meehl & Yonce, 1994). The MAMBAC procedure was computed with 10 replications designed to stabilize the curves. MAXEIG (Waller & Meehl, 1998) is a multivariate extension of Meehl and Yonce’s (1996) maximum covariance (MAXCOV) procedure. The purpose of both MAXCOV and MAXEIG is to assess the association between two or more output indicators at different levels of an input indicator. If the construct is taxonic then the MAXCOV or MAXEIG curve will peak in the subsample containing a roughly equal number of taxon and complement members. With higher base rate taxa the curve tends to peak to the left of center, whereas with lower base rate taxa just the opposite occurs—the curve tends to peak to the right of center. It should be noted, however, that indicator skew can influence where a curve peaks (Ruscio et al., 2006). Dimensional constructs, by comparison, display flat or nonpeaked curves because indicators remain relatively constant across subsamples in a dimensional construct. The principal difference between MAXCOV and MAXEIG is that MAXCOV computes the covariance between two output indicators, whereas MAXEIG estimates the relationship among indicators in the first eigenvalue of the indicator covariance matrix (Waller & Meehl, 1998). Traditional MAXEIG with conditional eigenvalues of five indicators forming the output and the remaining indicator forming the input were calculated in the present study. MAXEIG was calculated with 50 overlapping windows in which each window overlapped 90% with its neighbors. Ten replications were calculated with each procedure to minimize the obfuscating effect of tied scores and the standard base rate procedure was used to classify cases. Simulated taxonic and dimensional curves were created for MAMBAC and MAXEIG with a bootstrapping technique (B = 20 for each structure) that takes into account the unique distributional and correlational properties of the research data (Ruscio, Ruscio, & Meron, 2007). The degree of fit between the averaged data curve and each of the two simulated models was then evaluated by means of the comparison curve fit index (CCFI). The CCFI is the ratio of the root mean square residual (RMSR) of fit between the averaged curve and simulated dimensional curve to the sum of the RMSR of fit between the averaged curve and simulated dimensional curve and the RMSR of fit between the averaged curve Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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and simulated taxonic curve: CCFI = FitRMSR-dim / (FitRMSR-dim + FitRMSR-taxon). A CCFI of .50 denotes equally good (or poor) fit between the data and the simulated taxonic and dimensional curves. The farther the CCFI falls below .50 (to a minimum of .00), the greater the support for dimensional structure. The farther the CCFI rises above .50 (to a maximum of 1.00), the greater the support for taxonic structure. Several Monte Carlo studies attest to the utility of the CCFI as a measure of relative fit (Ruscio, 2007; Ruscio & Marcus, 2007; Ruscio et al., 2007). L-Mode (Waller & Meehl, 1998) is the third taxometric procedure employed in this study. L-Mode calculates the first (and largest) principal factor of the indicators, in this case the six actuarial risk measures included in this study, and plots the distribution of participants’ scores on this single latent factor. Taxonic constructs generally split into two groups, giving the factor curve a bimodal appearance. Dimensional constructs, by contrast, generally form a single group and give rise to a factor curve with a unimodal appearance, although taxa have been known to form unimodal patterns and dimensional constructs can sometimes give rise to bimodal results (Waller & Meehl, 1998). The RMSR values used to calculate the CCFI for L-Mode were computed by measuring the smallest Euclidean distance between each point on the data plot to corresponding points on the taxonic and dimensional comparison curves. Relative fit was quantified by inserting the taxonic and dimensional RMSR values into the CCFI equation. Because calculating a taxon base rate with L-Mode can be problematic, Ruscio and Walters (2008) recommend selecting a meaningful range of taxon base rate estimates, inputting these values directly into L-Mode, and taking the average CCFI value as an indicator of latent structure. This approach to L-Mode was found to produce impressive results in a recent Monte Carlo study (Ruscio & Walters, 2008). RESULTS PRETAXOMETRIC ANALYSES

