Overt and Relational Victimization in Latinos and European Americans: Measurement Equivalence Across Ethnicity, Gender, and Grade Level in Early Adolescent Groups

Journal of Early Adolescence30(1) 171 –197

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DOI: 10.1177/0272431609350923http://jea.sagepub.com

Overt and Relational Victimization in Latinos and European Americans: Measurement Equivalence Across Ethnicity, Gender, and Grade Level in Early Adolescent Groups

Eric S. Buhs,1 Meredith McGinley,2 and Michael D. Toland3

Abstract

This study examined the factorial invariance and construct validity equivalence of a selfreport of victimization and exclusion (SVEX) for Latino and European American early adolescent participants (fifth and sixth grades; mean age 11.3). The instrument included an expanded set of relational victimization items that more thoroughly tapped exclusion behaviors relevant to developmental and crosscultural use. Confirmatory factor analyses techniques demonstrated acceptable (partial) factorial invariance across ethnic groups, fifth and sixth graders, and across gender. Linkages between the SVEX scores, peer nominations, internalizing indices, and three demographic variables also supported construct validity equivalence for the SVEX. Findings supported

1University of Nebraska–Lincoln2University of Illinois at Chicago3University of Kentucky

Corresponding Author:Eric S. Buhs, 226 Teachers College Hall, Department of Educational Psychology, University of Nebraska–Lincoln, Lincoln, NE, 68588Email: [email protected]

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172 Journal of Early Adolescence 30(1)

a twofactor model similar to that of Crick and colleagues (e.g., Crick & Grotpeter, 1995) and suggested that the instrument provided an acceptable level of equivalence for overt and relational victimization forms across these groups.

Keywords

Victimization, ethnicity, invariance, exclusion

Investigations of peer aggression and victimization suggest that a significant proportion of children and youth are regularly victimized in school (e.g., approximately 8%10% of school age children, see Nansel et al., 2001; Olweus, 1994) and indicate that frequent victims of peer aggression are more likely than less victimized peers to experience short and longterm adjustment problems (Boivin & Hymel, 1997; Buhs, Ladd, & Herald, 2006; Hodges & Perry, 1999). Evidence also demonstrates that youth victimize peers using varied forms of aggression, including overt (e.g., physical abuse, verbal taunts) and relational (behaviors intended to damage others’ relationships) types. Crick and colleagues’ (Crick, 1995; Crick & Grotpeter, 1996), for example, developed overt (direct physical and verbal victimization) and relational aggression (indirect attempts to damage relationships) constructs and operationalizations that are well established and widely used in research (see Crick et al., 1999, for a review). Despite this work and the numerous empirical studies of these forms of peer victimization, important aspects of victimization instruments used to measure these constructs have not been adequately examined.

While a number of published selfreport instruments tap victimization constructs (e.g., Crick & Bigbee, 1998; Dill, Vernberg, Fonagy, Twemlow, & Gamm, 2004; Hawker & Boulton, 2000; Hodges & Perry, 1999; Mynard & Joseph, 2000; Nishina & Juvonen, 2005; Sandstrom & Cillessen, 2003; Schwartz, Gorman, Nakamoto, & Toblin, 2005), few studies have examined the equivalence of these measures across the various groups (i.e., examining properties beyond means, standard deviations, and internal consistency) that are an emerging focus of much victimization research. Confirmatory factor analysis (CFA) has helped create useful methods for evaluating the hypothesized factor structures and scale/item invariance across groups. Construct validity equivalence, in addition to factorial invariance, requires an examination of the similarities of the intercepts and slopes of the latent constructs on related constructs across the groups of interest. Factorial invariance and construct validity equivalence are important to establishing the comparability of



Buhs et al. 173

observed score differences across groups, yet they have not been examined in aggression/victimization instruments (see Knight & Hill, 1998, for a discussion of measurement equivalence).

While there are studies available in the literature that have carefully examined victimization across gender groups (Crick et al., 1999; Underwood, 2003) and within various ethnic contexts (see Graham, Taylor, & Ho, 2009), there has not been a parallel focus on measurement equivalence. Similarly, the empirical picture of potential victimization changes linked to school structure and development (e.g., from fifth to sixth grade) is also less clear and studies have presented conflicting findings (see Galen & Underwood, 1997; Underwood, 2003). The accuracy of the instruments used may be a factor in these disparate findings as well. Other examinations of victimization (Underwood, Scott, Galperin, Bjornstad, & Sexton, 2004) indicated that social exclusion may also be an important aspect of relational victimization. Exclusion behaviors have not been adequately tapped by most current instruments and this may also have contributed to poorer measurement of victimization.

Examinations of group differences in victimization and related phenomena have thus been hampered by two central problems addressed here: (a) the instruments used may not measure culturally or gradelevel appropriate aspects of the constructs that would allow potential group differences to be accurately identified (i.e., non–European American groups, see Peña, 2007, for a review of concerns with crosscultural research in developmental psychology) and (b) the crossgroup equivalence of these instruments (i.e., factorial invariance and construct validity equivalence) have not been thoroughly examined across groups of interest. Both problems need to be addressed for empirical work to adequately establish that group differences/similarities uncovered accurately reflect differences and are not measurement artifacts.

