PCC ethnic Racial Identity & Friendship in Early Adolescence Questions

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Child Development, May/June 2017, Volume 88, Number 3, Pages 710–724
The title for this Special Section is Context and Ethnic/Racial Identity, edited by
Eleanor K. Seaton, Stephen Quintana, Maykel Verkuyten, and Gilbert C. Gee
Ethnic-Racial Identity and Friendships in Early Adolescence
Deborah Rivas-Drake
Adriana J. Uma~
na-Taylor and David R. Schaefer
University of Michigan
Arizona State University
Michael Medina
University of Michigan
The current study examined how adolescents’ ethnic-racial identity (ERI) informed the demographic diversity
of their friendship network (Goal 1) and the extent of similarity between adolescents’ and their friends’ ERI
(Goal 2). Participants were sixth and seventh grade students (N = 353; Mage = 11.88, SD = .73; 50% girls; 29%
African American, 31% White, 13% Latino) in the Midwestern U.S. Results from longitudinal cross-lagged
models (Goal 1) indicated that having more diverse friendships at T2 was associated with greater T3 ERI
exploration among all youth. In addition, boys who reported higher ERI resolution at T1 had more diverse
friendships at T2. Furthermore, ﬁndings from longitudinal social network analyses (SNA; Goal 2) suggested
that inﬂuence drove similarity between adolescents and their friends in ERI exploration and resolution.
Similar to many Western countries, the United
States is becoming more ethnically and racially
diverse. In such contexts, understanding the process
by which youth form friendships with diverse peers
in school settings will become increasingly important. This is particularly true because peers comprise a critical group of signiﬁcant others in the
lives of adolescents (Brown & Larson, 2009); having
more friendships with individuals from other ethnic-racial groups has been associated with better
youth adjustment (Davies, Tropp, Aron, Pettigrew,
& Wright, 2011; Graham, Munniksma, & Juvonen,
2014; Munniksma & Juvonen, 2012); and school is
where youth have the potential to spend their time
engaging with peers of ethnically diverse backgrounds. Moreover, just as identity formation is a
salient and normative task of adolescence (Erikson,
1968), the development of one’s ethnic-racial identity (ERI) is now recognized as a salient and important aspect of normative development among youth
The authors gratefully acknowledge Dr. Robert J. Jagers at the
University of Michigan as well as The Origins Program and the
participating school for their partnership in this research.
Correspondence concerning this article should be addressed to
Deborah Rivas-Drake, University of Michigan, 530 Church Street,
Ann Arbor, MI 48109. Electronic mail may be sent to drivas@umich.edu.
in diverse societies (Williams, Tolan, Durkee, Francois, & Anderson, 2012) that can promote positive
psychosocial functioning and academic adjustment
(Rivas-Drake et al., 2014). Although youth in ethnically heterogeneous school contexts have opportunities to form diverse friendships, the extent to which
they do so may depend on their emerging ERI
beliefs, which are known to inform dispositions
toward ingroup and outgroup members (Phinney,
Cantu, & Kurtz, 1997; Whitehead, Ainsworth, Wittig, & Gadino, 2009). Accordingly, the current study
had two primary goals. First, we examined the
extent to which ERI predicted ethnic-racial demographic diversity of friendship networks over time.
Our second goal focused more speciﬁcally on how
youths’ ERI informed their selection of friends with
similar levels of ERI. Using social network analyses
(SNA), we tested the hypothesis that youth with
higher levels of ERI would be more likely to have
friendship ties with youth who had similarly high
levels of ERI.
© 2017 The Authors
Child Development © 2017 Society for Research in Child Development, Inc.
All rights reserved. 0009-3920/2017/8803-0003
DOI: 10.1111/cdev.12790
Ethnic-Racial Identity and Friendships
Ethnic-Racial Identity and Peer Relationships
Grounded in an Eriksonian framework of identity formation (Erikson, 1968; Marcia, 1994), and
Uma~
na-Taylor and colleagues’ (2014) conceptualization of ERI as a multidimensional, psychological
construct that encompasses the beliefs and attitudes
that individuals have about their ethnic-racial
group and the processes by which these develop
over time, the current study focused speciﬁcally on
youths’ exploration of their group membership and
resolution, or sense of clarity, about its meaning
(Uma~
na-Taylor, Yazedjian, & B
amaca-G
omez,
2004). The ERI components of exploration and resolution capture the developmental processes by
which individuals explore their ethnic background
and resolve the meaning of their ethnicity, respectively (Uma~
na-Taylor et al., 2004). These components of identity formation are important for
ensuring that individuals develop a sense of self
that gives them conﬁdence to make decisions about
the future and to develop positive interpersonal
relationships (Erikson, 1968). ERI exploration
expands knowledge of one’s group, and ERI resolution provides for a sense of clarity regarding one’s
group membership. As elaborated below, ERI
exploration and resolution have been associated
with numerous indicators of positive youth development; we argue that these beneﬁts may extend to
the realm of adolescents’ peer relationships.
An abundance of empirical work has provided
support for the beneﬁts that a more achieved ERI
(i.e., higher exploration, higher resolution) can have
on adolescents’ adjustment. For example, studies
with pooled ethnic samples have found exploration
and resolution to be uniquely and positively associated with self-esteem among ethnic minority high
school and college students (Uma~
na-Taylor et al.,
2004). With African American youth, higher exploration was associated with lower delinquency in
early and middle adolescence (French, Seidman,
Allen, & Aber, 2006), and both exploration and resolution were positively associated with self-esteem
among college students (Uma~
na-Taylor & Shin,
2007). Similarly, with Latino youth, exploration and
resolution were each uniquely and positively associated with self-esteem among high school (Uma~
naTaylor, Vargas-Chanes, Garcia, & Gonzales-Backen,
2008) and college (Uma~
na-Taylor & Shin, 2007) students. Among Asian American college students,
resolution was positively associated with selfesteem (Uma~
na-Taylor & Shin, 2007). Few studies,
however, have examined the links between ERI and
adolescents’ peer relationships. Understanding the
711
extent to which ERI informs peer network characteristics, especially diversity of friendships, is essential given that friendships with diverse peers are
known to predict important adjustment outcomes
for both ethnic minority (Chen & Graham, 2015;
Graham et al., 2014) and ethnic majority youth
(e.g., Vervoort, Scholte, & Scheepers, 2011; Wilson
& Rodkin, 2013).