The 12 available sex offender actuarial indicators (MnSOST-R, RM2000, RRASOR, Static–99, Static–2002, A-SOAP static, A-SOAP dynamic, SORAG, SVR-20, SRA sexualization, SRA socioaffective, SRA self-management) were converted to normal scores (M = 0, SD = 1) and summed. Indicator validity was measured with Cohen’s d, using the mean taxon base rate (46.1%) obtained when traditional cut scores for moderately high risk were applied to several of the actuarial scales (range = 35.4% to 54.3%) to divide the group into putative taxon and complement members. Weak indicator validity (d < 1.25) was recorded for the A-SOAP static, A-SOAP dynamic, SRA sexualization, and SRA socioaffective indicators, thereby resulting in their elimination from the analyses. Two additional indicators, RRASOR and Static–2002, were dropped from the analyses because they overlapped extensively with the most popular and heavily researched sex offender actuarial risk scale (i.e., Static–99). This left six indicators for taxometric analysis (MnSOST-R, RM2000, Static–99, SORAG, SVR-20, and SRA self-management). The means, standard deviations, skew, indicator validity, and interrater reliability estimates for each of the six indicators employed in the main taxometric analyses are listed in Table 1. Indicator validity was above the threshold (Cohen’s d = 1.25) recommended by Meehl (1995) for effectively distinguishing between the putative taxon and complement groups in all six individual indicators, the mean of the six indicators (d = 1.60), the Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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Figure 1:    Average Mean Above Minus Below a Cut Note. Summed input data curve for the six actuarial risk indicators (darker line) in comparison to simulated taxonic and dimensional data (lighter lines represent one standard deviation above and below the mean).

MAMBAC analysis (d = 1.83), the MAXEIG analysis (d = 1.84), and the L-Mode analysis (d = 1.78). Nuisance covariance in the complement was slightly elevated above the level recommended by Meehl for optimal implementation of the taxometric method (i.e., .30) but was still well below the mean full-scale correlation (full-sample r = .60, taxon within-group r = .28, complement within-group r = .40). In addition, the mean within-group correlations for both the putative taxon and complement were below .30 at the higher base rate levels (.53 to .56) identified in the MAMBAC and MAXEIG analyses. MAMBAC

Summed input MAMBAC for six variables produces six curves in which each variable serves once as an output indicator and the five remaining variables serve as a composite input indicator. A mean base rate of .53 (SD = .07) was found for the six summed input MAMBAC curves and the mean MAMBAC curve produced a CCFI of .404, consistent with dimensional structure. The mean MAMBAC data curve and simulated taxonic and dimensional curves are reproduced in Figure 1. A review of the six individual MAMBAC data curves revealed that the left end, the right end, or both ends of each distribution were elevated above all other points on the curve, as one would expect of a dimensional construct. MAXEIG

In the traditional MAXEIG procedure each variable serves once as the input indicator and the conditional eigenvalue of the remaining variables serves as the output indicator. The average base rate across the six MAXEIG/HITMAX curves was .56 (SD = .07). MAXEIG Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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Figure 2:   Average Maximum Eigenvalue Note. Traditional data curve for the six actuarial risk indicators (darker line) in comparison to simulated taxonic and dimensional data (lighter lines represent one standard deviation above and below the mean).

yielded a CCFI of .379, which is more consistent with dimensional latent structure than it is with taxonic latent structure (see Figure 2). A review of the six individual MAXEIG curves failed to show signs of a taxonic peak on any of the curves. L-MODE

L-Mode was calculated four times using taxon base rates identified in the previously reported MAMBAC and MAXEIG analyses (.53 to .56 in .01 increments). Like the relative fit findings for MAMBAC and MAXEIG, this procedure produced results more consistent with dimensional latent structure than with taxonic latent structure (CCFI range = .289 to .369, M = .334). A visual comparison of the L-Mode data curve as it matches up against the taxonic and dimensional comparison curves is furnished in Figure 3. SEXUAL ACTUARIAL FACTOR SCORES

Participant scores on the five factors identified in Knight and Thornton’s (2007) factor analysis of static items on sex offender actuarial risk measures (Criminal Persistence, Sexual Persistence, Youth, Violent Stranger Assaults, Male-Victim Choice) were also included as indicators in a series of taxometric analyses (N = 458). Application of these homogeneously grouped indicators did not substantially alter the results or conclusions of the taxometric analyses performed on the six sexual actuarial risk measures. Specifically, MAMBAC (CCFI = .349), MAXEIG (CCFI = .472), and L-Mode (CCFI range = .393 to .508, M = .454) were all more consistent with dimensional latent structure than with taxonic latent structure.

