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Testing multidimensional models of youth civic engagement: Model comparisons, measurement invariance, and age differences

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Despite recognition that youth civic engagement is multidimensional, different modeling approaches are rarely compared or tested for measurement invariance. Using a diverse sample of 2,467 elementary, middle, and high school-aged youth, we measured eight dimensions of civic engagement: social responsibility values, informal helping, political beliefs, civic skills, environmental behavior, volunteering, voting intentions, and news consumption. We compared correlated unidimensional factors, higher-order factor, and bifactor models and tested for measurement invariance and latent mean differences by age. The correlated unidimensional factors model best fit the data, yet higher-order and bifactor models fit adequately. Metric and scalar invariance was found across models. Latent means varied depending on the dimension of civic engagement and the multidimensional model examined. Findings favored the correlated unidimensional factors model; implications of each model are discussed. This study informs future research on youth civic engagement and has broad relevance for any developmental scientist studying a multidimensional construct.
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RUNNING HEAD: Multidimensional Measurement of Civic Engagement by Age
Testing Multidimensional Models of Youth Civic Engagement:
Model Comparisons, Measurement Invariance, and Age Differences
Laura Wray-Lake
University of Rochester
Aaron Metzger
West Virginia University
Amy K. Syvertsen
Search Institute
Citation:
Wray-Lake, L., Metzger, A., & Syvertsen, A. K. (2016). Testing multidimensional models of
youth civic engagement: Model comparisons, measurement invariance, and age
differences. Applied Developmental Science. doi:0.1080/10888691.2016.1205495
This version does not include changes made in the final proofing stages of publication. Link to
published article:
http://www.tandfonline.com/doi/full/10.1080/10888691.2016.1205495
Acknowledgements: This work was funded by a grant from the John Templeton Foundation. The
opinions expressed in this presentation are those of the authors and do not necessarily reflect the
values of the John Templeton Foundation. We are grateful to the schools and the youth who
participated in the study. We thank Jennifer Shubert, Ben Oosterhoff, Brian Lake, Lauren Alvis,
Rebecca Olson, Michael Warren, Chen-Yu Wu, and Maura Shramko for their assistance in this
investigation, and Todd Little for his comments.
Multidimensional Measurement of Civic Engagement by Age 2
Abstract
Despite recognition that youth civic engagement is multidimensional, different modeling
approaches are rarely compared or tested for measurement invariance. Using a diverse sample of
2,467 elementary, middle, and high school-aged youth, we measured eight dimensions of civic
engagement: social responsibility values, informal helping, political beliefs, civic
skills, environmental behavior, volunteering, voting intentions, and news consumption. We
compared correlated unidimensional factors, higher-order factor, and bifactor models and tested
for measurement invariance and latent mean differences by age. The correlated unidimensional
factors model best fit the data, yet higher-order and bifactor models fit adequately. Metric and
scalar invariance was found across models. Latent means varied depending on the dimension of
civic engagement and the multidimensional model examined. Findings favor the correlated
unidimensional factors model; implications of each model are discussed. This study informs
future research on youth civic engagement and has broad relevance for any developmental
scientist studying a multidimensional construct.
KEYWORDS: positive youth development; measure development; civic development; structural
equation modeling; measurement model comparisons; multiple group models; age differences
Multidimensional Measurement of Civic Engagement by Age 3
Testing Multidimensional Models of Youth Civic Engagement:
Model Comparisons, Measurement Invariance, and Age Differences
Developmental science seeks to understand complex, multidimensional phenomena
(Overton, 2015). Multidimensionality implies that there are numerous parts to a larger whole and
is indicated when two or more separable scales fit under the same conceptual umbrella. Many
developmental constructs are recognized as multidimensional, and multidimensional thinking has
ushered in theoretical and empirical advancements in areas such as prosociality (Padilla-Walker
& Carlo, 2014), personality (Chen, Hayes, Carver, Laurenceau, & Zhang, 2012), temperament
(Rothbart, 2012), empathy (Decety, 2012), well-being (Ryff, 2014), and positive youth
development (Bowers, Li, Kiely, Brittian, Lerner, & Lerner, 2010). However, there are numerous
ways to model multidimensionality of a given construct, and each approach comes with different
theoretical assumptions and empirical implications. Too often, measurement models are not
explicitly tied to theory or empirically justified by comparing alternative models.