Victimization Constructs and Hypothesized Factor StructureThe current study examined a twofactor model of victimization similar to that of Crick (1995). Relational victimization refers to behaviors intended to harm through “purposeful manipulation and damage of their peer relationships” (Crick, 1995, p. 711). Relational victimization is typically tapped by items such as “tells lies about you to make other kids not like you anymore” and “keeps others from liking you by saying mean things about you” (Crick & Grotpeter, 1996). Overt victimization factors typically include physical (e.g., hitting) and verbal behaviors (e.g., insults) intended to directly harm others. Relational and overt victimization tend to be moderately to highly




correlated, but evidence suggests that they are distinct aspects independently linked to adjustment (e.g., Crick & Grotpeter, 1996; Loeber & Hay, 1997; Vaillancourt, Brendgen, Boivin, & Tremblay, 2003). Crick and others hypothesized that overt victimization addresses goals or themes of physical dominance and instrumentality and differs from relational forms that address relational themes (i.e., “establishing close, intimate connections” Crick & Grotpeter, 1995, p. 710).

Augmenting the relational victimization construct: social exclusion. We propose that exclusion behaviors related to sets of themes or goals that are likely salient to crosscultural (e.g., collectivist beliefs–see below), gender and developmental differences in victimization have not been adequately addressed in previous instruments. Findings suggest that exclusion may be central to more accurate conceptions of victimization (e.g., Buhs et al., 2006; Bukowski & Sippola, 2001; Sandstrom & Cillessen, 2003; Underwood et al., 2004). Exclusion may be especially important in school contexts because it has been linked to later academic and social–emotional adjustment (Buhs, 2005; Buhs et al., 2006). Though relational victimization variables may include items describing exclusion (e.g., Crick, 1995), they have typically included too few to adequately address these behaviors and may have displayed construct underrepresentation (Messick, 1995). Although direct examination of group differences was not a focus of the current study and the limited sample size made extended analyses addressing meanlevel group differences untenable, establishing an acceptable level of equivalence for an instrument that represents exclusion behaviors will be an important component of future studies of such differences. Sandstrom and Cillessen (2003) constructed a measure with an exclusion construct (e.g., being ignored, not being allowed to join a game), though they used a daily diary method that differed from traditional selfreports. They modeled exclusion as a distinct factor (i.e., exclusion, overt and relational factors). CFA analyses from this study indicated good fit and showed that the exclusion factor moderately correlated with relational aggression—because of this, a threefactor structure was also examined here (below).

Factorial Invariance, construct validity equivalence and potential gender, ethnic and grade-level differences. Researchers (see Crick & Grotpeter, 1996; Rubin, Bukowski, & Parker, 2006; Underwood, 2003) continue to debate the impact of gender on victimization, though the general contention that gender is linked to group differences has received empirical support. The “two cultures theory” (Maccoby, 1998) suggests that boys and girls develop distinct cultures within the segregated gender groups typical in childhood and adolescence. These differences are construed as impacting the goals and themes related to



Buhs et al. 175

victimization. Accordingly, girls’ peer relations tend to display a greater focus on interrelatedness and group inclusion than boys. If this is so, then we suggest that a greater focus on exclusion behaviors (see Underwood et al., 2004) in measurements of victimization across gender groups is warranted. This also suggests it is possible that girls view different behaviors as evidence of overt and relational victimization forms—test of factorial invariance will examine the current instrument for potential differences in item function across groups. Construct validity equivalence analyses examined hypothesized links to peer nominations of similar victimization behaviors and to internalizing outcomes (e.g., Crick & Grotpeter, 1996; Hoglund, 2007).

Following parallel conceptual arguments to those presented for gender differences, we argue that the potential differences in victimization forms and behaviors need to be examined across ethnic groups. First, several aspects of culturally relevant theory suggest that appropriate victimization constructs need to adequately tap exclusion behaviors in Latino groups. Latino culture has frequently been described as more interdependent/collectivist than typical European American groups (Leyendecker & Lamb, 1999). The values of Simpatia (conformity, empathy, and harmony in family/community relations; Marin & Marin, 1991) and Personalismo (social warmth and reciprocity with family/group; Cuellar, Arnold, & González, 1995) suggest that these themes and behaviors are more heavily emphasized by Latinos. Evidence that Latino youth tend to display higher levels of prosocial behavior than European Americans (e.g., Knight & Kagan, 1977; Schwartz, Zamboanga, & Jarvis, 2007) can also be construed as evidence of a collectivist orientation. Given these differences Latino youth may thus display different victimization behaviors (i.e., more subtle, less severe). Graham (2006) has also suggested that when the aggression/victimization originates within one’s own, numericalmajority group (Latino students in this study comprised the majority proportion of their groups) these nonnormative aspects of victimization contribute to a greater significance for those behaviors in that context (i.e., the misfit hypothesis—see also Bellmore, Nishina, Witkow, Graham, & Juvonen, 2007). Relational victimization and exclusion, in particular, may thus communicate stronger messages about group membership and adherence to group norms (Bukowski & Sippola, 2001).

This conceptual framework and related findings do not only present us with precise hypotheses about the frequency/rate of victimization in Latino groups but also about the potential form and relative effects of victimization. Given the emergent state of examinations of victimization in Latino contexts and the differences in prosocial behaviors, it is unclear whether rates among Latinos might be higher or lower than other groups (some findings suggest




lower relative rates of general victimization in early adolescence; see Graham et al., 2009)—the measure developed here may allow more accurate estimates of selfreported rates and links to adjustment. For the purposes of our construct equivalence analyses, we expected that the factor means would be similar across ethnic groups and that the relationships to internalizing outcomes would be slightly greater for Latinos relative to European Americans.