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Figure 3:   Latent Mode Factor Analysis Note. Data curve (p = .54) for the six actuarial risk indicators (darker line) in comparison to simulated taxonic and dimensional data (lighter lines represent one standard deviation above and below the mean).

PCL-R AND COERCIVE-PRECOCIOUS SEXUALITY ITEMS

Four dichotomized coercive-precocious sexuality items, similar to the items included in the G. T. Harris et al. (2007) study, were combined to form a single coercive-precocious sexuality variable (prior sexual victimization, sexual promiscuity, force someone into sex before age 15, one or more juvenile serious sexual offenses). The 5-point (0 to 4) coerciveprecocious sexuality scale and two PCL-R factor scores (old Factor 1 and old Factor 2) served as indicators in a taxometric analysis of psychopathic sexuality (N = 503). Similar to the results obtained with the actuarial risk measures, psychopathic sexuality, as measured by coercive-precocious sexuality and the two old factors of the PCL-R, produced dimensional results in MAMBAC (CCFI = .307), MAXEIG (CCFI = .419), and L-Mode (CCFI range = .278 to .372, M = .310). DISCUSSION

Consistent with previous taxometric research conducted on PCL-defined psychopathy (Edens et al., 2006; Guay et al., 2007; Walters, Duncan, et al., 2007; Walters, Gray, et al., 2007) and inconsistent with G. T. Harris et al.’s (2007) recent PCL-R study on psychopathic sexuality, the results of the present investigation indicate that the latent structure of sexual violence risk, as defined by six popular actuarial risk measures (MnSOST-R, RM-2000, Static–99, SORAG, SVR-20, and SRA self-management), five orthogonal factors of static items, and psychopathic sexuality (PCL-R old Factor 1 and 2 scales and coercive-precocious sexuality), is continuous (dimensional) rather than categorical (taxonic) in nature. In other words, sexual violence risk in persons referred for evaluation at a sex offender clinic is a quantitative rather than qualitative distinction or a difference of degree rather than a difference