Adolescents’ ERI may inform the ethnic-racial
diversity of their friendship network. New agegraded developmental competencies (e.g., gains in
social and cognitive maturity) provide youth with
tools with which to navigate their ever-expanding
social world (Uma~
na-Taylor et al., 2014). Indeed,
during adolescence youth are often exposed to an
expanded array of peers within the middle school
context. As adolescents explore their growing social
world with increasing autonomy, their own ERI
and the ways in which they choose to relate to their
social groups become more salient. Instead of conceptualizing race and ethnicity as purely literal and
observable categories as is the case in childhood
(Quintana, 1998), adolescents can consider more
complex social differences between themselves and
their peers. This shift to a more nuanced understanding of the ERI throughout adolescence is normative, and it is possible that youth who have
engaged in greater exploration about their ethnicracial background, and who have a more conﬁdent
and secure sense of ERI, may ﬁnd it easier to
engage with and befriend a more diverse group of
individuals. It is important to note the alternative,
that greater identiﬁcation with one’s ethnic-racial
group might engender greater outgroup prejudice
or derogation and thus impede intergroup friendship, but a plethora of studies have clariﬁed that
this occurs only in conditions of negative emotion
or threat (cf. Brewer, 2001, 2010). Moreover, consistent with notions from identity theory (Erikson,
1968), adolescents who have explored their ethnicracial background or feel more secure about this
aspect of their identity may be less likely to limit
their friendship networks to ingroup peers because
their self-conﬁdence and comfort with this social
identity may result in a relatively greater level of
comfort in establishing ethnically diverse friendships. If so, then having greater ERI exploration
and resolution would facilitate, rather than hinder,
diverse friendships.
Although previous work has not examined this
speciﬁc possibility, on a closely related topic, Phinney et al. (1997) found that youth from an ethnically diverse sample who reported higher ERI
(exploration and resolution composite) evaluated
712
Rivas-Drake, Uma~
na-Taylor, Schaefer, and Medina
outgroup members more positively. Most recently,
Whitehead et al. (2009) found that higher ERI
exploration was associated with more positive attitudes toward outgroups among Asian American,
Latino, and White ninth grade students. We contend that positive attitudes toward individuals from
a broad range of ethnic-racial backgrounds likely
result in youth with a more advanced ERI having
more diverse friendship networks. Accordingly, we
expected that, given the availability of such opportunities, adolescents who had explored or had a
clearer sense of their ERI would be more likely than
their counterparts with lower ERI to seek diverse
friendships. Beyond the selection of a more ethnically and racially diverse peer group (i.e., in terms
of ethnic-racial demographic characteristics), however, youth also may more discriminately select
friends based on similar levels of ERI.
Adolescents’ ERI and Peers’ ERI: Do Birds of a Feather
Flock Together?
Graham et al. (2014) recently demonstrated that
exposure to diversity is beneﬁcial to youth but only
to the extent that students take up opportunities to
make friendships across ethnic groups. Importantly,
some work suggests that more diverse schools create more opportunities for diverse friendship ties
but can lower the odds of such ties (Hamm, 2000;
Moody, 2001). In Graham et al.’s study, adolescents
in ethnically diverse schools had greater opportunities to engage in cross-ethnic friendships at the
classroom level, but it was youth who reported
having cross-ethnic friendships who then reported
signiﬁcantly fewer feelings of vulnerability (i.e.,
more safe, less victimized, and less lonely). Thus, as
the literature on adolescent intergroup relations
suggests (cf. a recent review by Thijs & Verkuyten,
2014), structural diversity is a necessary but insufﬁcient condition for individuals to beneﬁt from exposure to such diversity (see also Pettigrew, 1998).
It is possible that adolescents are initially drawn
to one another based on superﬁcial similarities (e.g.,
perceived shared group membership), but more
sophisticated identity processes (i.e., ERI beliefs)
become important for sustaining the friendship.
Indeed, in a cross-sectional study of college student
friendship dyads, Syed and Juan (2012) found that
friends demonstrated similarity in both ERI exploration and ERI commitment. As such, our second
goal was to examine the extent to which youths’
ERI informed their selection of friends with particular ERI beliefs. Although there is abundant sociological evidence of ethnic-racial demographic
homophily in social networks (McPherson, SmithLovin, & Cook, 2001; Wimmer & Lewis, 2010),
there is comparatively less knowledge about homophily with regard to ERI, net of homophily as a
function of ethnic-racial group membership.
Sociodemographic homophily (e.g., of race/ethnicity category membership) may occur in tandem
with identity homophily (i.e., in ERI beliefs), but
these two dimensions are not isomorphic. Based on
prior ﬁndings indicating that youth gravitate
toward and attract peers with similar characteristics
(McPherson et al., 2001), we hypothesized that adolescents are more likely to seek friendships with
youth who had similar levels of ERI versus those
with dissimilar levels of ERI.
However, homophily among friends has been
demonstrated to be a function of both selection, such
that individuals with prior similarity select each
other as friends, and socialization, whereby individuals inﬂuence one another via continued exposure to
each other (Kandel, 1978). Peer socialization theorists, more speciﬁcally, underscore the transactional
nature of such inﬂuences (e.g., Brown, Bakken,
Ameringer, & Mahon, 2008). Moreover, Erikson
(1956) theorized that youths’ identity development
is relational, as youth “learn to be most [themselves]
where [they] mean most to others—those others, to
be sure, who have come to mean most to [them]”
(p. 57). Consistent with this idea, a number of
empirical studies suggest that peers may regulate
the expression of ERI among adolescents (e.g., Carter, 2005; Lee, 1996; Pollock, 2004; Syed & Juan,
2012; Way, Santos, Niwa, & Kim-Gervey, 2008; Yip,
Douglass, & Shelton, 2013), but none have been
able to demonstrate such inﬂuence while accounting for selection processes. The current study examined the alternative possibility that adolescents’ ERI
would be informed by peers’ ERI while taking into
consideration factors that informed their friendship
formation in the ﬁrst place. Our longitudinal
design, coupled with a social network analytic
approach, thus enabled a relatively more rigorous
examination of whether selection or socialization
processes best explained potential homophily in
friends’ ERI.