Hypotheses about victimization linked to grade level and school structure are also relevant to the current study. Early adolescence and the transition to middle school is the period where cliques and crowd structures emerge (Brown, Mory, & Kinney, 1994; Collins & Steinberg, 2006). These are contexts where we expected relational victimization/exclusion to be salient as youth develop more complex groups and as adult sanctions for overt aggression also tend to become more severe—evidence suggests that overt aggression thus becomes less frequent relative to relational forms. Findings also suggest that the reorganization of peer groups at the transition to middle school affects victimization in these gradelevel groups (Long & Pelligrini, 2003) and that exclusion may play a central role in this context (Bukowski & Sippola, 2001; Sandstrom & Cillessen, 2003; Underwood et al., 2004). We argue that greater representation of exclusion behaviors in selfreports used with these gradelevel groups is thus required. We also hypothesize that our construct validity equivalence analyses may display greater relational victimization means for sixth graders relative to fifth graders (because of potential gender difference and because we lack the sample size to examine gender groups within/across grade level, we were unable to examine hypotheses about overt vs. relational victimization means).

Selfreports that adequately represent overt and relational victimization thus need to be developed, evaluated, and will need to demonstrate equivalence across gender, ethnic, and gradelevel contexts. The invariance analyses presented here were one important step in establishing some of the measurement components that will help ascertain whether group differences are measurement artifacts or accurately reflect observed differences (see Knight & Hill, 1998; Knight, Tein, Prost, & Gonzales, 2002 for a discussion of measurement equivalence).

The Current StudySelf-report of victimization. Numerous victimization instruments have been

introduced by scholars (e.g., Crick & Grotpeter, 1996; Mynard & Joseph, 2000; Hodges & Perry, 1999; Nishina & Juvonen, 2005; Sandstrom & Cillessen, 2003; Schwartz et al., 2005). Selfreports, in particular, are commonly used



Buhs et al. 177

with children and adolescents (Crick & Grotpeter, 1996; Ladd & KochenderferLadd, 2002; Pellegrini & Bartini, 2000; Sandstrom & Cillessen, 2003) and we examined one here for several reasons. First, observers may be less accurate raters in early adolescence because of the intimate knowledge of peer relationships required to make accurate judgments about the peers’ intentions (e.g., differentiating between friendly and aggressive teasing). Second, relative to observations or teacher/peer reports, selfreports allow for a more parsimonious application of invariance analyses (e.g., as compared to teacher ratings that may reflect greater group biases). Finally, as noted above, selfreports allow reporting of victimization conducted outside of observers’ view; a skill adolescents may develop to a greater degree than younger children. Because findings indicate that selfreport data may include significant biases affecting validity (Ladd & KochenderferLadd, 2002; Sandstrom & Cillessen, 2003), our evaluation of validity evidence included data from other sources (i.e., peer reports).

The current instrument includes items common to other selfreports of victimization but differs from others primarily by including more items tapping exclusion. Prior selfreports included few such items that described behaviors that were clear, observable markers of exclusion (e.g., the SEQS included a single exclusion item; Crick & Grotpeter, 1996—see Storch, Crisp, Roberti, Bagner, & MasiaWarner, 2005, for a CFA examination of the Social Experience Questionaire Self Report Form (SEQS). The current instrument included more items describing highly public displays of exclusion (see Table 1) so that this might be more accurately reflected in our operationalization of the construct.

Ethnicity. The current study drew Latino and European American participants from small cities in predominantly rural, agricultural regions. Latino populations have increased rapidly in the regions that were the context of the current study (Gouveia, Carranza, & Cogua, 2005), and the proportion of Latino students in many schools in these areas is rapidly increasing. The potential differences in victimization experiences for Latino groups discussed above suggest that instruments that allow for more accurate detection of differences will contribute to more culturally sensitive educational and social support and interventions.

Grade level. Measures of victimization need to be able to produce valid and reliable scores at the transition to middle school because victimization appears to be frequently used to establish and maintain group structures across this transition (Long & Pelligrini, 2003). Fifth and sixth graders were selected here because, in each of the participating school districts, this range included the transition from several elementary schools to a single middle school and allowed us to examine instrument properties for students on either side of this transition.




Table 1. SelfReported Victimization Items, Alphas, and CFA Standardized Factor Loadings, Item Error Variances, and Item R2

Item error Item Items Loading variance R2

Item stem: How often do the kids at school do the following:

Overt victimization (a = .89) Threaten to hurt or beat you up? .63 .61 .39Tease you in a mean way or say .82 .34 .66 rude things to you?

Push you around at school? .80 .37 .64Hit, kick, or push you in a mean .65 .58 .42 way at school?

Insult you in order to hurt you? .75 .43 .57Hit you?a — Call you bad names? .79 .37 .63Say mean things to you?a —

Relational aggression (a = .91) Relational victimization items (subscale a = .84)say they won’t be your friend .61 .63 .38 in order to hurt you or get their way?

say bad things about you to other kids .76 .42 .58 at school?

stop talking to you or ignore you .64 .59 .41 when they are mad at you?

tell other kids not to be your friend? .76 .43 .57tell lies, gossips or spread bad rumors .76 .42 .58 about you?