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in kind. When one is interpreting the results of this study, it is important to keep in mind that taxometric results are evaluated using a consistency testing approach instead of the more commonly employed significance testing approach. Hence, results obtained from 503 men evaluated at the MTC for sexual offenders were consistent in showing greater concordance between the data and a dimensional model than between the data and a taxonic model across three reasonably independent and nonredundant taxometric procedures (MAMBAC, MAXEIG, L-Mode) using an objective estimate of relative fit (CCFI). The taxometric method was developed by Meehl (1995, 2004) to test the latent structure of theoretical constructs. Using taxometrics without a clear theoretical model in mind has consequently been discouraged (Lenzenweger, 2004). The atheoretical nature of sex offender actuarial risk measures would seem to make them a poor choice for taxometrics. Meehl (1995, 1999, 2004) nonetheless acknowledged that although he originally conceived of the taxometric method as a deductive, confirmatory procedure, there is nothing mathematically or conceptually inconsistent with using taxometrics as an inductive, exploratory tool: “I do not, however, oppose exploratory taxometrics that is not theory driven” (Meehl, 2004, p. 42). Moreover, as we argued in the introduction, the taxonic assumptions of G. T. Harris et al. (2007) in their conceptualization of psychopathic sexuality and the practical implications on decision rules of the latent structure of actuarials provide sufficient reason to conduct a taxometric analysis of popular actuarial risk measures. Although most sex offender actuarial risk measures were not generated with a particular theory in mind, this does not mean that some theoretical model might not account for them. At the outset of this study we predicted, based on current taxometric research on psychopathy, that sexual violence risk would have a dimensional latent structure. Now that this dimensional structure has been corroborated, we can begin to speculate about the nature of sexual violence risk. Although the results of a taxometric analysis cannot offer a full accounting of how a model of sexual violence risk should look, they can furnish vital clues on some of its features. The strongest implication of taxonicity is that a specific etiology might underlie the construct examined (Meehl, 1973, 1992). Consequently, the rejection of taxonicity strengthens the viability of the contrary hypothesis of a complex etiology and the presence of many different and additive causative variables. The present findings also have important implications for clinical practice, especially assessment. Although taxonic constructs require items that effectively discriminate between the taxon and complement, dimensional constructs require clinical measures that assess a construct along the entire length of the dimension (Ruscio et al., 2006). Consequently, measures of dimensional constructs frequently contain more items and more items with varied content than measures of taxonic constructs. A brief measure such as the RRASOR or Static–99 might suffice if sexual violence risk were taxonic, but a dimensional construct would be better served by a more complex and nuanced measure. Moreover, the measure should aim at equal discrimination across the entire range of the measure rather than focusing on items that maximally discriminate between high and low sexual violence risk. Including both static and dynamic risk items in one’s assessment would also seem advisable, although there is nothing in the structural results of this study that bears directly on the issue of static versus dynamic risk items. The future of sex offender actuarial risk assessment, it would seem, rests on our ability to make theoretical sense of the variables that have been found to predict sexual recidivism and develop an assessment tool that adequately reflects this theoretical model. The current study was an initial attempt to provide the structure for such a model. Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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Another measurement implication of the dimensionality of sexual violence is that there is no set taxonic boundary between groups, and so any cutting score employed will be arbitrary, although not necessarily capricious or whimsical. Cutting scores can be used with dimensional constructs to maximize predictability and minimize false positive and false negative predictions. Nevertheless, cutoff scores on a dimensional construct are pragmatic rather than intrinsically fixed and can be adjusted depending on the question being asked, the population being studied, or the context under which the evaluation is being conducted. Eventually, it may be necessary to replace cutting scores with sliding confidence intervals. The dimensional results obtained in the present study and their implications for the cutting scores that clinicians use to appraise sexual violence risk would appear to be particularly pertinent to civil commitment practices, policies, and procedures. If the current preliminary findings are crossvalidated in other samples and populations, then we will need to ensure that the threshold for civil commitment is drawn in such a way as to maximize the cost-effective use of this form of preventive detention, balancing the perceived gains (e.g., avoidance of further offending, providing services to high-need offenders) with the perceived costs (e.g., inappropriate and unnecessary loss of liberty for some offenders, financial cost to the taxpayer). The principal limitation of this study is that it was conducted on a group of mostly White male sex offenders who had been referred for evaluation for possible civil commitment as sexually dangerous. A logical question at this juncture is whether the present findings generalize to lower risk sex offenders, non-White sex offenders, and female sex offenders. In addition, the present study took place in the United States. We therefore need to know whether these findings generalize to other parts of the globe where sex offending is also a problem. One aspect of generalizability that was not limited in this study was the range of actuarial measures included in the analyses. Not only were three of the four most clinically popular sex offender risk measures (MnSOST-R, Static–99, SVR-20; McGrath et al., 2003) and three of the five most heavily researched sexual risk measures (MnSOST-R, Static–99, SORAG; Barbaree et al., 2001) included in this study, but dynamic risk factors were reasonably well represented as well (MnSOST-R, SVR-20, SRA). Taxometric research using more varied populations of sex offenders is therefore indicated and, in fact, required before definitive conclusions can be reached on the latent structure of the sexual violence risk construct. It could be argued that the present sample contained too few low-risk participants to allow a proper taxometric analysis of the sexual violence risk construct. A disproportionate number of high-risk individuals could have swamped the much smaller complement and prevented the two-group pattern associated with a taxon from surfacing. Hence, there may have been a qualitative distinction between high and low sexual violence risk participants but just too few low-risk individuals to provide evidence of a taxon. The problem with this argument is that only about half of the 503 participants were putative taxon members, using either the mean taxon base rate attained by such popular actuarial measures as the Static–99, SORAG, and MnSOST-R (46.1%) or the taxon base rate estimates from the MAMBAC (53%) and MAXEIG (56%) analyses, thus leaving a complement of sufficient size to perform a taxometric analysis. An even higher taxon base rate of alcohol use disorders was observed in a recent study conducted on male prisoners applying for inpatient drug treatment, and yet the results showed undeniable evidence of a taxon using the same taxometric procedures as those employed in the present investigation (Walters, 2008). The lay public holds many views toward sex offenders, not all of which are valid. Many in the lay public, for instance, perceive most, if not all, sex offenders as being at high risk Downloaded from http://cjb.sagepub.com at BRANDEIS UNIV LIBRARY on February 25, 2009

