Development and Validation of a Stages of Change Measure for Men in Batterer Treatment

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Cognitive Therapy and Research, Vol. 24, No. 2, 2000, pp. 175-199 Development and Validation of a Stages of Change Measure for Men in Batterer Treatment Deborah A. Levesque, 1 Richard J. Gelles, 2 and Wayne F. Velicer 3 The Transtheoretical Model of Change offers a promising stage-based approach to client–treatment matching to increase the efficacy of batterer treatment. This paper describes the development and validation of the URICA–Domestic Violence (URICA-DV), a four-dimensional stage measure assessing batterers’ readiness to end their violence. Two hundred fifty-eight batterers in treatment at two Rhode Island agencies completed a questionnaire that included the URICA-DV, demographics, and measures expected to vary systematically with stage in a manner predicted by the Transtheoretical Model. A cross-validated cluster analysis yielded seven stage clusters based on URICA-DV scores: Reluctant, Immotive, Nonreflective Action, Unprepared Action, Preparticipation, Decision-making, and Participation. Findings provide preliminary evidence of validity of the URICA-DV. For example, participants in the most advanced stage clusters were most likely to have used strategies to end the violence in the last year. They engaged in less partner blame and valued the Pros and minimized the Cons of changing more than counterparts in the earlier stage clusters. Longitudinal research to assess the predictive validity of the URICA-DV is necessary. KEY WORDS: male batterers; stages of change; transtheoretical model. Court-ordered batterer treatment continues to emerge as one of society’s inter- ventions of choice for men who assault their wives and partners, despite ongoing questions about its efficacy (National Research Council & Institute of Medicine, 1998). Although one narrative review of the outcome research concludes that bat- terer treatment reduces recidivism (Saunders & Azar, 1989) and one reports ‘‘cau- tious optimism’’ (Feldman & Ridley, 1995), others withhold judgment, citing small treatment effects (Rosenfeld, 1992; Tolman & Bennett, 1990), methodological flaws 1 Correspondences concerning this article should be sent to Deborah Levesque, Ph.D., Pro-Change Behavior Systems, Inc., P.O. Box 756, West Kingston, Rhode Island 02892; E-mail: [email protected] 2 Formerly of the Department of Sociology and Anthropology, University of Rhode Island, 2 Chafee Road, Kingston, Rhode Island; currently affiliated with the School of Social Work, University of Pennsylvania, Philadelphia, Pennsylvania. 3 Cancer Prevention Research Center, University of Rhode Island, 2 Chafee Road, Kingston, Rhode Island 02881. 175 0147-5916/00/0400-0175$18.00/0 2000 Plenum Publishing Corporation

Transcript of Development and Validation of a Stages of Change Measure for Men in Batterer Treatment

Cognitive Therapy and Research, Vol. 24, No. 2, 2000, pp. 175-199

Development and Validation of a Stages of ChangeMeasure for Men in Batterer Treatment

Deborah A. Levesque,1 Richard J. Gelles,2 and Wayne F. Velicer3

The Transtheoretical Model of Change offers a promising stage-based approach toclient–treatment matching to increase the efficacy of batterer treatment. This paperdescribes the development and validation of the URICA–Domestic Violence(URICA-DV), a four-dimensional stage measure assessing batterers’ readiness toend their violence. Two hundred fifty-eight batterers in treatment at two Rhode Islandagencies completed a questionnaire that included the URICA-DV, demographics,and measures expected to vary systematically with stage in a manner predicted bythe Transtheoretical Model. A cross-validated cluster analysis yielded seven stageclusters based on URICA-DV scores: Reluctant, Immotive, Nonreflective Action,Unprepared Action, Preparticipation, Decision-making, and Participation. Findingsprovide preliminary evidence of validity of the URICA-DV. For example, participantsin the most advanced stage clusters were most likely to have used strategies to endthe violence in the last year. They engaged in less partner blame and valued the Prosand minimized the Cons of changing more than counterparts in the earlier stageclusters. Longitudinal research to assess the predictive validity of the URICA-DVis necessary.

KEY WORDS: male batterers; stages of change; transtheoretical model.

Court-ordered batterer treatment continues to emerge as one of society’s inter-ventions of choice for men who assault their wives and partners, despite ongoingquestions about its efficacy (National Research Council & Institute of Medicine,1998). Although one narrative review of the outcome research concludes that bat-terer treatment reduces recidivism (Saunders & Azar, 1989) and one reports ‘‘cau-tious optimism’’ (Feldman & Ridley, 1995), others withhold judgment, citing smalltreatment effects (Rosenfeld, 1992; Tolman & Bennett, 1990), methodological flaws

1Correspondences concerning this article should be sent to Deborah Levesque, Ph.D., Pro-ChangeBehavior Systems, Inc., P.O. Box 756, West Kingston, Rhode Island 02892; E-mail: [email protected]

2Formerly of the Department of Sociology and Anthropology, University of Rhode Island, 2 ChafeeRoad, Kingston, Rhode Island; currently affiliated with the School of Social Work, University ofPennsylvania, Philadelphia, Pennsylvania.

3Cancer Prevention Research Center, University of Rhode Island, 2 Chafee Road, Kingston, RhodeIsland 02881.

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0147-5916/00/0400-0175$18.00/0 2000 Plenum Publishing Corporation

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in research designs (Eisikovits & Edleson, 1989; Hamberger & Hastings, 1993), andunexplained discrepancies in results (Tolman & Edleson, 1995). A meta-analyticreview of published and unpublished outcome research found no overall effect forbatterer treatment across seven studies relying on partner reports of recidivism(Cohen’s h � .06, ns), and a fairly small effect across 11 studies relying on policereports and court records (Cohen’s h � .19, p � 0.01) (Levesque, 1998). The overallimpact of treatment on the problem of male-to-female violence is further diluted,as a significant portion of the target group does not complete treatment. In anationwide survey of batterer treatment programs, Pirog-Good and Stets (1986)found that estimates of program attrition averaged 40% across programs. A similarrate of 36% was found across studies in a meta-analysis of 21 treatment outcomestudies reporting on treatment dropout (Levesque, 1998).