Social Exclusion Items (subscale a = .86) leave you out of what they are doing? .72 .48 .52not pick you for a group activity .65 .58 .42 or game?

not invite you to a party or social .62 .62 .38 gathering?

leave you out of conversations, games .82 .33 .67 or activities?

choose not to sit near you .80 .36 .64 when you want to sit with them?

Note: All standardized factor pattern loadings were significant at the p < .05 significance level.a. Items dropped (see text).



Buhs et al. 179

Gender. Prior conceptual frameworks and empirical findings have suggested differences in frequency and type of victimization linked to gender (see Crick at al., 1999; Underwood, 2003, for reviews)—the evidence is mixed, but some findings suggest that victimization may differ in female groups relative to males. Our examination of factorial invariance and construct equivalence across gender groups was important because these conflicting findings from prior studies need to be further explored with instruments established as capable of accurately detecting potential genderlinked differences.

MethodParticipants

Data used here were gathered from 270 Latino and European American children (160 girls, 144 Latinos) who were part of a larger investigation of children’s peer relations and school adjustment. They were assessed in public schools (fifth and sixth grades, M age = 11.3, SD = .69) located in two small Midwestern cities located in rural areas. Written, informed parental consent and youth assent was obtained from all participants. Sample ethnic composition was 0.7% African American, 1.0% Asian American, 48% European American, 42.4% Hispanic, and 7.9% other (only European American and Latino participant data were used here). The proportion of students in the two districts who were eligible for government subsidized lunch programs were 75.1% and 33.6%, respectively. Students completed questionnaires administered by the first author and trained graduate assistants in classroom/grade level groups (10 fifthgrade classrooms, 5 sixthgrade groups). All fifth and sixthgrade students were invited to participate. Participation rates ranged from 64% to 92%. Teachers indicated that all participating Latino students were performing at or near grade level in English language skills and students completed all measures in English. In classroom groups with Latino students, Latinos comprised from 56.3% to 100% of the ethnic composition of those classrooms.

MeasuresStudents completed a 27item Selfreport of Victimization and Exclusion (SVEX) that included overt and relational victimization items (six items and five items, res pectively) and social exclusion (five items—included in the relational factor). Items were drawn from established victimization selfreports (Crick & Grotpeter, 1995; Hawker & Boulton, 2000; Hodges & Perry, 1999;




Nishina & Juvonen, 2005; Sandstrom & Cillessen, 2003; Schwartz et al., 2005) with additional social exclusion items added (see Table 1). Additional items were developed from youth responses to openended questions about victimization from previous pilot data with a subset of these participants. Students were instructed in the use of the 5point frequency response scale (1 = almost never, 3 = sometimes, 5 = almost always) regarding their victimization at school (Overt: M = 1.73, SD = .85; Relational: M = 1.96, SD =.87)

Victimization: peer reports. Peer nominations of victimization were gathered from participants using peer rosters of classmates. Students made limited nominations (three per item) of peers on four items tapping overt (one verbal and one physical item, combined), relational, and social exclusion behaviors (one item each, combined). Peer nominations are based on information drawn from multiple raters—singleitem scales may thus produce high interrater reliability (see Coie, Terry, Lenox, Lochman, & Hyman, 1995). Students nominated peers who “were often left out of conversations, games and activities” (social exclusion), “other kids gossiped about or said bad things about behind their backs” (relational victimization), and who “were hit, pushed and kicked” and “get called bad names” (overt victimization). Scores were summed and standardized within groups (Overt: M = –.03, SD = .89; Relational: M = –.03, SD =.85).

Internalizing symptoms. Subsets of the Center for Epidemiological Studies–Depression measure (CESD; Radloff, 1991) and the Multidimensional Anxiety Scale for Children (MASC; March, 1997) indicated depressive and anxious symptoms. Both measures are established and have exhibited acceptable reliability and validity across the range of participants in the current study (Crockett, Randall, Shen, Russell, & Driscoll, 2005; March & Parker, 2004). Scores on the respective items were summed and the mean taken to create the depression and anxiety scores. The CESD (five items) included items such as “I felt depressed” and exhibited an alpha of .72 (M = 1.98, SD = .83). The Social Anxiety (e.g., “I worry about other people laughing at me”) scale of the MASC was used to indicate anxiety symptoms (8 items; a= .83, M = 1.16, SD = .75).

AnalysesConfirmatory Factor Analysis (CFA) was used to examine the hypothesized twofactor model (overt and relational victimization factors) and competing one and threefactor models while taking measurement error into account. The threefactor model was drawn from Sandstrom and Cillessen (2003—see above) and the onefactor model was examined because of evidence that the overt and relational factors are typically moderately correlated. Prior to testing measurement invariance and construct validity equivalence, the fit of the



Buhs et al. 181

measurement model was assessed using the SatorraBentler Scaled c2 (SBc2; Satorra & Bentler, 1988), an appropriate test when data is multivariate nonnormal (see descriptive statistics below). Because using the chisquare test alone is problematic (see Brown, 2006), fit was evaluated using a set of indices: the comparative fit index (CFI), the root mean square error of approximation (RMSEA), and the standardized root mean square residual (SRMR). When using the SBc2, a nonsignificant p value is desired. Because the other fit indices lack probability distributions, researchers have suggested cutoffs to determine model fit. Fit was labeled acceptable when the CFI was greater than .90 (Medsker, Williams, & Holahan, 1994), the RMSEA had a value less than .08, and the SRMR had a value less than .10 (Hu & Bentler, 1999; Kline, 1998; Weston & Gore, 2006).