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for recidivism (Hanson, Morton, & Harris, 2003), a view challenged by experts in the field who point to recidivism studies showing widely divergent outcomes for sexual offenders classified into groups on the basis of static and dynamic risk factors. Results from the present study confirm this heterogeneity of outcomes but suggest that it might better be represented by a quantitatively ordered dimension rather than by qualitatively distinct categories. The lay public also appears to view sex offenders as distinct from other groups of offenders, but most offenders—sex offenders and non–sex offenders alike—are criminally versatile and prone to committing both sexual and nonsexual crimes (Hanson & MortonBourgon, 2005; D. A. Harris, Smallbone, Dennison, & Knight, 2007; Simon, 1997). The results of the present study indicate that risk for sexual offenders, like risk among generic criminals, is distributed as a dimension. Clear evidence of dimensionality in risk for sexual aggression should not be generalized to conclude that there are no taxa among sexual offenders. Although Knight and Guay (2006) have argued for a dimensional model of rapists, there are notable differences between rapists and child molesters (e.g., Bard et al., 1987; Blanchard et al., 2003; Bogaert, 2001; Cantor, Blanchard, Robichaud, & Christensen, 2005; Cantor et al., 2007). Therefore, different latent structures might characterize each group. Unfortunately, there were too few pure child molesters and rapists in the present sample to conduct separate taxometric analyses on each group. Sexual violence risk was introduced in this study as the concept underpinning popular sex offender actuarial risk measures; additional research will be required to determine whether this construct is meaningful and whether it is dimensional across various populations, contextual considerations, and referral questions. REFERENCES Barbaree, H. E., Seto, M. C., Langton, C. M., & Peacock, E. J. (2001). Evaluating the predictive accuracy of six risk assessment instruments for adult sex offenders. Criminal Justice and Behavior, 28, 490-521. Bard, L. A., Carter, D. L., Cerce, D. D., Knight, R. A., Rosenberg, R., & Schneider, B. (1987). A descriptive study of rapists and child molesters: Developmental, clinical, and criminal characteristics. Behavioral Sciences and the Law, 5, 203220. Beech, A. R., Fisher, D., & Thornton, D. (2003). Risk assessment of sex offenders. Professional Psychology: Research and Practice, 34, 339-352. Blanchard, R., Kuban, M. E., Klassen, P., Dickey, R., Christensen, B. K., Cantor, J. M., et al. (2003). Self-reported head injuries before and after age 13 in pedophilic and nonpedophilic men referred for clinical assessment. Archives of Sexual Behavior, 32, 573-581. Boer, D. P., Hart, S. D., Kropp, R. P., & Webster, C. D. (1997). Manual for the Sexual Violence Risk–20. Vancouver, Canada: British Columbia Institute Against Family Violence. Bogaert, A. F. (2001). Handedness, criminality, and sexual offending. Neuropsychologia, 39, 465-469. Brown, S. L. (2002). The dynamic prediction of criminal recidivism: A three wave prospective study. Forum on Corrections Research, 14(1), 24-27. Campbell, T. W. (2003). Sex offenders and actuarial risk assessment: Ethical considerations. Behavioral Sciences and the Law, 21, 269-279. Cantor, J. M., Blanchard, R., Robichaud, L. K., & Christensen, B. K. (2005). Quantitative reanalysis of aggregate data on IQ in sexual offenders. Psychological Bulletin, 131, 555-568. Cantor, J. M., Kuban, M. E., Blak, T., Klassen, P. E., Dickey, R., & Blanchard, R. (2007). Physical height in pedophilic and hebephilic sexual offenders. Sexual Abuse: A Journal of Research and Treatment, 19, 395-407. Craig, L. A., Browne, K. D., Beech, A. R., & Stringer, I. (2004). Personality characteristics associated with reconviction in sexual and violent offenders. Journal of Forensic Psychiatry and Psychology, 15, 532-551. Craig, L. A., Browne, K. D., Stringer, I., & Beech, A. (2005). Sexual recidivism: A review of static, dynamic and actuarial predictors. Journal of Sexual Aggression, 1, 63-82.