In this paper, we illustrate how to assess multidimensionality using youth civic
engagement as an example. This study has three aims: (a) Describe and empirically compare
multidimensional models to determine which model(s) best capture youth civic engagement, (b)
Examine measurement invariance by age to evaluate the quality of measures, and (c) Test mean
differences by age to provide evidence of age differences in civic engagement across late
childhood and adolescence. We examine three distinct approaches to modeling
multidimensionalitycorrelated unidimensional factors, higher-order factor, and bifactor models
– and compare these to a unidimensional single latent variable model. Findings inform future
theory and research on youth civic engagement and illustrate broader measurement and
conceptual implications of different modeling approaches.
Multidimensional Measurement of Civic Engagement by Age 4
A Multidimensional View of Civic Engagement
Civic engagement is defined as the behaviors, values, knowledge, and skills that
comprise political and prosocial contributions to community and society (Sherrod & Lauckhardt,
2009). Youth express commitments to society in vastly different ways; thus, taking a
multidimensional view of civic engagement is necessary for fully understanding youth’s
experiences. Multidimensional conceptualizations of civic engagement are being articulated with
increasing clarity (Amnå, 2012; Haste & Hogan, 2006; Sherrod & Lauckhardt, 2009) and
advance the field by recognizing that civic behavior is multifaceted and includes actions as
diverse as voting, volunteering, activism, and environmental conservation. It is conceptually
important to measure multiple civic behaviors because youth gravitate towards different civic
actions based on background, contexts, interests, and opportunities (Wray-Lake & Sloper, 2015).
Contemporary scholarship has also recognized that sociocognitive components (e.g., values,
skills, knowledge) are essential to defining and understanding civic engagement (Flanagan,
2013; Metzger & Smetana, 2009; Voight & Torney-Purta, 2013). In the current study, we
embrace the view that civic engagement has multiple dimensions. Whereas there are probably
more ways to express civic engagement than any single study can measure, we examine eight
dimensions of youth civic engagement that include various behaviors and sociocognitive
components and are thought to be relatively common and accessible to a wide age range of
youth: social responsibility values, informal helping, political beliefs, civic skills, environmental
behavior, volunteering, voting intentions, and news consumption.
Multidimensional measurement approaches can inform research on youth civic
engagement in three key ways: First, multidimensional measurement models can inform
fundamental definitional and conceptual questions about civic engagement. Despite some
Multidimensional Measurement of Civic Engagement by Age 5
consensus that civic engagement is multidimensional, there is debate about whether dimensions
of civic engagement form a coherent whole (e.g., Zaff et al., 2010) or whether civic engagement
is comprised of distinct separable components (e.g., Geller, Voight, Wegman, & Nation, 2013).
As summarized in Table 1 and described below, this question has implications for how civic
engagement is conceptualized in theoretical models and how it is promoted in policy and
practice. Distinct measurement models have not been empirically tested simultaneously or
compared with rigor, and the current study addresses this research gap.
Second, multidimensional measurement models may provide more nuanced information
about age differences in civic engagement and thus contribute to emerging developmental theory
of youth civic engagement (Lerner, Wang, Champine, Warren, & Erickson, 2014). Empirical
research on age differences in youth civic engagement is limited to single dimensions such as
informal helping (Carlo, Crockett, Randall, & Roesch, 2007) or social responsibility values
(Wray-Lake, Syvertsen, & Flanagan, 2016), but lacks cohesive examination across multiple ages
and measures. Our findings contribute to developmental research by examining age differences
in civic engagement levels across late childhood through adolescence. As described further
below, different measurement models may offer divergent conclusions about age differences.
Third, civic measurement is an active area of study, marked by several notable attempts
to disseminate comprehensive survey measures, yet more measurement work is needed,
particularly from a developmental perspective (Flanagan, Syvertsen, & Stout, 2007; Syvertsen,
Wray-Lake, & Metzger, 2015; Zaff et al., 2010; cf. Torney-Purta, Cabrera, Roohr, Liu, & Rios,
2015). We help fill this void by testing convergent validity of civic measures and examining
measurement invariance of youth civic engagement across ages. To provide evidence of
convergent validity, we link civic engagement measures to purpose. Purpose is a long-term
Multidimensional Measurement of Civic Engagement by Age 6
commitment to a goal that is larger than the self, and through civic engagement youth often find
a sense of purpose (Damon, Menon, & Bronk, 2003; Malin, Ballard, & Damon, 2015). Civic
engagement is broadly conceptualized in this work; thus a general civic engagement factor may
be strongly linked to purpose. Specific dimensions of civic engagement may differentially
predict purpose and provide evidence of divergent validity, a possibility that remains untested.