Six increasingly restrictive models of measurement invariance (configural, metric, strong, strict, latent factor means, and latent factor correlations) were examined for each betweengroup comparison (see Knight & Hill, 1998; Millsap & Kwok, 2004; Widaman & Reise, 1997). Configural invariance constrained items to associate with the same factors across groups, but factor loadings, unique error variances, and item intercepts were freely estimated. Metric invariance constrained the factor loadings to be equal across groups, but unique error variances and item intercepts were freely estimated. Assuming metric invariance, strong invariance was tested by constraining item intercepts to be equal across groups, but unique error variances were freely estimated. Given evidence of strong invariance, strict invariance constrained unique item error variances to be equal across groups. Evidence of strong or strict measurement invariance is one component necessary for meaningful comparisons of scores across groups (Gregorich, 2006; Knight & Hill, 1998; Little, 1997; Millsap & Kwok, 2004; Widaman & Reise, 1997).

Construct validity equivalence tests assessed functional and scalar equivalence of the victimization scales across groups. First, group mean differences on the latent victimization factors and differences on the relations among the two factors were examined (Table 2). Next, separate structural equation models were used to regress each of the four construct validity variables (depression, anxiety, overt victimization peer nominations, relational victimization peer nominations) onto each of the latent selfreport factors (see Crick & Grotpeter, 1996; Hoglund, 2007 for findings linking internalizing problems to victimization). These analyses compared an unconstrained model to one that constrained the slopes and scale intercepts between the victimization factors and the construct validity scores to be equal across groups (Table 3). Slope and intercept equivalence indicated that a latent factor was associated with the same score on the construct validity variable for each group.




Table 2. ChiSquare Difference Tests and Fit Indices for the Measurement Invariance Tests Across Ethnic (Latino and EuropeanAmerican), Gender, and Age Groups for the TwoFactor Model

Model c2 df Dc2a D df CFI RMSEA SRMR

Ethnic group Configural 392.65 206 — — .90 .08 .06 Metric 420.13 220 19.82 14 .89 .08 .08 Strong 457.70 234 38.81* 14 .88 .08 .08 Partial strong 436.45 230 16.40 10 .89 .08 .08 Partial strict 444.89 242 4.71 12 .89 .08 .08 Latent means 448.27 244 3.30 2 .89 .08 .08 Latent 448.67 245 0.24 1 .89 .08 .09

correlationGender group Configural 338.08 206 — — .92 .07 .06 Metric 372.57 220 24.46* 14 .91 .07 .08 Partial metric 363.06 218 19.31 12 .92 .07 .07 Partial strong 395.47 230 32.19* 12 .90 .07 .08 Partial strongb 381.37 229 18.50 11 .91 .07 .07 Partial strict 412.95 242 18.93 13 .90 .07 .08 Latent meansc 425.55 244 13.25* 2 .89 .07 .08 Latent 414.79 243 1.28 1 .90 .07 .10

correlationd

Grade group Configural 382.98 206 — — .90 .08 .06 Metric 406.54 220 18.46 14 .89 .08 .07 Strong 430.42 234 24.89* 14 .89 .08 .07 Partial strong 424.64 233 18.78 13 .89 .08 .07 Partial strict 451.20 248 16.09 15 .88 .08 .08 Latent means 458.44 250 7.15* 2 .88 .08 .08 Partial latent 452.37 249 1.03 1 .88 .08 .08

means Latent 394.38 229 1.45 1 .88 .08 .10

correlation

Note: CFI = comparative fit index; RMSEA = root mean square error of approximation; SRMR = standardized root mean square residual.a. As the SatorraBentler scaled chisquare was used, a corrected chisquare difference test was implemented. Thus, the resulting values are not exactly equal to the chisquare of the nested model subtracted from chisquare of the nonnested model.b. The second partial strong model includes an intercept in addition to the initial partial strong model, see text.c. Both latent means were freed between gender groups.d. Model is compared to partial strict model because both means were freed on previous step.*p < .05.



Tabl

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the

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403.

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396.

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183



184

Tabl

e 3.

(co

ntin

ued)

S

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df

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Buhs et al. 185

A c2 difference test was also used to compare a more restricted (nested) model with measurement invariance constraints (e.g., metric invariance) and a model without such constraints (e.g., configural invariance). When the c2 difference test demonstrated no significant differences, the more restrictive level of invariance was accepted. Conversely, if a significant difference occurred, the less restricted model was retained. Because chisquare

criteria are sensitive to trivial modifications, we also examined whether the Dc2 was accompanied by a meaningful drop in the practical fit indices (see Browne & Cudeck, 1993; Kline, 1998). In the event of unacceptable fit, minor revisions in model structure could be carried out within constraints provided by conceptual frameworks (above) and relevant measurement practice. Modification indices (i.e., the Lagrange Multiplier) were used to identify which parameters (e.g., standardized factor loadings/slopes, item/factor intercepts, etc.) were significantly different across the groups and might be independently estimated. After these parameter estimates were freed, partial invariance was established if followup chisquare tests were not significant and fit was similar to the initial model (Byrne, Shavelson, & Muthén, 1989).