In recent years, the field has displayed a growing interest in client–treatmentmatching to increase the impact of interventions for battering men (e.g., Healey,Smith, & O’Sullivan, 1998; Holzworth-Munroe & Stuart, 1994). Treatment tendsto be highly structured, psychoeducational, and ‘‘one-size-fits-all,’’ neglecting indi-vidual differences that might influence treatment effectiveness and participationrates. Efforts are underway to identify subtypes of batterers who might benefit fromalternative interventions or therapeutic approaches. In a review of the literature onbatterer typologies, Holtzworth-Munroe and Stuart (1994) found that researcherstend to classify batterers along three dimensions—severity of marital violence,generality of the violence, and psychopathology—and proposed that a typologicalsystem based on the three dimensions would identify three subtypes of batterers:Family Only, Dysphoric/Borderline, and Generally Violent/Antisocial.

No doubt, the classification of batterers using one or more descriptive dimen-sions produces groups of men who look different from each other. The real question,however, is whether these typological systems have clear, empirically based implica-tions for treatment and criminal justice intervention. In a comparison of feministcognitive–behavioral and psychodynamic group treatment for batterers, Saunders(1996) found no main effect for therapeutic approach, but found an interactionbetween personality traits and approach. Clients with dependent personality wereless likely to reoffend following psychodynamic group treatment, and those withantisocial personality were less likely to reoffend following feminist cognitive–behavioral treatment. The interaction accounted for less than 5% of the variancein recidivism rates, however.

THE TRANSTHEORETICAL MODEL OF CHANGE

The Transtheoretical Model of Change offers an alternative approach to client–treatment matching. Since early 1980s, the model has been shown to be remarkablyrobust in its ability to explain individual change across a variety of addictions andother maladaptive behaviors that, like partner violence, are considered to be majorpublic health problems (e.g., DiClemente & Hughes, 1990; Prochaska & DiClem-ente, 1983; Prochaska, Norcross, Fowler, Follick, & Abrams, 1992; Prochaska, Redd-ing, Harlow, Rossi, & Velicer, 1994). The Transtheoretical Model systematically

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integrates a number of theoretical constructs central to change: stages of change,decisional balance (Janis & Mann, 1977), self-efficacy (Bandura, 1977), and pro-cesses of change. A large body of empirical data supports the validity of the model’stheoretical constructs and the hypothesized relationships between them. Expertsin the field of domestic violence have already begun to anticipate the model’susefulness in the evaluation and treatment of battering men (Begun, Strodhoff,Weinstein, Shelley, & Short, 1997; Daniels & Murphy, 1997; Dutton, 1995; Dutton,Bodnarchuk, Kropp, Hart, Ogloff, 1997; Levesque, Gelles, & Velicer, 1997; Mur-phy & Baxter, 1997).

Briefly, the Transtheoretical Model understands change as progress, over time,through a series of stages: Precontemplation, Contemplation, Preparation, Action,and Maintenance. Nearly 20 years of research on a variety of health behaviors hasidentified interventions that work best in each stage to facilitate change and minimizeresistance. This research can serve as a foundation on which to build stage-matchedinterventions for battering men.

Stages of Change

Stages of change is the Transtheoretical Model’s central organizing construct.Longitudinal studies of change have found that people move through a series offive stages when modifying behavior on their own or with the help of formalintervention (DiClemente & Prochaska, 1982; Prochaska & DiClemente, 1983). Inthe first stage of change, the precontemplation stage, individuals deny they have aproblem and thus are resistant to change, are unaware of the negative consequencesof their behavior, believe the consequences are insignificant, or have given up thethought of changing because they are demoralized. They are not thinking aboutchanging in the next 6 months. Individuals in the contemplation stage are morelikely to recognize the benefits of changing. However, they continue to overestimatethe costs of changing and, therefore, are ambivalent and not quite ready to change.They are seriously considering making a change within the next 6 months. Individu-als in the preparation stage have decided to make a change in the next 30 days andhave already begun to take small steps toward that goal. Individuals in the actionstage are overtly engaged in modifying their problem behaviors or acquiring new,healthy behaviors. Individuals in the maintenance stage have been able to sustainchange for at least 6 months and are actively striving to prevent relapse. Themaintenance stage lasts until termination, when there is negligible chance of relapse.The stages form a simplex pattern in which adjacent stages are more highly corre-lated with each other than with more distant stages (Prochaska, DiClemente, Vel-icer, Ginpil, & Norcross, 1985). For most people, the change process is not linear,but spiral, with several relapses to earlier stages before they attain permanentbehavior change (Prochaska & DiClemente, 1983, 1986).

The stage construct has received empirical support across studies of behaviorchange in several areas, including alcohol abuse (DiClemente & Hughes, 1990),psychological distress (Prochaska, Rossi, & Wilcox, 1991), and safe sex practices(Prochaska et al., 1994). For example, smokers in Preparation are twice as likelyto be abstinent at 1 month posttreatment than are Contemplators, who in turn are

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twice as likely to be abstinent than Precontemplators. The pattern continues at 6months posttreatment (DiClemente et al., 1991). Research comparing stage distribu-tions across behaviors and populations found that about 40% of preaction individualswere in Precontemplation, 40% in Contemplation, and only 20% in Preparation(Velicer et al., 1995; Laforge, Velicer, Richmond, & Owen, 1999). These data suggestthat if we offer action-oriented interventions to all battering men in treatment,we are mis-serving the majority who are not prepared to change. Stage-matchedinterventions can have a greater impact than action-oriented, one-size-fits-all pro-grams by increasing participation and increasing the likelihood that individuals willtake action. Stage-matched interventions for smokers more than double the smokingcessation rates of the best traditional interventions available (Prochaska, DiClem-ente, Velicer, & Rossi, 1993; also see Strecher et al., 1994). Stage-matched interven-tions have out-performed one-size-fits-all interventions for exercise acquisition(Marcus et al., 1998), dietary behavior (Campbell et al., 1994), and mammographyscreening (Rakowski et al., 1998). Violent offenders might be assigned to stage-matched orientation sessions or psychoeducational groups, or provided with adju-vant stage-matched interventions in traditional mixed groups.

Application of the Transtheoretical Model to Violence Desistance

Measure development is the first step in the application of the TranstheoreticalModel of Change to the problem of partner violence. Psychometrically sound andvalid measures of stages of change, decisional balance, self-efficacy, and processesof change are critical initially in testing to examine how well the TranstheoreticalModel constructs, and the established relationships between them, characterize theprocess of change among assaultive men. Measures also provide the tools for as-sessing change over time and provide the data that guide client–treatment matchingto increase the impact of interventions. The present study focuses on the develop-ment and initial validation of a stage of change measure that assesses men’s readinessto end their use of violence in their relationships.