The Current Study
In sum, the current study was designed to
address two related, yet unique questions. First, to
what extent do adolescents’ ERI exploration and
resolution inform the demographic ethnic-racial
diversity of their friendship network? To do so,
Goal 1 focuses on examining the role of ERI in
Ethnic-Racial Identity and Friendships
friendship diversity using Simpson’s diversity
index, which is increasingly used to measure compositional diversity in developmental science. This
index does not simply capture diversity in terms
of minority versus majority representation (or invs. out-group) but rather estimates the extent to
which diversity is a function of increased representation of multiple groups. Second, beyond
demographic characteristics, to what extent do
adolescents select friends who are more similar to,
rather than different from, them with respect to
their psychologic, subjective sense of ERI exploration or resolution? Given prior work noting
mean level gender differences in ERI (e.g., Spencer, Icard, Harachi, Catalano, & Oxford, 2000), the
current study included gender as a control in all
analyses. In addition, because ethnic-racial salience
can vary signiﬁcantly based on ethnic-racial
minority versus majority status (e.g., Vervoort
et al., 2011), our analyses for Goal 1 examined
potential moderation by majority/minority status.
Finally, our analyses for Goal 1 explored moderation by grade cohort. Our SNA for Goal 2 also
took into consideration gender, ethnicity/race, and
grade cohort.
713
American, 31% are White, 4% are other, and 13%
are multiracial.
Procedure
Data were collected as part of the school’s efforts
to understand social, academic, and emotional
development among its students given it was
implementing a social emotional learning approach
to support a positive school climate. Time 1 (T1)
data were collected during Spring of 2014; Time 2
(T2) and Time 3 (T3) data were collected 6 months
and 1 year later during Fall of 2014 and Spring of
2015, respectively. Student surveys were administered by teachers during homeroom; students were
assured of the conﬁdentiality of their responses
(i.e., with the statement that “your individual
answers will be private and will never be shared
with anyone at this school” on the survey cover
sheet). Surveys were de-identiﬁed such that all
names were removed and replaced with ID codes
by an external consultant who is not afﬁliated with
the university research team or with the school.
After this de-identiﬁcation process, the surveys
were given to the research team for analysis. The
project was determined to be exempt by the University of Michigan IRB.
Method
Participants
This study draws on data collected at a Midwestern middle school. Of the initial full sample at Time
1 (N = 353), retention rates across waves were 87%
at Time 2 and 80% at Time 3. For Goal 1, 20 cases
were dropped because they were missing data for
ethnicity and gender, which were needed for
planned multigroup comparisons, and two additional cases were dropped because they were missing data on all ERI and friendship variables. The
analytic sample for Goal 1 (cross-lagged models)
thus includes 331 students in sixth (n = 167) or seventh (n = 164) grades (Mage = 11.88, SD = .73). This
sample is socio-demographically diverse: 50% are
girls; 8% are Asian American and Paciﬁc Islander,
29% are African American, 13% are Latino, 1% are
Native American, 31% are White, 4% are other, and
14% are multiracial. For Goal 2, 13 cases were
dropped because they did not have valid ERI data
at any wave. Thus, this analytic sample comprises
340 students in sixth (n = 171) or seventh (n = 169)
grades (Mage = 11.87, SD = .72). This sample is also
socio-demographically diverse: 48% are girls; 8%
are Asian American and Paciﬁc Islander, 28% are
African American, 13% are Latino, 1% are Native
Measures
Ethnic-Racial Identity
ERI exploration and resolution were assessed
with the Ethnic Identity Scale (Uma~
na-Taylor et al.,
2004). Exploration items inquire about the extent to
which youth have engaged in behaviors to learn
more about their ethnicity (seven items; e.g., “I
have participated in activities that have taught me
about my ethnicity;” T1 a = .82; T2 a = .85; T3
a = .88). For resolution, items asked youth to indicate the extent to which they had a sense of clarity
regarding their ethnicity (four items; e.g., “I have a
clear sense of what my ethnicity means to me;” T1
a = .90; T2 a = .93; T3 a = .92). All items were
scored on a 4-point Likert-type scale (1 = Does not
describe me at all, 4 = Describes me very well), and
higher mean values on each scale indicate greater
exploration and resolution, respectively.
Friendship Diversity
Youth were asked to list their friends, or who
they “hang out with and talk to” in their grade,
which is a common name generation approach
714
Rivas-Drake, Uma~
na-Taylor, Schaefer, and Medina
among youth in this age group (Ryan, 2001); this is
notably the kind of friendship identiﬁed by Davies
et al. (2011) as being most consistently related to
intergroup dynamics. Students could list “as many
or as few” names; thus, there were no limits on
nominations. The ethnic or racial category for each
student listed as a friend was then used to calculate
a proportion of each ethnic-racial category represented in the friendship group (e.g., proportion
White, proportion Latino, etc.). These proportions
were then used to calculate Simpson’s index of
diversity in their ethnic-racial composition, as
described in Juvonen, Nishina, and Graham (2006).
This is a measure of entropy, in that it assesses both
the number and evenness of groups represented in
a given context (Page, 2010). Substantively, this
index reﬂects the relative probability that two randomly selected students are from different ethnicracial groups. The possible range is 0–1, and higher
scores indicate more diversity.
Demographic Information
Ethnic-racial category was obtained from youths’
self-reported information. In the demographic portion of the questionnaire and in an open-ended
question just before items pertaining to ERI,
students were asked to indicate with which
ethnic-racial labels they identiﬁed (multiple
responses permitted). From these responses, ethnicracial categories were identiﬁed that corresponded
to six categories available in the U.S. Ofﬁce of Civil
Rights 2011–2012 report of school demographics
(http://ocrdata.ed.gov/). The seventh category
(“Other”) was added to accurately reﬂect students’
self-identiﬁcation with a category other than the
ﬁrst six (e.g., “Mixed”). Majority/minority status
was dummy-coded such that a 1 = White and
0 = all others. Gender was also reported by students and coded 1 for male and 0 for female. Grade
level was obtained from school records; each grade
level was coded as 1 (i.e., sixth, seventh) and 0 for
all else, resulting in two dummy codes.