ResultsDescriptive Statistics

Item means for the overall sample ranged from 1.40 to 2.23 (SDs ranged from .89 to 1.30). Items were positively skewed (values ranging from .37 to 2.51) and negatively to positively kurtotic (values ranging from –.65 to 5.99). The normalized value of Mardia’s index of multivariate kurtosis was 71.92. This indicated that the distribution was not multivariate normal and the SatorraBentler maximum likelihood parameter estimates with standard errors and a meanadjusted chisquare test statistic was used. In Mplus (Muthén & Muthén, 2004), the SBc2 is referred to as the MLM chisquare (Mplus 5.21 was used to conduct all analyses).

The Factor ModelsAn initial test of the twofactor model showed unsatisfactory fit for the overall sample, SBc2(134) = 353.92, p < .01, CFI = .88, RMSEA = .08, SRMR = .06. We explored improving model fit by examining items for redundancy and examining the model estimation results. Our conceptual framework and significantly correlated error estimates for some items suggested modifications.




Error terms of the items “How often do the kids in your school hit, kick, or push you in a mean way at school?” and “How often do the kids in your school hit you?” were highly correlated. Because of the similarity/redundancy between them, the latter was dropped from the overt factor. A second overt victimization item, “Say mean things to you,” correlated with other items and also loaded on the relational factor; because it measured a less precise set of behaviors it was also removed. After removing the two items, the revised model displayed adequate fit for data from the total sample (see Table 4). Standardized factor loadings for the overall twofactor model were positive and significant (.61 to .82; see Table 1). This model was also tested separately for each group; indices indicated adequate fit for all groups (Table 4).

We also evaluated onefactor and threefactor models (above). The twofactor model fit the data better than the onefactor model (onefactor estimates: c2 (104) = 283.05, p < .05, CFI = .89, RMSEA = .08, SRMR = .06). Fit for the threefactor model (overt, relational, and exclusion factors), was similar to that of the twofactor model (threefactor estimates: c2 (101) = 210.21, p < .01, CFI = .93, RMSEA = .06, SRMR = .05). To determine the best fitting model, we considered comparisons of the Akaike information criterion (AIC; Akaike, 1987) and the BIC Bayesian information criterion (Schwarz, 1978), as well as the collective difference in fit indices. Chisquare difference tests were not implemented because the two and threefactor models are not true nested models. In the comparison of twofactor and threefactor models, the

Table 4. Results for the TwoFactor Model for the Overall Sample, European Americans, Latinos, Boys, Girls, Fifth Graders, and Sixth Graders

Model c2 (df = 103) CFI RMSEA SRMR

Overall 234.99* .92 .07 .05Ethnic group European Americans 187.99* .90 .08 .06 Latinos 204.79* .89 .09 .06Gender group Boys 137.58* .95 .06 .05 Girls 206.78* .89 .08 .06Grade group Fifth graders 206.92* .89 .09 .06 Sixth graders 175.97* .91 .07 .06

Note: CFI = comparative fit index; RMSEA = root mean square error of approximation; SRMR = standardized root mean square residual.*p < .05.



Buhs et al. 187

AIC and BIC suggested that the threefactor model fit was not appreciably better than the twofactor model (2 vs. 3; AIC: 10942.65 vs. 10978.547; BIC: 11154.87 vs. 11126.17). In addition, the collective difference in the model fit indices was not remarkable (2 vs. 3: CFI .92 vs. 93; RMSEA .07 vs. .06; SRMR .05 vs. .05). However, there was a greater improvement in fit when comparing the one and twofactor models according to the information criterion indices (1 vs. 2; AIC: 11052.37 vs. 10978.55; BIC: 11225.09 vs. 11154.87) as well as the collective fit indices (1 vs. 2: CFI .88 vs. 92; RMSEA .08 vs. .07; SRMR .06 vs. .05). Given the greater support and parsimony of the twofactor model, it was retained for all subsequent analyses.

Measurement InvarianceEthnic groups. Results of all measurement invariance analyses are summa

rized in Table 2. Fit indices for configural invariance indicated adequate fit for the model. A subsequent c2 difference test indicated that metric invariance could be assumed across the ethnic groups. Next, a test for strong invariance (constraining item intercepts be equal) returned a significant c2 difference test. Partial strong invariance was then tested, allowing four intercepts to be freely estimated across the European American and Latino groups. Modification indices suggested that two item intercepts (“Insult you in order to hurt you?” and “Not invite you to a party or social gathering when they know you want to go?”) were higher for European Americans and two others (“Choose not to sit near you when you want to sit with them?” and “Hit, kick, or push you in a mean way at school?”) appeared higher for Latinos (ps < .05). When these intercepts were freely estimated, this partial strong invariance model demonstrated fit that was not significantly different from the metric invariance model. Finally, the last model tested partial strict invariance by imposing additional cross ethnicgroup equality constraints on all corresponding item error variances (except those of the three items identified above). The overall partial strict invariance model indicated acceptable model fit, and the c2 difference test between this model and the partial strong invariance model was not significant. The partial strict invariance model was retained as the bestfitting model.

Gender groups. A test for configural invariance across gender groups indicated adequate model fit (see Table 2). The next model (testing metric invariance) constrained all factor loadings to be equal across groups. The c2

difference test showed a significant loss in fit for this model relative to the configural invariance model. Modification indices suggested that two item loadings (“Threaten to hurt or beat you up?” and “Hit, kick, or push you in a




mean way at school?”) were higher for boys (p < .05). Freely estimating these loadings produced a revised model of partial metric invariance that showed no significant improvement in fit relative to the configural invariance model. The partial strong invariance model was then estimated (excluding the two items identified above) and showed a significant loss of fit in relation to the metric invariance model. Modification indices suggested that one item intercept (“Stop talking to you or ignore you when they are mad at you?”) was significantly higher for girls (p < .05). Freely estimating this intercept produced a revised model of partial strong invariance that showed no significant improvement in fit relative to the metric invariance model. The final model constrained item error variances across groups to test strict invariance (except for the three items noted above). Results from the c2 difference test indicated that this model did not differ from the partial strong invariance model; that model was retained as the bestfitting model.