Stage of change can be assessed using continuous measures that represent eachof the different stages. Although individuals progress from one stage to another,they can have attitudes and exhibit behaviors that characterize more than one stageat the same time. Their profiles or patterns of scores on the various measurescharacterize their readiness to change. The first measure of this kind, the Universityof Rhode Island Change Assessment (URICA), was developed to assess psychother-apy patients’ readiness to address the ‘‘problem’’ (unspecified) that brought them totreatment (McConnaughy, DiClemente, Prochaska, & Velicer, 1989; McConnaughy,Prochaska, & Velicer, 1983). The URICA has four dimensions representing Precon-templation, Contemplation, Action, and Maintenance. The instrument’s developersfound that subjects did not discriminate Preparation from Contemplation and Ac-tion (items designed to measure the Preparation dimension tended to load on theother two dimensions), and thus excluded the Preparation items and dimensionfrom the scale. They identified profiles of URICA scores that represent the Prepara-tion stage, however (McConnaughy et al., 1983).

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DEVELOPMENT AND VALIDATION OF THE URICA-DV

This paper focuses on the development and validation of the URICA–DomesticViolence (URICA-DV), a brief measure for stage classification based on theURICA. This measure was designed specifically to assess battering men’s readinessto end their use of violence in their relationships. Although the goal of mostbatterer programs is the cessation of both physical and psychological aggression,an individual conceivably can be in different stages of readiness to end these twotypes of behavior. Thus, we chose not to combine them and to focus only on physicalviolence in this preliminary work. As in the original URICA, each of the URICA-DV dimensions represents one of the stages of change. Cluster analysis is used toidentify a small set of homogeneous batterer subtypes based on patterns of scoreson the separate URICA-DV dimensions. Construct validity of the measure is as-sessed by examining the relationship between the URICA-DV stage clusters andattitudes and behaviors that should vary systematically by stage in a manner pre-dicted by the Transtheoretical Model.

Before moving on, it is important to highlight some of the limitations of thisstudy. Our sample consisted of men drawn from batterer programs in Rhode Island.Agencies distributed the surveys to most of their domestic violence groups duringa 2-week period, so the sample represents the range of clients in treatment. Somerepresentation of men in the early stages of change was expected, given the generalimpression among clinicians that many batterers in treatment are unmotivated toend their violence (e.g., Ganley, 1987; Daniels & Murphy, 1997), and given thehigh rate of court-mandated (vs. self-referred) clients in treatment. However, oursample excluded men who do not attend treatment (e.g., offenders who are notcaught, offenders who are caught and incarcerated, individuals who refuse to at-tend), and men who have remained violence-free for some time (e.g., long-termtreatment successes, men who make and sustain significant changes without treat-ment). The exclusion of these groups may result in a more truncated stage distribu-tion than we might find in a community sample. Although the content and dimen-sionality of the URICA-DV scales are expected to be invariant across differentsamples of batterers (the assumption of factorial invariance; Thurstone, 1947),distributions of scores on the measures and the types of clusters derived from thesemeasures may differ from sample to sample. Finally, reliance on a clinical sampleand the study’s cross-sectional design limits the kinds of hypotheses that can bedrawn and tested.

With these caveats in mind, we hypothesize the following among batteringmen in treatment:

1. Individuals in the earlier stage clusters will be more likely to be new clients.Rationale: New clients have had little exposure to treatment and little timeto progress through the stages.

2. Individuals in the more advanced stage clusters will be more likely to haveused strategies in the last 6 months to end the violence in their relationships.Rationale: Individuals in the more advanced clusters should be more likelyto have taken concrete steps to achieve their behavioral goal.

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3. Individuals in the more advanced stage clusters will report fewer incidentsof psychological, mild, and severe aggression in the last year. Rationale: Adecrease in aggression should accompany a commitment to change andefforts to end the violence.

4. Individuals in the more advanced stage clusters will report less partnerblame. Rationale: Men in the more advanced stage clusters should displaylower levels of defensiveness and resistance to change.

5. Individuals in the early stage clusters will value the Cons of ending theviolence more than the Pros; individuals in the more advanced clusters willvalue the Pros more than the Cons; the Pros will begin to outweigh theCons somewhere before the Action stage is reached. Rationale: These finalhypotheses are based on the relationship between stage of change anddecisional balance, another core construct of the Transtheoretical Model,as discussed in more detail below.

METHOD

Item Generation

The sequential system for scale development described by Jackson (1970, 1971)and Comrey (1988) was used. At the outset, the URICA (McConnaughy et al.,1983) and conceptual definitions of the stages of change constructs from the Trans-theoretical Model guided item generation for the five URICA-DV scales: (1) Pre-contemplation, (2) Contemplation, (3) Preparation, (4) Action, and (5) Mainte-nance. Ten focus groups, each consisting of 8 to 15 assaultive men in group treatment,were conducted at two agencies in Rhode Island to provide further informationnecessary for item development, such as the depth and breadth of ideas that charac-terize clients’ phenomenological view, and the language they use to describe theirattitudes and behaviors. The programs offered by the agencies, typical of programsavailable today for men who assault their partners, are l8–25 weeks in length,psychoeducational, and focus on anger management, sex role and gender issues,and coping and communication skills. One of the agencies also specializes in thetreatment of substance abuse. Treatment group leaders who participated in a 4-hour training session on the Transtheoretical Model of Change conducted thefocus groups in lieu of regularly scheduled program activities. Focus groups wereconducted until little new information was forthcoming. The group leaders and thefirst author generated items for the five URICA-DV scales, incorporating the men’sideas and the language noted during the focus groups. All items employed a 5-point Likert-type response format (1 � strongly disagree to 5 � strongly agree).

Two experts on the Transtheoretical Model of Change, from the Universityof Rhode Island, sorted items into five categories based on the conceptual definitionsof the stage dimensions to assess content validity. Items that were sorted intodifferent categories by the experts were dropped from the item pool or rewritten.A final list of 53 items was selected for administration on the basis of clarity ofexpression, lack of redundancy with other items, and the degree to which they

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represented the five stages as conceptually defined. Seven to 18 items representedeach of the stage dimensions.