Analysis Plan
Goal 1
Our ﬁrst goal was to examine theprospective
associations of youths’ ERI with the demographic
(ethnic-racial) diversity of their friends. A crosslagged model tested the association of prior ERI on
later friendship diversity. Data were analyzed using
Mplus 7.2 (Muthen & Muthen, 2015), and full
information maximum likelihood was used to handle missing data. We examined variability by majority/minority group status, cohort, and gender. As a
preliminary step, we conducted a multigroup analysis with majority/minority group status using the
dummy code for “White” (1 = White, 0 = all other
groups) as the indicator of majority status. We then
conducted a multigroup analysis for each ERI model
to examine differences by cohort using a dummy
code for grade at T1 (1 = seventh, 0 = sixth). Finally,
we conducted a multigroup analysis to examine differences by gender using a dummy code (where
1 = male, 0 = female). For each multigroup analysis,
we started with a model that allowed all the parameters to vary freely and then compared it with a
model that constrained all coefﬁcients to be equal; if
this test indicated that this assumption of equality
was untenable, we then tested models that sequentially constrained the parameters of the key study
constructs to be equal across groups. We conducted
chi-square difference tests to assess whether the ﬁt
of a constrained model was signiﬁcantly different
from those in which parameters were allowed to
vary freely across groups. A signiﬁcant change in v2
suggests that the given equality constraints across
groups are untenable. In all analyses, we followed
recommended thresholds of .90 for comparative ﬁt
index (CFI) and a standardized root mean square
residual (SRMR) and root mean square error of
approximation (RMSEA) of < .05 with a 90% conﬁdence interval < .08 for RMSEA (Hu & Bentler, 1999; Kline, 2005) to assess ﬁt. Goal 2 Our second goal was to explore the extent to which early adolescents tended to select friends who were similar to them in terms of their psychologic, subjective sense of ERI (i.e., exploration and resolution). To do so, we estimated a series of stochastic actor-based models (SABMs; Snijders, van de Bunt, & Steglich, 2010). SABMs permitted us to examine the extent of homophily on ERI exploration and resolution among friends while controlling for friend selection on other important characteristics (e.g., ethnicity/race) and possible peer inﬂuence on ERI. We provide a brief overview of the SAB model here and point the reader to the Appendix for more detailed information on model speciﬁcation. Our SAB model has two functions: one to model network change and the other to model change in ERI. The network function treats each dyad as the unit of analysis and estimates the liklihood of observing a Ethnic-Racial Identity and Friendships tie based upon several effects representing individual and network properties. The key effect of interest is whether ties are more likely in dyads comprising youth who are similar in ERI. In estimating this effect we control for several other friend selection processes that could also promote friendships among youth with similar ERI, among them similarity on race/ethnicity, reciprocity, and triad closure. Simply observing similarity in ERI among friends is not sufﬁcient to infer homophilous selection because such similarity could be a product of peer inﬂuence. The ERI function controls for the possibility that youth inﬂuenced one another’s ERI. The ERI function predicts each youth’s level of ERI using friends’ ERI and several other characteristics that might affect ERI (e.g., one’s ethnicity/race, mother’s immigration status, gender). In this manner, the SABM allows for endogenous change in both ERI and friendships, enabling us to differentiate the effects of selection and inﬂuence while controlling for confounding processes. Data were analyzed using the RSiena function within R (Ripley, Snijders, Boda, V€ or€ os, & Preciado, 2015). To prepare the data for the SABMs, ERI exploration and resolution were recoded into ordinal measures, which was necessary for the SABM to estimate their change across waves (Ripley et al., 2015). Speciﬁcally, we rounded ERI values to the nearest integer, creating a measure that ranged from 1 to 4. Cases missing data on exploration and resolution were coded as missing and retained during model estimation using standard SABM imputation procedures (Huisman & Steglich, 2008). We estimated a joint model for students in sixth and seventh grade. This approach respects that ties only exist between students in the same grade but constrains effects to be equal for each grade thereby maximizing power. As part of our follow-up diagnostics we tested whether ERI effects differed in strength between grades (and found no such differences). We performed additional diagnostics to address potential time heterogeneity and ensure adequate goodness of ﬁt. Results Goal 1: Examination of Cross-Lagged Models for ERI and Friendship Diversity Preliminary Results Youth reported having engaged in ERI exploration (T1 M = 2.59, SD = .69; T2 M = 2.67, SD = .71; and T3 M = 2.62, SD = .79) and having 715 somewhat high feelings of ERI resolution (T1 M = 2.92, SD = .82; T2 M = 3.04, SD = .81; and T3 M = 2.98, SD = .82). Friendships were also somewhat diverse on average (T1 M = 0.51, SD = .22; T2 M = 0.58, SD = .23; and T3 M = 0.66, SD = .19). At the bivariate level, T1 exploration was not signiﬁcantly correlated with T1 friendship diversity (r = .09, p = .15) but was signiﬁcantly associated with T2 friendship diversity (r = .16, p = .02); T2 exploration was signiﬁcantly correlated with friendship diversity at T2 (r = .28, p < .001) but not at T3 (r = .08, p = .28). T3 exploration was not signiﬁcantly correlated with friendship diversity at T3 (r = .08, p = .24). T1 resolution was signiﬁcantly correlated with friendship diversity at T1 (r = .20, p = .001) and T2 (r = .24, p < .001). T2 resolution was signiﬁcantly correlated with friendship diversity at T2 (r = .35, p < .001) but not at T3 (r = .12, p = .09). T3 resolution was not signiﬁcantly correlated with T3 friendship diversity (r = .09, p = .18). Primary Results The cross-lagged model tested the cross-time association between ERI and friendship diversity (see Fig. 1). We ﬁrst compared the baseline model (freely estimated parameters) to a fully constrained model, which constrained all coefﬁcients to be equal across majority/minority status groups. The fully constrained model did not differ signiﬁcantly from the model in which hypothesized paths were allowed to vary freely (Dv2 = 31.97, Ddf = 26, p > .05). Therefore, we proceeded to test a multigroup model in which we used grade cohort as the
grouping variable.
Our initial test of model constraints suggested it
was not tenable to constrain all hypothesized paths
and covariances to be equal across grade groups
(Dv2 = 39.04, Ddf = 26, p < .05); therefore, we proceeded to test models in which we sequentially constrained each of the hypothesized paths. First, we examined models in which we constrained the T1 exploration?T2 friendship diversity, T1 resolution path?T2 friendship diversity, T2 exploration?T3 friendship diversity, and T2 resolution?T3 friendship diversity paths to be equal across grade cohorts, respectively; ﬁndings of v2 difference tests for each of these models indicated that we could constrain these paths to be equal (T1 exploration? T2 friendship diversity: Dv2 = 1.27, Ddf = 1, p > .05;
T1 resolution?T2 friendship diversity: Dv2 = 1.27,
Ddf = 2, p > .05; T2 exploration?T3 friendship
diversity: Dv2 = 2.43, Ddf = 3, p > .05; T2 resolution?T3 friendship diversity Dv2 = 2.45, Ddf = 4,
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Rivas-Drake, Uma~
na-Taylor, Schaefer, and Medina
Figure 1. Relationship of ERI exploration (a) and resolution (b) with friendship diversity (n = 331).