Distinct Approaches to Modeling Multidimensional Constructs
We articulate three distinct approaches to multidimensional measurement models in the
context of studying youth civic engagement. Although there are other viable multidimensional
measurement model approaches – such as multiple higher-order factors, multitrait-multimethod
models, or mixture models we examine three models that are theoretically justified for civic
engagement and can be empirically compared: a correlated unidimensional factor model, higher-
order factor model, and bifactor model. Previous studies have compared these three models to
demonstrate how empirical models align with distinct theoretical notions (Brunner, Nagy, &
Wilhelm, 2012; Reise, 2012): These tutorials walk scholars through the mathematical details
behind each model. Our paper highlights the conceptual rationale underlying each model and
discusses the implications of each model for understanding youth civic engagement.
Approach 1: Correlated Unidimensional Factors
One approach to thinking about a multidimensional construct entails assuming that
multiple specific dimensions of a construct fit together conceptually but are best measured
distinctly. That is, the multidimensional construct is a conceptual idea but not a measurable
construct. This idea is statistically represented as a correlated unidimensional factor model, also
termed a first-order factor model, in which a construct is conceived of as distinct, but related,
pieces. Regarding civic engagement, the construct would be modeled by first-order latent factors
Multidimensional Measurement of Civic Engagement by Age 7
such as social responsibility values, informal helping, political beliefs, civic skills, environmental
behaviors, volunteering, voting intentions, and news consumption (see Figure 2). An assumption
of the correlated unidimensional factor model is that individual latent variables are conceptually
related. Importantly, however, the model does not require that the direction or magnitude of
these correlations be specified in advance (Brunner et al., 2012), allowing for flexibility in how
much and in what ways the dimensions are related. For scholars who philosophically value
specificity, correlated unidimensional factors have a strong theoretical appeal. Correlated
unidimensional factor models assume that differences between dimensions are more important to
study than their shared variance.
Many civic scholars embrace the correlational unidimensional factor approach by
operationalizing civic engagement as multiple separate variables (e.g., Crocetti, Jahromi, &
Meeus, 2012; Geller et al., 2013; Metzger & Smetana, 2009; Mahatmya & Lohman, 2012).
Research has found that youth engage in different types of civic activities based on their
motivation, gender, family and community bonds, identity status, and sociocognitive judgments
(Metzger & Smetana, 2009; Wray-Lake & Sloper, 2015). This work showcases how
developmental theory can be advanced by documenting specificity of processes for different
civic dimensions and offering evidence of discriminant validity in predicting key outcomes.
Research has also highlighted consistency of correlates across dimensions of civic engagement
(e.g., Boyd et al., 2011), providing evidence for processes that generalize across dimensions. In
our study, separate estimation of eight dimensions of civic engagement allows for identifying
differences and similarities in age differences across these dimensions. Pinpointing specificity
can move theory, research, and applied efforts beyond generalities and potentially address the
critique that positive developmental research often relies on the balance principle and concludes
Multidimensional Measurement of Civic Engagement by Age 8
that “good leads to good” (Heider, 1958). Correlated unidimensional factors models may be able
to offer precise applied recommendations about specific pathways to specific constructs.
Approach 2: Higher-Order Factor
A second approach to multidimensionality is to model a higher-order construct, which
represents the theoretical notion that a construct is multifaceted and hierarchically structured.
Higher-order factor models build directly on a correlated unidimensional factor model by starting
with unique first-order latent variables and defining a second-order factor as the shared variance
among first-order constructs (see Figure 3). In other words, the higher-order factor explains
intercorrelations among the first-order constructs (Chen, Sousa, & West, 2005; Chen et al.,
2012). If a researcher’s conceptualization of a construct truly lies at the global level, then
examining separate individual factors (as in a correlated unidimensional factors model) would be
unsatisfying because specific dimensions are considered only parts of the whole. Likewise, by
emphasizing shared variance among dimensions, distinctions are relegated to the background.
The higher-order factor model views a multidimensional construct as an integrated whole, and
the theoretical benefits to this approach lie in providing broad understanding of a construct.