Participants

Study participants were 292 males involved in group counseling for partnerviolence. They were drawn from the two Rhode Island agencies mentioned above.Group facilitators collected data during group sessions, once again, in lieu of regu-larly scheduled activities. Men were informed of the nature of the research, assuredof anonymity, and given the opportunity to decline participation without penalty.The handful of men who did decline most often cited difficulty reading or under-standing English as their reason. Eleven participants were excluded because theirsurvey responses were clearly spurious, and 23 were excluded because their surveyswere largely incomplete, leaving N � 258.

Participants recorded their responses on preprinted optical scan forms thatallowed only five response options per question. Thus, all demographic data arecategorical. Of the 258 participants retained for the study, 19% had been in counsel-ing for less than 1 month, 32% for 1–2 months, 38% for 3–5 months, and 11% for6 months or more. Nineteen percent of participants were 24 years of age or younger,21% were 25–29 years of age, 40% were 30–39 years of age, and 20% were 40 yearsof age or older. Seventy-eight percent described themselves as white non-Hispanic;9% as black non-Hispanic; 6% as Hispanic; and 7% as ‘‘other.’’ Fifty-eight percentwere married, and 78% had one or more children. A majority held at least a highschool degree (65%) and were employed full-time (62%). Seventy-five percent hadlived, at some point, with their most recent victim. Ninety-four percent of the studyparticipants were mandated to treatment by the courts, and 26% reported priorinvolvement in treatment to address the problem of partner violence.

Procedure

The URICA-DV items were administered as part of a 240-item paper-and-pencil survey that took approximately 50–60 min to complete. The URICA-DVitems were preceded by the following definition of partner violence: ‘‘In the ques-tions below, ‘violence’ refers to your physical aggression toward your partner. Thisincludes any of the behaviors listed below and other acts that can cause physicalpain or injury.’’ Eleven mild and severe physical aggression items from the ModifiedConflict Tactics Scales (MCTS; Pan, Neidig, & O’Leary, 1994) were listed (e.g.,threatening to hit or throw something at your partner, slapping your partner, forcingyour partner to have sex). The instructions continued, ‘‘Please indicate how muchyou disagree or agree with each of the following statements. Base your responseson how you’re feeling and acting NOW. Please answer using a 5-point scale with1 � Strongly disagree to 5 � Strongly agree.’’

The survey included questions to assess demographics (age, race, education,employment status, income, marital status, relationship status, and number of chil-dren) and months in batterer treatment. Five additional measures were includedto evaluate the construct validity of the URICA-DV.

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Social Desirability

Social desirability was assessed using a 13-item short form of the Marlowe–Crowne Social Desirability Scale (Crowne & Marlowe, 1960; Reynolds, 1982). TheMarlowe–Crowne SF-13 has adequate internal reliability (rKiR�20 � .76) and is highlycorrelated with the standard 33-item version of the Marlowe–Crowne (r � .93)(Reynolds, 1982). The response options were altered from true/false to a 5-pointLikert scale, ranging from 1 � completely true to 5 � completely false.

Strategies for Ending the Violence

A series of questions assessed if participants used any strategies in the last 12months in an effort to end their violent behavior in a dating or marital relationship.Individuals were asked to consider the following 11 strategies and list any othersthey may have used: (1) talking to the partner; (2) talking to friends or family; (3)talking to a priest, pastor, or rabbi; (4) talking to a medical health professional; (5)one-on-one counseling; (6) couple’s counseling; (7) batterers’ group; (8) other grouptherapy; (9) self-help manual or books; (10) leaving the relationship temporarily;and (11) leaving the relationship permanently.

Relationship Violence

History of relationship violence was assessed using the Modified Conflict TacticsScales (MCTS; Pan et al., 1994), which has an improved factor structure over theoriginal Conflict Tactics Scales developed by Straus (1979). The MCTS asks subjectshow often their partners, and how often they themselves, used each of a series ofstrategies to resolve conflict in their relationships over the past year, beginningwith ‘‘rational’’ strategies, and progressing to strategies representing psychologicalaggression (e.g., ‘‘did something to spite your partner’’), mild physical aggression(e.g., ‘‘pushed, grabbed, or shoved your partner’’), and severe physical aggression(e.g., ‘‘beat up your partner’’).

Partner Blame

This four-item scale, which emerged as a byproduct of other instrument devel-opment work by the first author (Levesque, 1998), assesses the extent to whichbattering men attribute blame for their violence to their partners. Men are askedto indicate their level of agreement (1 � strongly disagree to 5 � strongly agree)with each of the following statements: (1) ‘‘My partner was to blame for my violentbehavior’’; (2) ‘‘If my partner would just leave me alone I wouldn’t have a problemwith violence’’; (3) ‘‘If my partner treated me better I wouldn’t have a problemwith violence’’; and (4) ‘‘My partner is the one with the problem, not me.’’ Thescale’s Cronbach’s alpha is .67.

Decisional Balance

The Decisional Balance Inventory (DBI; Velicer, DiClemente, Prochaska, &Brandenburg, 1985), derived from the work of Janis and Mann (1977), consists oftwo scales, the Pros of change and the Cons of change. In an integrative report of12 studies, Prochaska et al. (1994) found that the balance of Pros and Cons was

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systematically related to stage of change in all 12 behaviors (e.g., smoking, condomuse, quitting cocaine, weight control) examined: the Cons of changing to a health-promoting behavior outweighed the Pros in the Precontemplation stage, the Prossurpassed the Cons in the middle stages, and the Pros outweighed the Cons in theAction stage. From these 12 studies, Prochaska (1994) discovered the degree ofchange in Pros and Cons needed to progress across the stages of change: To progressfrom Precontemplation to Action involved approximately a one standard deviationincrease in the Pros of making the healthy behavior change, and a .5 standarddeviation decrease in the Cons.

The decisional balance measure for battering men (Levesque, 1998) iscomposed of three 7-item scales that measure two Pros constructs (general andchildren-focused) and a single general Cons construct. Participants are asked torate the importance of each item in their decision to end their violence. Sampleitems include, ‘‘If I ended the violence I’d receive more love and kindness frommy partner’’ (General Pros); ‘‘Children are happier in a violence-free home’’(Children-Focused Pros); and ‘‘If I ended my violent behavior, my partner wouldtake advantage of me’’ (General Cons). All items employ a 5-point Likert-typeresponse format (1 � not at all important to 5 � extremely important). Cronbach’salphas range from .85 to .87, indicating good internal reliability. Scale scoresare calculated by taking the unweighted sum of the seven items composing eachscale. Correlations with social desirability range from .02 for General Pros to�.29 for General Cons.