Note. Dashed lines represent nonsigniﬁcant paths. Unstandardized coefﬁcients and standard errors shown. When parameters were
free to vary across groups, two coefﬁcients are presented. Covariances among ERI dimensions within and across time and between
ERI and friend diversity within each timepoint were also included in the models but are not shown for ease of presentation.
**p < .01. p > .05). Finally, we examined models in which we
constrained the reverse paths from friendship diversity-to-ERI to be equal across cohorts. Results of the
v2 difference tests for these models respectively suggested that each of these four diversity-to-ERI paths
could also be constrained to be equal across cohorts
(T1
friendship
diversity?T2
exploration:
Dv2 = 2.45, Ddf = 5, p > .05; T1 friendship diversity?T2 resolution: Dv2 = 2.64, Ddf = 6, p > .05; T2
friendship diversity?T3 exploration: Dv2 = 2.82,
Ddf = 7, p > .05; and T2 friendship diversity?T3
resolution: Dv2 = 5.35, Ddf = 8, p > .05).
Our ﬁnal multigroup comparisons modeled gender as the grouping variable. Our initial test of
model constraints suggested it was not tenable to
constrain all hypothesized paths and covariances to
be equal across gender (Dv2 = 54.85, Ddf = 26,
p < .05); therefore, we proceeded to test models in which we sequentially constrained each of the hypothesized paths as before. Results of v2 difference tests for each of these models indicated that we could constrain the T1 exploration?T2 friendship diversity path to be equal across gender (Dv2 = 1.35, Ddf = 1, p > .05). However, results of
the v2 difference test indicated that we could not
constrain the T1 resolution?T2 friendship diversity
path to be equal across gender (Dv2 = 14.48,
Ddf = 2, p < .05), and, thus, it was allowed to vary in subsequent models. Results of the T2 exploration?T3 friendship diversity (Dv2 = 1.58, Ddf = 2, p > .05) and T2 resolution?T3 friendship
diversity (Dv2 = 1.62, Ddf = 3, p > .05) tests indicated these paths could be constrained to be equal.
Finally, results of the v2 difference tests for the
diversity?ERI paths, respectively, suggested that
each of these four diversity-to-ERI paths could also
be constrained to be equal across cohorts (T1
friendship diversity?T2 exploration: Dv2 = 1.82,
Ddf = 4, p > .05; T1 friendship diversity?T2 resolution: Dv2 = 1.82, Ddf = 5, p > .05; T2 friendship
diversity?T3 exploration: Dv2 = 4.62, Ddf = 6,
p > .05; and T2 friendship diversity?T3 resolution:
Dv2 = 5.39, Ddf = 7, p > .05).
As shown in Figure 1, the ﬁnal model was one
in which stability, prior ERI?later friendship diversity, and prior friendship diversity?later exploration paths were constrained to be equal across
gender, with the exception of the T1 ERI resolution?T2 friendship diversity path. The ﬁnal model
ﬁt the data adequately (CFI = .96; RMSEA = .07
[.04, .11]; and SRMR = .08. Results indicated that
T1 ERI resolution was positively associated with T2
friendship diversity for boys (b = .32) but not for
girls (b = .10). In addition, T2 friendship diversity
was signiﬁcantly associated with T3 ERI exploration
(boys: b = .22, girls: b = .16) for all youth. Thus,
boys who earlier reported greater resolution of ERI
later had more diverse friends, and all youth who
Ethnic-Racial Identity and Friendships
had more diverse friends in the fall semester of the
subsequent academic year (T2) reported engaging
in more exploration of their ERI in the following
spring semester (T3).
Goal 2: Examination of ERI Homophily in Friendship
Table 1 reports results of SAB models for ERI
exploration and ERI resolution; because of space
constraints, all technical aspects and controls are
presented in the Appendix. We note that the model
for ERI exploration converged adequately, as indicated by an overall maximum convergence ratio of
.144. With regard to Goal 2, we begin with how
ERI exploration affected youths’ choice of friends.
As shown under the Network (friendship) function
section, the positive ERI ego effect indicates that
youth with greater ERI exploration selected more
friends overall (b = 0.11, SE = 0.04, p < .001) but, as indicated by the nonsigniﬁcant ERI alter effect, were no more or less likely to be selected as a friend. In terms of homophily on ERI exploration, the coefﬁcient for selection based on ERI similarity was in the hypothesized positive direction but not signiﬁcant (b = 0.20, SE = 0.18, p = .28). However, the estimate for peer inﬂuence (i.e., average similarity in the ERI function section) on ERI exploration was statistically signiﬁcant (b = 4.78, SE = 1.67, p < .001). These results indicate that youth and their friends tended toward similar levels of ERI exploration over time. The convergence in ERI exploration among friends was not a product of youth selecting friends with similar ERI, but rather, driven by youth adapting their exploration to the same level as that of their friends. We now turn to the results for ERI resolution, shown in the second column of Table 1; this model also converged adequately as indicated by an overall maximum convergence ratio of .134. ERI resolution had a positive effect (i.e., ERI ego term) on youths’ tendency to select friends (b = 0.12, SD = .04, p < .001) but no signiﬁcant effect (i.e., ERI alter term) on their likelihood of being selected as a friend. Here, again we ﬁnd evidence of homophily among friends but not as a function of selection. The coefﬁcient for ERI similarity in resolution for friend selection was not signiﬁcant (b = 0.29, SE = 0.19, p = .13). Rather, we found a statistically signiﬁcant positive effect of peer inﬂuence (average similarity) on ERI resolution (b = 4.60, SE = 1.54, p < .001). These results suggest that, over time, youth tended to have similar ERI resolution as their friends. This similarity occurred not because of youth selecting similar friends but instead was a 717 Table 1 Coefﬁcients and Standard Errors for ERI Friendship Stochastic ActorBased Models Exploration Resolution b SE b SE 0.786*** 0.830*** 1.090*** 0.772*** 0.136*** 0.075*** 0.025*** 0.037*** 12.749 11.916 16.814 11.780 1.988 2.128 0.331 0.306 0.917*** 0.790*** 1.207*** 0.855*** 0.136*** 0.078*** 0.024*** 0.037*** 0.018*** 0.213 0.019*** 0.038*** 0.329 0.038*** 0.029*** 0.212 0.028*** 0.034 0.041*** 0.184 0.037 0.044† 0.036*** 0.037*** 0.019*** 0.063 0.117 0.291 0.007 0.069 0.217 0.201 0.056 0.034† 0.037*** 0.192 0.038 0.043 0.037*** 0.038*** 0.019*** 0.024*** 0.064 0.025*** 0.043† 0.077 0.042† 0.071 0.112 0.075 0.454*** 0.215*** 0.318*** 0.400*** 0.072 0.180 1.666*** 0.160 0.370 0.225*** 0.323 0.507* 0.255 0.237 1.837 1.812 1.601 2.345 0.260 0.226 4.596 0.009 0.051 0.624 0.160 0.394 0.084 0.342 0.318*** 0.360*** 0.351*** 0.550*** 0.079*** 0.142 1.539*** 0.153 0.352 0.226*** 0.281 0.459 0.229 0.232 1.675 0.551*** Network (Friendship) function Rate, 6th grade T1–T2 12.838 Rate, 6th grade T2–T3 12.007 Rate, 7th grade T1–T2 16.803 Rate, 7th grade T2–T3 11.839 Outdegree 2.011 Reciprocity 2.136 Transitive triplets 0.329 Transitive reciprocated 0.302 triplets Number of actors at 0.208 distance 2 Indegree—popularity 0.332 (sqrt) Outdegree—activity 0.206 (sqrt) ERI alter 0.009 ERI ego 0.105 ERI similarity 0.200 Male alter 0.011 Male ego 0.074 Male same 0.221 Race/ethnicity same 0.176 Transitive triplets 9 7th 0.059 grade T1–T2 Transitive triplets 9 7th 0.070 grade T2–T3 0.071 Transitive reciprocated triplets 9 6th grade T2–T3 Male same 9 7th grade 0.103 T2–T3 ERI function Rate, 6th grade T1–T2 2.248 Rate, 6th grade T2–T3 1.074 Rate, 7th grade T1–T2 1.418 Rate, 7th grade T2–T3 1.669 Linear shape 0.031 Quadratic shape 0.051 Average similarity 4.784 Male 0.114 Asian 0.087 Black 0.628 Latino 0.329 Other race 1.040 Multi-ethnic 0.014 Mother’s immigration 0.358 status Latino 9 7th grade 1.171 T1–T2 Latino 9 7th grade 1.047 T2–T3 Black 9 6th grade T2–T3 0.631† 0.690 Note. SE = Standard error. *p < .05. ***p < .001. †p < .10. 