Modeling civic engagement as a higher-order factor model implies that civic engagement
is best represented by the shared variance across multiple behavioral and sociocognitive
components. The theoretical assumption is that civic engagement is best defined as an
individual’s coordination of beliefs, actions, and skills into a measurable whole, and examining
one or a few dimensions of civic engagement would lead to partial understanding. Zaff and
colleagues (2010) discussed the construct of Active Engaged Citizenship as a developmental
integration of civic actions, skills, connections, and duties, arguing that fully engaged individuals
will possess elevated levels of all components. Some scholars have adopted this view implicitly
Multidimensional Measurement of Civic Engagement by Age 9
by recognizing distinct dimensions of civic engagement but then summing or averaging them
(e.g., Kahne & Sporte, 2008; Lenzi et al., 2012). Civic engagement conceived of as a higher-
order factor model could enhance parsimony by avoiding redundancy in predicted pathways
across multiple dimensions of civic engagement that share variance. By identifying factors that
explain variance in civic engagement as a whole, a higher-order model could lead to more
generalizable conclusions about developmental processes and avoid piecemeal analyses that
emphasize distinctions and may capitalize on elevated Type-I error rates that result from multiple
statistical tests. The higher-order approach may have practical utility for policy, because it is
more parsimonious to consider civic engagement as an integrated whole.
Approach 3: Bifactor
There are merits to viewing a multidimensional construct in terms of its specific and
general parts. Typically these ideas are competing, yet a bifactor modeling approach allows
researchers to simultaneously examine both. Bifactor modeling partitions variance into a general
latent variable that accounts for commonality among items (e.g., general civic engagement
factor) and a set of specific latent variables (e.g., volunteering, political behavior, social
responsibility values) comprised of unique variance over and above the general factor (Chen et
al., 2012). The underlying assumptions are that civic engagement is a measurable construct
understood by integrating across dimensions, and each dimension can also be uniquely
understood. A bifactor model is typically estimated by loading all items onto a general factor and
all the items onto their respective specific factors (see Figure 4). The general and specific latent
factors are assumed to be orthogonal (Reise, 2012). Although some argue that bifactor models
differ more conceptually than mathematically from second-order models (Little, 2013), the main
mathematical difference pertains to the proportionality constraint: bifactor models allow for
Multidimensional Measurement of Civic Engagement by Age 10
more variability in ratios between general and specific factor loadings for an item, whereas
loadings are implicitly constrained to be proportional in a higher-order model (Gignac, 2016).
When items load differently onto the general versus the specific factor, a bifactor model will
typically fit the data better than a higher-order factor model (Gignac, 2016). In addition, bifactor
models are better able to determine whether specific factors exist beyond the general factor and
offer a more straightforward way to examine unique predictors or outcomes of specific factors
(Chen et al., 2012). Like the correlated unidimensional factors model, bifactor models can offer
evidence of discriminant validity. By allowing for prediction of differences between dimensions
and predicting shared variance, bifactor models can contribute to theory in acknowledging both
specific and general processes and can offer a refreshing balance of general and specific
recommendations for policy and practice.
Measurement Invariance by Age
Measurement invariance tests (i.e., equivalence of parameters such as factor loadings,
intercepts, error variances) across groups such as age, gender, ethnicity, or socioeconomic status
are important for determining whether measures are equally valid across groups and represent a
crucial first step to achieve before means or structural paths can be compared (Kline, 2015).
Although thorough measurement studies should test measurement invariance across multiple
groups of interest, invariance by age is absolutely essential from a developmental perspective:
Assumptions of measurement variance by age must be met before drawing inferences about
cross-sectional age differences or longitudinal age-related change (Horn & McArdle, 1992;
Widaman, Ferrer, & Conger, 2010).
Different levels of invariance can be reached (Meredith, 1993). Metric invariance refers
to equivalence of factor loadings across groups or time; this is also called weak invariance and is
Multidimensional Measurement of Civic Engagement by Age 11
seen as a minimal requirement for comparing constructs across groups or time (Little, 2013).
Scalar invariance refers to equality of intercepts, and having both metric and scalar invariance is
considered strong invariance. Having equivalent item-level means across groups after factoring
out shared variance due to factor loadings is a prerequisite to interpreting latent variable mean
differences (Little, 2013). Intercept differences could indicate problems with measurement or
reflect substantive nuance in specific indicators not being captured by the construct. For
example, if a global construct fails to account for the meaningful variance in a specific
dimension of civic engagement, unique variance could get pushed down to indicator level.
Finally, in higher-order and bifactor models, invariance of the first-order disturbances (i.e.,
variances of specific or lower-order factors) must be tested (Chen et al., 2005). This invariance
gives confidence that lower-order latent variables (in a higher-order model) or specific latent
variables (in a bifactor model) are equivalent across groups or time.
Measurement invariance tests by age have not been featured in published work for youth
civic engagement measures, with the exception of Zaff and colleagues’ (2010) longitudinal
measurement invariance tests. Without broad measurement of civic engagement across ages and
tests of measurement invariance by age, developmental research on youth civic engagement will
stall, as this is an essential first step to answering fundamental questions about developmental
change and processes. Cross-sectional studies can contribute to this work by testing if the
measurement model structure is reasonably equivalent across age, and then testing for latent
mean differences by age.