Grade-level groups. Fit indices for configural invariance indicated adequate fit for the twofactor model across the two grade groups (Table 2). Given configural invariance, metric invariance was tested and the results indicated no significant difference between the configural and metric invariance models (see Table 2). Next, for the strong invariance model, the c2 difference test showed a significant loss in fit relative to the metric invariance model. Modification indices suggested that one item intercept (“Push you around at school?”) was significantly higher for fifth graders (p < .05). Freely estimating this intercept produced a revised model of partial strong invariance that showed no significant improvement in fit relative to the metric invariance model. Finally, a c2 difference test compared the difference between the partial strong and partial strict (excluding the item above) invariance models and showed no significant difference in fit. The strict invariance model was thus retained as the bestfitting model for the gradegroup comparison.

Construct Validity EquivalenceAll groups. The invariance test of the latent factor means and correlations

indicated that both parameters were invariant across ethnic groups and the correlation was invariant for all three sets of comparison groups. However, latent factor means were not invariant across gender and grade groups; a significant c2 difference test was returned for both tests. For gender groups, modification indices suggested that both means be freely estimated for boys and for girls. The overt factor mean was significantly higher for boys and the relational factor mean was significantly higher for girls (ps < .05). For grade groups, modification indices suggested that the relational mean be freely



Buhs et al. 189

estimated for fifth and sixth graders. The relational factor mean was significantly higher for fifth graders than sixth graders (p < .05).

Except for anxiety in the ethnic group construct equivalence analyses, all construct intercepts and slopes were invariant across all groups (European American/Latino, boys/girls, and fifthgrade/sixthgrade; see Table 3 for a summary). Modification indices suggested that the intercept for anxiety was significantly higher for European Americans (p < .05), and this intercept was allowed to vary between ethnic groups. For all groups in the ethnicity, gender and grade analyses, the following path coefficients were positive and significant: relational victimization and anxiety (bs ranged from .15 to .20); relational victimization and depression (bs ranged from .39 to .49); relational victimization and relational victimization, peer nominations (bs ranged from .17 to .25); overt victimization and depression (bs ranged from .32 to .41); and overt victimization and overt victimization peer nominations (bs ranged from .14 to .27). The path coefficient between overt victimization and anxiety was not significant in any of the groups.

DiscussionThe results from this study present several important contributions to the literature on victimization by examining the crossgroup equivalence of a selfreport measure of victimization. The twofactor CFA model fit our data well and indicated that overt and relational factors similar to those established by Crick and colleagues were replicated for the entire sample and across gender, ethnic, and gradelevel groups. This suggests that similar victimization constructs were tapped by this instrument for these groups. These findings extend previous research by examining this factor structure in Latino and European American groups, across the fifth and sixth graders, and with boys and girls. Our analyses provided further evidence that these constructs remain useful avenues for investigations of victimization for these groups. This examination of the SVEX instrument also demonstrated that the current set of items performed similarly across all of the groups examined (at the level of partial strong invariance or greater).

In addition, the social exclusion items added to the instrument also performed well across groups and these findings suggest that the addition of these items may allow researchers to accurately tap these important victimization behaviors. Exclusion may also prove to be viable as a distinct factor/construct (note that the threefactor model also fit the data well here) if future studies present additional evidence of distinct predictive relations to adjustment outcomes or other unique attributes relative to relational victimization.




Exclusion may, for example, be uniquely predictive of adjustment outcomes such as internalizing problems—prior findings have indicated that relational victimization, including limited indices of exclusion, independently predicted internalizing outcomes (relative to overt victimization). It is possible that, within studies that include larger subgroups of participants, more precise examinations of predictive relations would support a distinct role for exclusion, especially in more collectivist groups.

The construct validity equivalence information we gathered here indicated that the relational and overt factor scores predicted the internalizing outcomes and peer nominations of relational and overt victimization similarly across all of the groups (overt victimization, however, did not predict anxiety in any group) and there were no significant differences in slope or intercept across the models. The links to internalizing symptoms were, in general, consistent with prior findings (e.g., Crick & Grotpeter, 1996; Hoglund, 2007) and indicated an acceptable level of invariance. The finding that overt victimization did not predict anxiety may indicate that, in these groups, feelings of social anxiety are more dependent on other aspects of peer relationships (e.g., relational victimization). Some evidence suggests (Hoglund, 2007) that relational victimization is a more consistent predictor of internalizing problems in the age groups examined here (see the limitations section, below, for a discussion of the meanlevel differences in overt and relational victimization for girls and boys). In total, these findings suggest an acceptable level of equivalence across the groups examined here.