718 Rivas-Drake, Uma~ na-Taylor, Schaefer, and Medina product of youth adjusting their ERI resolution in accordance with their friends’ resolution. Discussion Given that school diversity has been shown to increase the salience of ERI (e.g., Yip et al., 2013), and interactions with diverse peers are known to predict important adjustment outcomes (Graham et al., 2014), the present study sought to elucidate how ERI exploration and resolution might inform friendship networks among youth in a heterogeneous setting. As noted in recent reviews, the developmental signiﬁcance of youths’ ERI during adolescence is well-established (e.g., Rivas-Drake et al., 2014; Uma~ na-Taylor et al., 2014). What is less clear is the role that speciﬁc dimensions of ERI play in youths’ engagement with signiﬁcant others in their everyday, proximal contexts. This is particularly the case as it regards the role of ERI in friendship networks in ethnically heterogeneous contexts such as the focal school in the present study. As discussed in detail next, the current ﬁndings shed light on the nuanced nature of how speciﬁc aspects of youths’ ERI can function as a lens through which youth experience their peer context, particularly in terms of their choices regarding with whom they spend their time and talk to at school. Furthermore, ﬁndings from the present study particularly underscore the critical role that context plays in ERI formation, as the ethnic-racial diversity of youths’ friendship networks signiﬁcantly predicted changes in ERI exploration over time, and there was strong evidence that youths’ ERI became more like their peers’ ERI over time, over and beyond what would be expected because of shared initial selection into the friendship and to homophily by ethnicity, race, gender, and other attributes. Our ﬁrst goal was to examine the extent to which youths’ ERI exploration and resolution, respectively, were prospectively associated with the demographic (ethnic-racial) diversity of their friends. Based on ERI development theory and models (Uma~ na-Taylor & Fine, 2004), we hypothesized that youth who were exploring or gaining clarity about their ERI may be more conﬁdent and comfortable in heterogeneous settings; our hypotheses, however, were only partially supported. We found that, among boys, higher ERI resolution was indeed prospectively related to having more diverse friends approximately 6 months later, suggesting that when ERI exploration and resolution are considered in tandem, resolution is a particularly salient predictor of friendship network diversity for boys. This sense of security in their ERI may facilitate boys’ ability to befriend others who are from different ethnic and racial groups. One possible mechanism may be that such youth are less prejudiced toward outgroups. This would be the case if having greater clarity about their own group does not necessarily imply ingroup bias but rather encourages youth to want to learn more about other groups, feel less anxiety about difference, or increase their perspective taking and empathy with outgroup members (see Pettigrew & Tropp, 2008). In addition, youth may be able to have strong ERI that does not necessarily impede intergroup contact if, for instance, the meaning of their ERI is one that can be inclusive of identiﬁcations with others along other dimensions (e.g., Brewer, 2010; Knifsend & Juvonen, 2012; Cameron, Rutland, Brown, & Douch, 2006). The capacity to navigate diversity in such ways seems especially critical in spaces in which there is potential for cross-group collaboration; youth who successfully interact with diverse ethnic-racial peers exhibit stereotype reduction (Smith, Boulton, & Cowie, 1993) and more positive intergroup attitudes (Cooper & Slavin, 2004). Although we did not ﬁnd a similar association for girls, an examination of descriptive statistics by gender revealed that, on average, girls tended to demonstrate higher friendship diversity in their peer group, and less variability on this construct, relative to boys (e.g., boys’ T2 M = 0.52, SD = .26; girls’ T2 M = 0.64, SD = .18); thus, it is possible that we were unable to detect a signiﬁcant association for girls, given the more limited variability. Given that the current study is the ﬁrst, to the best of our knowledge, to prospectively examine these associations over time, it will be important to test if these gender differences replicate in other samples. Our ﬁndings for Goal 1 also indicated that having more diverse friends at the beginning of the academic year was prospectively associated with increases in both boys’ and girls’ ERI exploration by the end of the academic year. Consistent with the notion that the context in which ERI is developing is crucial for informing salience of ERI and, in turn, adolescents’ engagement in identity-speciﬁc developmental processes such as ERI exploration (Uma~ na-Taylor & Shin, 2007), adolescents’ exposure to a more ethnically diverse friendship network may have prompted greater engagement in activities that helped youth learn more about their own ethnic-racial background. It is worthy of note that friendship diversity predicted increases in ERI exploration but not ERI resolution. This may be a Ethnic-Racial Identity and Friendships function of our focus on the period of early to middle adolescence, during which time youth are steeped in the preliminary stages of ERI formation in which they are increasingly being exposed to nonfamilial inﬂuences and to abstract concepts that they can more fully grasp, given increased cognitive abilities (Uma~ na-Taylor et al., 2014). Conceptually, this exposure is believed to result in more questioning and information seeking, as youth attempt to make sense of new experiences and to gain an understanding of how they ﬁt in to the world around them (Erikson, 1968). It will be interesting for future studies to examine if ﬁndings with samples capturing the developmental period of late adolescence demonstrate a comparable inﬂuence of friendship diversity on ERI resolution. These ﬁndings provide critical insights into ERI development during early to middle adolescence while raising new questions that encourage further exploration of potential directionality of ERI-peer relations. Of note, we found no grade cohort or majority/ minority status differences in the hypothesized paths of the cross-lagged models. The lack of grade cohort differences suggests that at this period (early adolescence) there may be fewer developmental differences in the posited relations than might be expected among older youth. However, the lack of majority/minority status differences appears to run counter to previous research on adolescents’ crossand same-group attitudes and friendship ties. For example, research has found racial differences in terms of how similarity in ERI related to friend selection among African American, Asian American, and European American