Measure Development

A 53 � 53 matrix of interitem correlations was calculated for the URICA-DV. In cases in which less than 10% of the URICA-DV values were missing,pairwise deletion was used to deal with missing values in the interitem correlations.In cases in which 10% or more of the values were missing, data were deleted in alistwise fashion, resulting in an N of 257.

Given what we know a priori about the content and dimensionality of URICAmeasures in other behavior domains, two confirmatory factor analyses were con-ducted using the SPSS LISREL program (Joreskog & Sorbom, 1989) to comparetwo measurement models most likely to represent the data. The first was a five-factorcorrelated factors model that included all five stage dimensions: Precontemplation,Contemplation, Preparation, Action, and Maintenance. The second was a four-factor correlated factors model that excluded the Preparation dimension and items(as the original URICA developed by McConnaughy et al., 1983). In both models,items were loaded on the factors they were designed to represent. Support for thefive-factor model would suggest that individuals tend to discriminate between allfive stage dimensions simultaneously, but that these dimensions overlap somewhatand are not orthogonal. Support for the four-factor model would suggest thatindividuals tend to discriminate best between four overlapping dimensions. Earlywork on the URICA suggests that individuals are unable to discriminate betweenPreparation and adjacent stages, and that the four-factor model will provide a betterfit of the data (see McConnaughy et al., 1983).

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Goodness of fit was assessed using the Nonnormed Fit Index (NNFI; Tucker &Lewis, 1973) and the Comparative Fix Index (CFI; Bentler, 1990), two fit indicesthat performed well in a simulation study examining the robustness of six fit indicesagainst various study conditions (Ding, Velicer, & Harlow, 1995). Given the presentstudy’s sample size (�250), anticipated factor loadings (�.50), and estimationmethod (maximum likelihood), the NNFI and CFI are expected to perform well.Potential values for these fit indices range from .00 to 1.00, with values above .90indicating good to excellent fit. Associated parsimonious fit indices were calculatedto adjust for the greater parsimony of the four-factor model. Using standard instru-ment development procedure, the correlations between the individual factors andcomponents (loadings) and the Cronbach’s coefficient alphas for each scale, withand without particular items included, were used to select the best items for eachof the URICA-DV scales. Complex items (items that loaded �.40 on two or morecomponents), items with low loadings (loadings of �.40 on all components), anditems that contributed negatively to the reliability of their respective scales weredeleted. To maximize the breadth of content reflected by the factors, redundantitems were also deleted. A decision was made to retain only the best five items foreach dimension. This represents a compromise between designing short scales thatreduce the response burden on participants and the competing desire to have anextensive sample of items from each of the stage dimensions.

Subtype Analysis

The sample was randomly split into two subsamples, A and B. A clusteringprocess (see Milligan & Cooper, 1987) was used to classify the heterogeneouspool of participants in subsample A into a small number of homogeneousbatterer groups based on their URICA-DV score profiles. The process wasreplicated for subsample B and the clusters emerging from the two subsampleswere compared. Squared Euclidean distance was selected as the similarity/dissimilarity measure, and Ward’s method (1963) as the clustering method. Ina review of the research on clustering procedures, Milligan and Cooper (1987)concluded that Ward’s method was generally the best hierarchical agglomerativeclustering technique for recovering underlying structure. Before beginning, partici-pants’ scores on the separate URICA-DV dimensions were summed and standard-ized by converting them to t-scores. Without standardization, variables withhigher means tend to have more influence than variables with lower means(Everitt, 1980). Ward’s method (1963) was used to cluster cases, and then groupsof cases, in a manner that minimized within-groups error sums of squares. Theclustering procedure continued until all cases were combined in a single cluster.The cluster analysis was conducted using SAS (SAS Institute, 1985). Since thereare no completely satisfactory methods available for determining the numberof clusters to retain (Everitt, 1980), the decision in this case was based onhierarchical dendrogram inspection and profile interpretability (Aldendefer &Blashfield, 1984). Three- to fifteen-cluster solutions were specified and examinedfirst for subsample A and then in the subsample B replication.

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Validity of the URICA-DV

Cluster replications (i.e., clusters that emerged from both subsamples A andB) were combined into single cluster groups in the following analyses. Plannedcomparisons were conducted to evaluate the construct validity of the URICA-DVstage clusters by examining their relationship to demographics and several measuresexpected to vary with stage in a manner predicted by the Transtheoretical Model.URICA-DV stage cluster was the grouping variable in all analyses. Categoricaldependent variables were dichotomized for ease of reporting. The following demo-graphic variables were examined: age (�30 years/�30 years), race (white non-Hispanic/other), years of education (�12 years/�12 years), employment status(full-time/other), income (�$10,000/�$10,000), marital status (married/single orcohabiting), relationship status (ongoing/ended), and any children (yes/no). Alsoexamined were social desirability, length of time in treatment (�1 month/�1month), use of strategies to end the violence in the last 6 months (yes/no), numberof incidents of psychological, mild, and severe aggression in the last year, level ofpartner blame, and Pros and Cons of ending the violence.

RESULTS

Measure Development

Two confirmatory factor analyses were conducted to compare the five-factorcorrelated factors model that included the Precontemplation, Contemplation, Prep-aration, Action, and Maintenance factors and a four-factor correlated factors modelthat excluded Preparation. The solution to the five-factor correlated factors modelwould not converge, indicating that it is a faulty model (Joreskog & Sorbom, 1989).It was suspected that the problem lay in the high correlation between the Preparationand Action factors, so a simpler correlated factors model that included only theitems assigned a priori to the Preparation and Action factors was run to examinethis. The simpler model would not converge, either. The correlation between thePreparation and Action factors could not be identified in the psi matrix, providingevidence that the individuals in our study could make little distinction between thePreparation and Action constructs as represented by the items.

The NNFI (Tucker & Lewis, 1973) and the CFI (Bentler, 1990) suggested thatthe four correlated factors model that excluded the Preparation factor and itemsmay provide a good fit of the data. The NNFI and CFI were .67 and .69, respectively.Chi square was 1874.17 with 896 df. Item analysis was conducted to delete baditems and optimize internal reliability and survey length. Items that were complex,had low loadings, or contributed negatively to the reliability of their respectivescales were deleted. In addition, redundant items were also deleted to maximizethe breadth of content reflected by the factors. Five items were retained for eachstage dimension, resulting in a brief 20-item instrument. The NNFI and CFI forthe refined four-dimensional 20-item model were .92 and .93, respectively, indicatingvery good fit. Chi square was 258.36 with 164 df.