The study and our findings had several important limitations. It is important to note that, though more rural schools and students tend to be an understudied population (especially rural non–European American groups), the findings here may not generalize to youth from larger urban areas. The small cities in this study each supported a few elementary schools and a single middle school. Students in these communities were likely more familiar with each other (on average) than students from larger schools/districts and this may have affected the strength of linkages between relational victimization and the validity outcomes—in contrast to the findings of Pelligrini and colleagues (Pelligini & Bartini, 2000), greater familiarity among the youth in these schools could foster more stable peer networks that might ameliorate victimization and related effects relative to youth in larger schools (also consistent with Bukowski & Sippola, 2001).

More extensive investigations of victimization effects within/across these groups will also be necessary to more fully understand potential links to important adjustment outcomes such as academic achievement and externalizing disorders. If victimization is linked to disengagement and victimization



Buhs et al. 191

effects are stronger when it originates within one’s own group, then accurate assessments of these linkages across the groups examined here will be key to creating schoolbased, culturally sensitive interventions designed to improve school adjustment.

In addition, while the SVEX instrument and scales demonstrated an acceptable level of equivalence here, invariance/equivalence was not uniform in all comparisons or necessarily displayed at the highest levels (several items displayed different item intercepts across groups). It is not unusual to find this level of variance in relatively complex instruments, but this may have indicated items did not function identically across groups and further examinations should be conducted. At least 80% of the items demonstrated strict invariance (the most restrictive conditions) across the groups, however, and this proportion will likely produce reliable results (Gregorich, 2006, p. 87). Finally, although the construct validity evidence generally displayed an interpretable pattern here and suggested equivalence, a single meanlevel difference emerged and indicated that boys reported greater levels of overt victimization and that girls displayed greater levels of relational victimization. Although not invariant, this finding is consistent with other evidence of similar patterns (e.g., Crick & Grotpeter, 1995) and is also consistent with theoretical frameworks (see Underwood, 2003, for a discussion). This instrument also likely displayed the limitations of selfreports relevant to measuring victimization, especially for studies relying on selfreported outcomes. The models predicting associations among victimization and the internalizing symptoms examined here were a good example of links where the magnitude of associations may be inflated due to sharedsource variance/response biases.

Finally, and perhaps most important, though there is a significant body of research surrounding potential socialization differences linked to Latino youth, families, and communities, it is essential to design investigations that explicitly tap relevant aspects of these constructs (e.g., individualist/collectivist socialization patterns, family behaviors, etc.) and directly evaluate links to peer processes and outcomes. This may be especially important in relatively more isolated rural areas where a smaller Latino community may be even more interdependent than is typical in larger urban areas. Latino youth in this sample reported feeling more isolated than they had in the western and southwestern urban contexts many of them had migrated from—such feelings, if present, may affect the effects of own as well as othergroup victimization.

Despite these limitations, this study demonstrated sophisticated CFA and structural equation modeling (SEM) techniques that can be used within developmental research to more closely examine the equivalence of instruments




across groups. To our knowledge, this study represents the first empirical examination of factorial invariance and construct validity equivalence across ethnic and gradelevel groups for a measure of aggression or victimization .The findings also demonstrated the utility of this particular instrument with the groups examined and indicated that it displayed acceptable levels of equivalence across gender, grade level, and Latino/European American youth. Conflicting findings in current literature regarding group differences in victimization may in part be due to shortcomings of the instruments used (see Graham et al., 2009; Underwood, 2003, for discussions of conflicting findings).

Finally, the availability of a selfreport instrument that allows for better representation and reporting of exclusion behaviors (in groups where these behaviors may emerge as central aspects of victimization) will allow youth to more accurately represent their peer experiences. Exclusion is an important part of relational victimization for youth and it is likely to be highly salient to the peer group as well as the victim. Consistent relational victimization and exclusion by group behaviors as described by items in this measure would be a very visible marker of social status (especially if it originates from members of one’s own group). This, along with other types of victimization, appears likely to contribute to adjustment processes by directly limiting youths’ access to peer academic and social–emotional support. The relative role of exclusion in victimization and related adjustment thus becomes central to interventions tailored for greater effectiveness in specific peer contexts (e.g., gender and ethnic groups). Accurate instruments tapping relevant victimization behaviors will be an important component for the development and evaluation of such interventions and related research.

Acknowledgment

The authors wish to thank the school districts and students and the University of Nebraska Latino Research Initiative for their support.

Declaration of Conflicting Interests

The authors declared that they had no conflicts of interests with respect to their authorship or the publication of this article.

Funding

The authors declared that data analyses and manuscript preparation was supported by Nebraska Tobacco Settlement Biomedical Research Enhancement Funds.

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Bios

Eric S. Buhs is an associate professor of Educational Psychology at the University of Nebraska–Lincoln and conducts research examining peer relations and links to academic and psychological adjustment. His recent work has focused on crossethnic differences in peer relations and school adjustment for students in the Great Plains region.

Meredith McGinley is a recent graduate of the Psychology program at the University of Nebraska–Lincoln and is currently a visiting senior research specialist in health sciences in the Department of Psychiatry at the University of Illinois at Chicago. She has focused her research on children’s social development and on the role of prosocial behavior.

Michael D. Toland is recent graduate of the quantitative, qualitative, and psychometric methods program in educational psychology at the University of Nebraska–Lincoln and is currently an assistant professor at the University of Kentucky in the Department of Educational, School, and Counseling Psychology. His work has applied structural equations modeling and measurement techniques to a broad range of developmental and educational research.



Overt and Relational Victimization in Latinos and European Americans: Measurement Equivalence Across Ethnicity, Gender, and Grade Level in Early Adolescent Groups

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