adolescents in the U.S. (e.g., Hamm, 2000). Also, among Dutch adolescents, the proportion of ethnic minority students in a classroom is differentially related to minority and majority students’ same-group attitudes (e.g., Vervoort et al., 2011). Additional investigations are necessary to tease out how majority/minority status and ERI function synergistically in different types of contexts. Our second goal was to explore the extent to which early adolescents tended to choose friends who were similar to them in their psychologic, subjective sense of ERI (i.e., exploration and resolution), above and beyond their similarity on other demographic characteristics (e.g., ethnicity/race, gender). Overall, the results were supportive of homophily but not through the process of selection as we had posited. Rather, after accounting for important network structural features and individual-level covariates, SABM results suggested that friends’ ERI became more similar over time. In 719 short, although many did indeed “ﬂock together” along ethnic-racial lines as expected, members of the ﬂock inﬂuence each other’s subjective, psychologic sense of identity. This opens up possibilities for youth from different ethnic-racial groups to form bonds based on their shared engagement in the process of developing their identities rather than demographic categories that are relatively more superﬁcial. In addition, there are a number of ways such inﬂuence may potentially emerge: mutual regulation of ERI expression; implicit and explicit information regarding how to interpret ethnic-racial situations and dynamics, especially in school; and modeling of how ERI “should” be performed. Given that we are unable to determine precisely how peers inﬂuence one another’s ERI construction, future research should seek to unpack this further. Together, these complementary ﬁndings underscore the ways in which youths’ ERI plays a role in their agency among peers within the school setting. Depending on the degree to which they are exploring or ﬁnding clarity in their ERI, early adolescents are actively co-constructing this aspect of the self within the context of their friendships. Given the broad inﬂuences of peers on youth in school, exploring the extent of adolescents’ impetus in changing and broadening their friend network is critical in understanding their academic and social experiences. Furthermore, the ﬁnding that ERI exploration and resolution serve as dimensions of homophily for youth suggests considerable thoughtfulness in their friendship patterns, as information regarding their peers’ stage of ERI development is not as readily available as are other characteristics along which peer homophily is evidenced (e.g., race, ethnicity, age, and gender). Limitations and Future Directions A few important caveats are worthy of mention. First, the study focused on one school and although it was ethnically and racially diverse (with no single numerical ethnic majority group), the subsample sizes were not large enough to fully explore ethnicracial differences among minority groups (e.g., Black vis-a-vis Latino) in the cross-lagged models (e.g., Chen & Graham, 2015). In addition, the crosslagged models assessed change over 6 months and 1 year, which are developmentally appropriate lengths of time to observe change in early adolescents’ friendships (e.g., Chan & Poulin, 2007) but may not be a long enough period to observe change in their ERI. The cross-lagged modeling approach 720 Rivas-Drake, Uma~ na-Taylor, Schaefer, and Medina itself, though commonly used in developmental research, is also only one way to attempt to establish directionality, and as is the case for numerous longitudinal survey-based studies, it is limited by its reliance on correlational data. Indeed, as Leszczensky (2013) argued, a multiple-differencescore modeling approach may be a useful avenue in future research seeking to establish causal directionality using nonexperimental data (cf. Allison, 2009). Using this alternative modeling approach, Leszczensky (2013) found that, among Turkish ninth and 10th graders in Germany, change in national identiﬁcation did not signiﬁcantly predict change in the proportion of interethnic friendships, and change in the proportion of interethnic friendships also did not signiﬁcantly predict change in the national identiﬁcation. Future work on ERI and friendship diversity should continue to weigh the advantages and limitations of cross-lagged modeling as compared with other approaches in attempting to model causality. Furthermore, although drawing on data collected at a single school facilitated the collection of a fairly complete peer network, which is rare, the generalizability of the results is limited in this regard. It is not possible to assess the extent to which the present social network analytic ﬁndings, for instance, would replicate in another school with similar demographics or one with very a different demography; collection of such data across multiple sites would undoubtedly be resource intensive but yield valuable insights into the universality of the present results. Another consideration for future research in this area is the measurement of friendships. In this study, we drew from prior work on cross-group friendships (e.g., Davies et al., 2011) and followed established protocols from prior peer studies by asking youth to name their friends based on who they “hang out with and talk to” (e.g., Ryan, 2001); however, as Vervoort et al. (2011) noted, the quality of the friendship may be particularly important in diverse schools that afford opportunities for crossgroup interactions (see also Syed & Juan, 2012). Because of resource and time limitations, we were unable to capture the quality of youths’ friendships, but as shown by Chen and Graham (2015), this is an important feature to consider in the design of future work in this area. Despite the noted limitations, it is important to consider the methodologic implications of the multiple peer methods implemented in the present study: Youth report on interactions (i.e., asking them to list their friends), an objective measure of friendship demography (i.e., Simpson’s diversity index constructed from nominees’ self-reported ethnicity/race), and examination of networks using a social network analytic approach (i.e., SABMs). All are useful and relevant for understanding ERI in context, and the use of multiple methods helps to provide complementary knowledge concerning how ERI informs youths’ experiences of their peer contexts. Though not feasible in the present study, additional research with qualitative methods such as individual interviews and focus groups has the potential to yield richer insights into the peer dynamics of diverse schools, generally, and the potential role of ERI in peer relations, in particular (cf. Way et al., 2008). In conclusion, this study represents a preliminary though critical step toward better understanding how ERI informs youths’ subjective experiences of diversity within an objectively diverse school setting (cf. Graham et al., 2014). Prior work has demonstrated a consistent association of various aspects of ERI with academic adjustment (e.g., motivation to learn, engagement with school, and grades) and psychosocial functioning (e.g., selfesteem, depressive symptoms, well-being) among Latino, African American, and Asian American adolescents (e.g., Rivas-Drake et al., 2014). 