186 Levesque, Gelles, and Velicer

The results of the confirmatory factor analyses suggest that study participantswere able to discriminate between four overlapping dimensions representing Pre-contemplation, Contemplation, Action, and Maintenance, but not between fivedimensions when Preparation was added. As in the work of McConnaughy et al.(1983), Preparation did not emerge as a unique dimension. Figure 1 presents thefour correlated factors model for the URICA-DV and the final items for the fourstage dimensions.

Overall, the model represents the expected simplex pattern in which adjacentstages are more highly correlated than nonadjacent stages. For example, Precontem-plation and Contemplation are relatively strongly correlated, whereas Precontem-plation and Maintenance are virtually uncorrelated (rs � �.602 and �.030, respec-tively).

Scale scores were calculated for each stage dimension by taking the unweightedsum of the five items representing the dimension. Scale means, standard deviations,Alphas and correlations with the Marlowe-Crowne SF-13 are presented in TableI. Coefficient Alphas ranged from .68 for the Maintenance scale to .81 for theAction. The Alpha may be relatively low for Maintenance because its items aremore demanding: they are lengthy (an average of 20 words each), and requireparticipants to consider two ideas simultaneously (the idea that they have changed,and the idea that they might relapse). The four URICA-DV scales were uncorrelatedwith social desirability.

Subtype Analysis

The cluster analysis for subsample A yielded an eight-cluster solution. Sevenmajor clusters accounted for 128 of 130 study participants who had complete data;one minor cluster accounted for the remaining 2 participants. In the subsample Breplication, the eight-cluster solution yielded six major clusters that accounted for108 of 113 participants who had complete data; two minor clusters accounted foran additional 5 participants. All six of the major clusters that emerged from subsam-ple B replicated the major subsample A clusters with respect to profile level, scatter,and shape. The standardized mean scale scores on the URICA-DV Precontempla-tion, Contemplation, Action, and Maintenance scales for the six major clusters thatemerged from both subsamples A and B and a final cluster that emerged only fromsubsample A are presented in Fig. 2. The seven clusters are described below in anorder that appears to represent a progression from the least to the most advancedin the change process.

1. Reluctant Cluster. This cluster is composed of 13 individuals from subsampleA and 15 individuals from subsample B. The individuals in this cluster wereabout average on Precontemplation, below average on Contemplation andMaintenance, and lowest (1 to 1�� standard deviations below the mean) onAction, representing a reluctance to make changes. This profile has a belowaverage level, a moderate degree of scatter, and its shape resembles a lineardecreasing function with a slight rise in the right tail.

2. Immotive Cluster. Seventeen individuals from subsample A and 10 individu-

Stages of Change Measure for Men in Treatment 187

Fig. 1. Four correlated factors model for the URICA-DV.

188 Levesque, Gelles, and Velicer

Table I. URICA-DV Psychometric Properties and Correlations with theMarlowe–Crowne SF-13

Scale Mean SD Alpha r

Precontemplation 10.42 3.65 .72 �.03Contemplation 17.78 4.09 .73 �.03Action 19.42 3.93 .81 .11Maintenance 16.03 3.93 .68 �.12

als from subsample B were in this cluster. The profile pattern of the individu-als in this cluster is similar to that of the Reluctant cluster, but elevated byup to one standard deviation on all four dimensions. These men scoredhigher than average on Precontemplation and lower than average on Con-templation and Action, suggesting that they are not engaged in the changeprocess. The profile is characterized by an average level, a high degree ofscatter, and a wide U shape. Individuals with such a profile are likely toretain the status quo.

3. Nonreflective Action Cluster. This cluster is composed of 7 individuals fromsubsample A and 20 individuals from subsample B. In the profile of the 27individuals in this cluster, Precontemplation, Contemplation, and Mainte-nance levels are similar to those in the Immotive profile described above.However, the Action level has risen by over one standard deviation. Overall,the profile is above average in level and scatter, and has a jagged shapewith peaks in the first and third dimensions. Because these clients have notyet done the reflective work that should precede Action, the cluster is labeled‘‘Nonreflective Action.’’

4. Unprepared Action Cluster. Eighteen individuals from subsample A and 9individuals from subsample B were in this cluster. The drop in Precontempla-tion among the 27 individuals in this cluster suggests progress over theNonreflective Action cluster. However, Contemplation still remains lowrelative to Action, suggesting that these individuals have not fully acknowl-edged the extent of the problem and may be unprepared to sustain thechanges they are making. This profile is below average in level. It has amoderate degree of scatter and an inverted ‘‘V’’ shape.

5. Preparticipation Cluster. The 40 individuals from subsample A and 37 indi-viduals from subsample B who were in this cluster display a leveling out ofPrecontemplation, Contemplation, Action, and Maintenance at the mean.These individuals are somewhat engaged in thinking about, making, andsustaining changes. The profile is average in level, has minimal scatter, andis roughly a horizontal line.

6. Decision-Making Cluster. Sixteen individuals from subsample A and 17individuals from subsample B appeared in this cluster. In comparison toindividuals in the Preparticipation cluster, these men were lower on Precon-templation and Maintenance and higher on Contemplation and Action. Theprofile is characterized by an average level, a moderate degree of scatter,

Stages of Change Measure for Men in Treatment 189

Fig. 2. Seven URICA-DV stage cluster profiles emerging from subsamples A and B.

190 Levesque, Gelles, and Velicer

and an inverted U shape. This cluster represents a transitional stage in whichindividuals are contemplating change and beginning to take action.

7. Participation Cluster. This cluster emerged in subsample A only. The 17individuals in this cluster are lower on Precontemplation and higher onContemplation, Action, and Maintenance than all previous clusters. Theyare thinking about the benefits of changing, actively working on ending theirviolence, and are acutely aware of the potential for relapse. The profile isabove average in level and has a moderate degree of scatter with a sharpinitial rise and then leveling.

The three minor clusters representing a total of six individuals varied widelyin levels of Precontemplation and Maintenance. However, all three were extremelylow (two to three standard deviations below the mean) on Contemplation andAction, possibly representing a resistant or negative reactive stance. Given theirsmall ns, these minor clusters are excluded from the analyses below.