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306   Criminal Justice and Behavior Thornton, D., Mann, R., Webster, S., Blud, L., Travers, R., Friendship, C., et al. (2003). Distinguishing and combining risks for sexual and violent recidivism. In R. Prentky, E. Janus, M. Seto, & A. W. Burgess (Eds.), Annals of the New York Academy of Sciences: Vol. 989. Sexually coercive behavior: Understanding and management (pp. 225-235). New York: New York Academy of Sciences. Vasey, M. W., Kotov, R., Frick, P. J., & Loney, B. R. (2005). The latent structure of psychopathy in youth: A taxometric investigation. Journal of Abnormal Child Psychology, 33, 411-429. Waller, N. G., & Meehl, P. E. (1998). Multivariate taxometric procedures: Distinguishing types from continua. Thousand Oaks, CA: Sage. Walters, G. D. (2008). The latent structure of alcohol use disorders: A taxometric analysis of structured interview data obtained from male federal prisoners. Alcohol and Alcoholism, 43, 326-333. Walters, G. D., Duncan, S. A., & Mitchell-Perez, K. (2007). The latent structure of psychopathy: A taxometric investigation of the Psychopathy Checklist–Revised in a heterogeneous sample of male prison inmates. Assessment, 14, 270-278. Walters, G. D., Gray, N. S., Jackson, R. L., Sewell, K. W., Rogers, R., Taylor, J., et al. (2007). A taxometric analysis of the Psychopathy Checklist: Screening Version (PCL:SV): Further evidence of dimensionality. Psychological Assessment, 19, 330-339.

Glenn D. Walters serves as drug program coordinator at the Federal Correctional Institution, Schuylkill, Pennsylvania. His research interests fall into three primary domains: the genetic correlates of crime, substance abuse, and problem gambling; psychological assessment of offenders, with an emphasis on criminal thinking and psychopathy; and the development of an overarching theory of criminal behavior. He has published more than 200 articles and book chapters and is the author of 14 books, including The Criminal Lifestyle (1990), Criminal Belief Systems (2002), and Lifestyle Theory: Past, Present, and Future (2006). Raymond A. Knight is the Mortimer Gryzmish Professor of Human Relations at Brandeis University. He has developed and validated both taxonomic and etiological models for rapists and child molesters and has completed a 25-year follow-up of sex offenders released from the Massachusetts Treatment Center. He is validating the Multidimensional Inventory of Development, Sex, and Aggression (the MIDSA), which is a computerized contingency-based inventory that provides a comprehensive assessment of multiple critical areas of adaptation for juvenile and adult sexual offenders. David Thornton is treatment director for Wisconsin’s sexually violent predator treatment program. He has been involved in the development of a number of risk assessment instruments, including the Static–99 and Static–2002. His current research interests include analysis of information from ratings made by psychologists applying the structured assessment of risk and need model to sexual offenders and testing the long-term predictive value of modern risk assessment instruments.

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