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Beyond and below racial homophily: ERG models of a friendship network documented on Facebook. American Journal of Sociology, 116, 583–642. doi:10.1086/653658 Yip, T., Douglass, S., & Shelton, J. N. (2013). Daily intragroup contact in diverse settings: Implications for Asian adolescents’ ethnic identity. Child Development, 84, 1425–1441. doi:10.1111/cdev.12038 Appendix: Stochastic Actor-Based Model Speciﬁcation Our SAB models contained two functions that were evaluated simultaneously: The network selection function and the ERI function (Steglich et al. 2010). The network function estimated the likelihood that friendships would form or persist over time (vs. not form or dissolve, respectively) based on several indicators of individual attributes and network structure. The ERI function estimated youths’ level of ERI based on their own attributes and friends’ ERI level. By estimating these functions simultaneously, the model allowed for endogenous change in both friendships and ERI. Ethnic-Racial Identity and Friendships Network Function The network function estimated change in friendship ties over time. For each time point, dyads were coded as having a tie present (1) or absent (0) if one youth (ego) nominated another youth (alter) as a friend. Conditioning on T1, the SABM predicted whether a new tie formed or, for dyads with existing ties, whether the tie persisted (vs. dissolving) at subsequent time points. The network function included several types of effects that predicted the likelihood of a friendship between two youth. To begin, the network function estimated endogenous network processes that could affect friendship change over time and artiﬁcially inﬂate the estimates of ERI on friend selection. Reciprocity captured the likelihood that a tie from A to B was matched by a tie from B to A. We included several effects to control for the tendency toward triad closure, such as in friendship cliques where youth have many friends in common. These effects included transitive triplets, which predict a friendship between A and C if, for instance, friendships were also present between A and B and B and C. We also included an interaction between this effect and reciprocity because they are usually not additive (Block, 2015). The number of actors at distance 2 effect is a variation on the effect of triad closure that controls for the tendency to have indirect connections to others. This effect is typically negative, suggesting that youth tend to avoid ties that create many indirect connections (perhaps by converting those indirect ties to direct ties). The indegree–popularity effect estimated how the number of incoming nominations predicted the likelihood of a youth receiving future nominations, while the outdegree– activity effect captured whether youth with more outgoing ties tended to send more ties at future time points. We used a square root transformation of these effects to give greater weight to differences in popularity/activity among less popular/active youth (e.g., one additional friend increases tie likelihood more for youth with few friends vs. youth with many friends). Last, the network function included an outdegree effect to control for the overall probability of a tie and rate effects to control for the volume of friendship change between each time point. These outdegree and rate effects were necessary to estimate the model but not of substantive interest. The network function also estimated how youths’ attributes affected friendship likelihood. These effects were speciﬁed at the level of the friendship sender (ego effects) and friendship 723 recipient (alter effects). For example, if boys nominated more friends than girls, the male ego effect would be positive, and if boys received more nominations than girls then the male alter effect would be positive. The similarity of ego and alter on an attribute might also affect tie likelihood. For a given dyad, similarity was measured as the absolute difference between the adolescents’ scores, which was then reverse coded and centered using the average similarity across all possible dyads (see Ripley et al., 2015). For these effects, higher values indicated greater similarity. Similarity effects were included for the ERI measures. For the categorical measures gender and ethnicity/race, we measured similarity as 1 if two adolescents were exactly the same, or 0 if they differed (using the attribute same effect). ERI Function The models included a behavior function to estimate change in ERI over time. Several effects are necessary to simply estimate the function. Two terms controlled for the distribution of ERI: the linear shape effect expressed the basic tendency toward higher or lower values of ERI, whereas the quadratic shape effect allowed for a nonlinear distribution. Like the friend selection function, the behavior functions also included rate parameters, which controlled for the volume of ERI change between time points. These three effects were necessary to estimate the model but were not of substantive interest in the current study. Several effects were included in the behavior functions as controls for change in ERI. We controlled for the effect of gender, mother’s immigration status, and ethnicity/race on ERI, the latter using dummy variables to represent Asian, Black, Latino, other, and multi ethnic (leaving White the reference category). Last, the primary effect of interest in the ERI function was peer inﬂuence, which was measured as average similarity. Average similarity was calculated as the sum of the absolute differences between ego’s score and the scores of the friends nominated by ego. The sum was reverse coded, divided by the number of alters, and centered based on the average level of similarity across all dyads (Ripley et al., 2015). A positive and statistically signiﬁcant effect for average similarity on ERI suggests that adolescents’ ERI was more likely to become similar to their friends or remain similar to their friends over time. After model estimation, we tested for heterogeneity in model effects over time and between 724 Rivas-Drake, Uma~ na-Taylor, Schaefer, and Medina grades following the procedure outlined by Lospinoso, Schweinberger, Snijders, and Ripley (2011). Grade heterogeneity would exist if an effect were stronger in one grade than the other; temporal heterogeneity would exist if an effect were stronger during one transition period, say T1–T2, than the other (e.g., T2–T3). Upon completion of model estimation, we used a score-type test to evaluate the composite hypothesis that all parameters have the same magnitude for each grade and each transition period. When the composite test indicated heterogeneity, we examined test statistics and provisional estimates for each effect. We then added interaction (s) between the effect and dummy variables representing grade and/or time period for the test statistic with the greatest magnitude, and re estimated the model. We repeated this procedure until obtaining a composite test indicating no heterogeneity in effects. The full model results, with interactions between effects and period, are shown in Table 1. This document is a scanned copy of a printed document. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material.

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