The Reluctant and Immotive clusters seem to represent different types ofPrecontemplation, the Preparticipation cluster seems to represent Contemplation,the Decision-Making cluster represents Preparation, and the Participation clusterrepresents Action. The Nonreflective Action and Unprepared Action clusters mayrepresent a kind of ‘‘pseudo’’ Action among individuals who experience pressureto participate in the change process when they are inadequately prepared to do so.If this is the case, Nonreflective and Unprepared Action clusters would be expectedto exhibit characteristics of both earlier and later stages.

Validity of the URICA-DV

Subsamples A and B cluster replications were combined into single clustergroups in the following analyses. The single Participation cluster from subsampleA was also included. Chi-square tests were conducted to assess differences amongthe seven URICA-DV stage clusters on eight demographic variables presumed tobe unrelated to stage to change: age, race, education, employment status, income,marital status, relationship status, any children. Results are summarized in TableII. Significant results were found only for race. Participants who classified themselvesas white non-Hispanic (as opposed to black non-Hispanic, Hispanic, Asian, or‘‘other’’) were overrepresented in the Unprepared Action (85.2%) and Preparticipa-tion (90.8%) clusters and were underrepresented in the Participation cluster (58.8%).

A one-way analysis of variance (ANOVA) revealed significant differences insocial desirability among the stage clusters. A Newman–Keuls post hoc test foundthat the Participation Cluster scored significantly lower on social desirability thanthe Unprepared Action cluster. Social desirability score means and standard devia-tions for the seven stage clusters are presented in Table II.

In the next set of analyses, the grouping variable was URICA-DV cluster, andthe dependent variables were behavioral and attitudinal variables expected to varyby stage cluster in a manner predicted by the Transtheoretical Model. Findings aresummarized in Table III. A chi-square test did not reveal a significant relationshipbetween URICA-DV stage clusters and length of time in treatment. However,

Tab

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Stages of Change Measure for Men in Treatment 193

findings were in the predicted direction. A chi-square test found a significant differ-ence among the URICA-DV stage clusters in use of concrete strategies to end theviolence in the last 6 months. Individuals in the Preparticipation and Decision-Making clusters were nearly twice as likely and individuals in the Participationcluster were 2 �� times as likely to have used strategies as individuals in the Reluctantand Immotive clusters.

Measures on all three MCTS were skewed to the more aggressive end of thescale. Although the sample averaged 15 incidents of mild physical aggression inthe previous year, 50% of men reported five or fewer incidents; although the sampleaveraged five incidents of severe aggression, more than 50% of men reported nosevere violence whatsoever. A square-root transformation of the aggression mea-sures was used to help normalize the distributions in the analyses that follow.

A multivariate analysis of variance (MANOVA) was conducted for the clustervariable with square root of total incidents of psychological, mild physical, andsevere physical aggression in the previous year as the dependent variables. TheMANOVA resulted in significant differences among the URICA-DV cluster profiles(Wilks’ lambda � .857, approximate F(18,637) � 1.98, p � 0.01). The results offollow-up univariate ANOVAs and Newman–Keuls multiple comparison tests aresummarized in Table III.

The follow-up tests showed that the stage clusters differed significantly intheir use of psychological aggression in the previous year. Surprisingly, men in thePreparticipation and Participation clusters reported significantly more incidents ofpsychological aggression than men in the Immotive cluster.

Univariate ANOVAs showed that individuals in different stage clusters alsodiffered significantly in degree of partner blame. Newman–Keuls multiple compari-son tests found that men classified in the Immotive, Nonreflective, and UnpreparedAction clusters engaged in more partner blame than men classified in the Prepartici-pation and Decision-Making clusters. The Nonreflective Action cluster also engagedin more partner blame than the Reluctant and Participation clusters.

Differences across the URICA-DV clusters were examined using MANOVAsin which the dependent variables were the two types of Pros of ending the violence(General, Children-Focused) and the Cons of ending the violence. The MANOVAsresulted in significant differences among the URICA-DV clusters (Wilks’lambda � .583, approximate F(18,617) � 7.19, p � 0.001). The follow-up testsshowed that men in the more advanced stage clusters tended to score significantlyhigher on the Pros than men in the earlier clusters. In general, the reversepattern was found for the Cons with one exception: Men in the most advancedstage cluster, Participation, did not score significantly lower than men in the earlierclusters. The decisional balance measures did not discriminate between the twoearliest clusters, Reluctant and Immotive, or between the two most advanced clus-ters, Decision-Making and Participation.

The decisional balance measures were then converted to standardized T-scoresand plotted together in an order representing possible progression through theURICA-DV stage clusters. Figure 3 illustrates that the Cons of ending the violenceoutweigh the Pros in the early stage clusters, and the Pros outweigh the Cons inthe later clusters. The crossover between the Pros and Cons takes place between

194 Levesque, Gelles, and Velicer

Fig. 3. Mean standardized decisional balance scores for seven URICA-DV stage clusters.

the Unprepared Action cluster (the second ‘‘pseudo’’ action cluster) and the Prepar-ticipation cluster. The Pros of changing increased by over one standard deviation,and the Cons of changing decreased by more than one-half standard deviation withprogression from the Reluctant to the Decision-Making cluster. However, the Consthen increased one-half standard deviation in the Participation cluster.

Given the significant differences in social desirability across the stage clustersand its correlation with some of the dependent variables examined (e.g., Cons ofending the violence), all analyses of variance reported above were repeated withsocial desirability as a covariate. This procedure produced no substantive changesin the significance or direction of findings reported in Table III. Social desirabilitywas unrelated to reports of violence cessation activities.

A final set of analyses was conducted to ensure that observed differences acrossthe stage clusters could not be accounted for by length of time in treatment, apotential confound. In all analyses, length of time in treatment (�1 month/1–2months/�3 months) was the grouping variable. The dependent variables were theattitudinal and behavioral variables examined above: use of strategies to end theviolence in the previous 6 months (yes/no), number of incidents of psychological,mild, and severe aggression in the previous year, level of partner blame, and Prosand Cons of ending the violence. None of the findings reached statistical significance.

DISCUSSION

As the first step in the application of the Transtheoretical Model of Changeto the problem of male-to-female partner violence, a stages of change measure, the

Stages of Change Measure for Men in Treatment 195

URICA-DV, was developed to assess battering men’s readiness to end their vio-lence. The URICA-DV is composed of four five-item scales that measure fourcorrelated but distinct constructs representing Precontemplation, Contemplation,Action, and Maintenance in individuals with a history of partner violence. As inthe early work on the development of the URICA for outpatient psychotherapyclients (McConnaughy et al., 1983), Preparation did not emerge as a unique dimen-sion, suggesting that individuals do not discriminate between Preparation and adja-cent stages. The four scales are psychometrically sound and uncorrelated with socialdesirability, and for the most part form the expected simplex pattern in whichdimensions representing adjacent stages are more highly correlated with each otherthan dimensions representing more distal stages (Prochaska et al., 1985).

Seven major profiles emerged when clients were clustered on their fourURICA-DV scale scores: (1) Reluctant, (2) Immotive, (3) Nonreflective Action,(4) Unprepared Action, (5) Preparticipation, (6) Decision-Making, and (7) Partici-pation. McConnaughy et al. (1983) identified six of these seven profiles amongpsychotherapy clients assessed at intake. The only cluster McConnaughy et al. didnot identify is Unprepared Action, which may represent a kind of ‘‘pseudoaction’’among individuals in our sample who experience extreme pressure (e.g., courtmandate) to participate in the change process before they are fully prepared to doso. McConnaughy et al. (1983) identified three clusters that did not emerge here:Noncontemplative Action, Uninvolved, and Maintenance. Their Noncontemplativecluster is similar to Nonreflective Action, and their Uninvolved cluster to Preprepa-ration. Their Maintenance cluster, which is about average on Precontemplation,Contemplation, and Action, and above average on Maintenance, may not haveemerged in the present study because our participants have not had enough timeto make and sustain changes. These differences highlight how our reliance on aclinical sample might limit our understanding of the process of violence cessationand change. To understand Maintenance, we would need to follow clients posttreat-ment or identify rehabilitated males in the community who have managed to remainviolence-free for some time. To understand the very early stages, we would needto assess men at treatment intake and/or gain access to men who refuse treatmentaltogether. The ‘‘minor’’ clusters representing different forms of resistance mayprovide a glimpse of what some individuals in the earliest stages might look like.Notably, neither McConnaughy et al. (1983) nor the present study identified aprofile that represents true Contemplation—a high level of Contemplation andaverage or below average levels of Precontemplation, Action, and Maintenance.We may need to turn to a nonclinical sample to understand individuals who areonly thinking about change.

The stage clusters were unrelated to demographic variables with one exception:Participants who classified themselves as white non-Hispanic were overrepresentedin the Unprepared Action and Preparticipation clusters, and were underrepresentedin the Participation cluster. These findings are difficult to interpret.

Overall, findings provide preliminary evidence of the construct validity of theURICA-DV. Men in the earlier stage clusters were slightly more likely to be newclients, and men in the later stages were significantly more likely to have usedviolence cessation strategies in the previous 6 months. As hypothesized, partner

196 Levesque, Gelles, and Velicer

blame tended to decrease with progression through the stages. The Pros of endingthe violence increased by more than one standard deviation with progressionthrough the stage clusters, and the Cons decreased by about one standard deviation.The Pros and the Cons intersected before the Preparticipation cluster.

One unanticipated finding was the relatively high frequency of psychologicalaggression reported by men in the Participation cluster. It was hypothesized thatindividuals in the later stages of change would report fewer incidents of psychologi-cal, mild and severe physical aggression in the last year, as they increased theircommitment to ending the violence and began to take small steps toward thatgoal. One possible explanation is that the anger management approach to violencedesistance used in treatment actually increases threats and other forms of psycholog-ical abuse (e.g., Gondolf & Russell, 1986). According to this view, partner violencehas little to do with anger; rather, it is rooted in the socially imposed patriarchalbelief that men have the right to dominate and control women. When men cannotuse physical violence to maintain control, they rely on nonviolent strategies. Futureresearch must examine the relationship between readiness to end these two typesof abuse.

Another explanation is that men furthest along in the change process are moresensitized to the abusiveness of their behavior and its consequences, and are morewilling to admit to past psychological aggression. There is other evidence of thisphenomenon in the literature. Barrera, Palmer, Brown, and Kalaher (1994) foundthat men who voluntarily sought treatment scored lower on a measure of denialand reported more incidents of violence than court-involved men (cf. Dutton &Starzomski, 1994). The relatively low social desirability among men in the Participa-tion cluster may indicate reduced psychological defensiveness. Their high meanContemplation and Maintenance scores on the URICA-DV and their higher thanexpected Cons score suggest that they are willing to admit that their violence is aproblem and recognize the risk of relapse. Alternatively, these men may truly beat increased risk of relapse.

The difficulty interpreting this final finding is due in part to the cross-sectionalnature of our design and to problems with the violence measure. First, we measuredincidents of verbal and physical aggression in the previous year. Indeed, we wouldnot assess the validity of the stage construct for smoking cessation by asking smokersto count the number of cigarettes smoked in the previous year. Instead, we wouldmeasure abstinence at follow-up. Second, the measure is based on self-report andsubject to social desirability and other biases.

Although the present study provides preliminary evidence of the validity ofthe URICA-DV, additional research is necessary to assess the relationship betweenthe profile clusters and measures of future behavior. Measures of behavior shouldbe drawn from a variety of sources, including partners, treatment agency staff, andofficial records. Research is underway to assess the predictive validity of theURICA-DV among men in three batterer treatment programs. The goal is toexamine whether stage of change at intake predicts treatment attendance, comple-tion, and gains (agency staff reports). Using pre–post measures, we will be able totest the assumption of factorial invariance across samples and time points anddetermine the clusters that characterize men very early and very late in treatment.

Stages of Change Measure for Men in Treatment 197

We will also be able to assess the probability of progression, regression, and nomovement among men in the various stage clusters. Other research will be necessaryto determine whether the URICA-DV predicts sustained violence desistance.

Until we have further evidence of the validity of URICA-DV, confirmatoryevidence of its factor structure, and more information about the range of profileclusters that characterize men in treatment, it is premature to use the URICA-DVfor treatment planning and treatment matching. It is our hope that the URICA-DV will serve instead as a useful tool to increase understanding of the process ofviolence desistance and change among battering men.

ACKNOWLEDGMENTS

An earlier version of this paper was presented at Program Evaluation andFamily Violence Research: An International Conference, Durham, NH, July, 1998.This research was supported in part by a grant from the Harry Frank GuggenheimFoundation. The authors wish to thank three anonymous reviewers for their helpfulcomments on earlier drafts of this paper.

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