Age Differences in Levels of Civic Engagement
Research on age differences in civic engagement is sparse, and our large and diverse
(albeit cross-sectional) sample of children and adolescents can add new evidence to this area.
Multidimensional Measurement of Civic Engagement by Age 12
The normative growth hypothesis posits that civic engagement increases across adolescence in
concert with normative age-related growth in identity, autonomy, and exposure to contextual
opportunities (Wray-Lake, Rote, Victorino, & Benavides, 2014). A mid-adolescence decline may
typify certain civic constructs, such as social responsibility values, which show declines during
middle adolescence and higher levels in elementary and high school (Wray-Lake et al., 2016).
Related constructs of prosocial behavior and social trust have shown declines across adolescence
(Carlo et al., 2007; Flanagan & Stout, 2010). Given divergent findings and a lack of research,
further investigation of age patterns in youth civic engagement is sorely needed.
Importantly, however, each multidimensional approach to modeling civic engagement
may offer a different conclusion for developmental theory. For example, the correlated
unidimensional factor model should provide the most nuanced age differences, as specific
dimensions may follow different age patterns, yet broad conclusions regarding an overall age-
related pattern could not be discerned in this model. The higher-order factor model should
provide evidence for age differences at the broadest level, yet distinctions may be washed out or
identified through intercept invariance tests. In a bifactor model, general and specific conclusions
can be drawn, yet age findings may differ most dramatically from other models, given that
variance is partitioned into shared and unique components.
The Current Study
Table 1 provides a summary of the different theoretical implications and practical value
of each multidimensional approach. To advance the study of multidimensional constructs in
developmental research in general and for civic engagement specifically, we address three aims.
Aim 1empircally compares different measurement models to determine which model best
represents our data on youth civic engagement. Three distinct multidimensional approaches are
Multidimensional Measurement of Civic Engagement by Age 13
compared to each other and to a unidimensional model (Model 0, see Table 1 and Figure 1). In
Model 0, civic engagement is assumed to be a unidimensional construct, with all indicators
equally loading onto the general factor. We hypothesize that youth civic engagement is
multidimensional, but make no predictions about which multidimensional model best fits the
data. Aim 2 is to evaluate the quality of civic engagement measures for developmental research.
We test metric and scalar measurement invariance by age (elementary, middle school, and high
school ages) for all empirically justified models, and convergent validity is tested by linking
civic engagement to purpose. Aim 3 documents mean age differences in civic engagement. We
interpret latent mean differences for all empirically justified models, anticipating that each model
may provide different conclusions for developmental theory on civic engagement.
METHOD
Youth ages 8 to 20 (M = 13.4, SD = 2.7) enrolled in grades 4-12 were recruited from 17
schools in three socioeconomically, racially, and ethnically diverse regions of the United States:
metropolitan California, urban Minnesota, and rural West Virginia. Student eligibility for free
and reduced lunch ranged from 26 to 95% (M = 60%) across schools indicating substantial
economic diversity across schools (National Center for Education Statistics, 2014).
Youth (N = 2,475) completed paper and pencil surveys in the classroom. Eight cases were
excluded due to problematic response patterns; they were identified as multivariate outliers and
failed attention check questions. Thus, 2,467 youth were used in analyses (56% female). The
sample was 51% White, 30% Hispanic or Latino/a, 10% Black or African American, 7% Asian,
4% American Indian or Alaska Native, 2% Native Hawaiian or Other Pacific Islander, and 9%
identified as another race-ethnicity. Youth reported primary caregivers’ level of education on a
3-point scale: high school or below (Mothers: 27%; Fathers: 31%; Other Adult: 21%), some
Multidimensional Measurement of Civic Engagement by Age 14
college (Mothers: 15%; Fathers: 14%; Other Adult: 14%), and college graduate or higher
(Mothers: 35%; Fathers: 33%; Other Adult: 20%). Some youth reported they “Don’t Know” their
parenting adults’ education level: Mothers: 23%; Fathers: 23%; Other Adult: 45%. Regarding
financial strain, 10% of youth reported their family had a hard time buying the things they need,
34% reported their family as having just enough money for the things they need, 48% reported
their family had no problem buying the things they need, and 9% reported their family had
enough money to buy almost anything they wanted. In addition, 8% of youth reported being
first-generation immigrants and 32% reported being second-generation immigrants.
To reduce participant burden, we employed a three-form planned missing design
(Graham, 2012). See Online Appendix A for more detail. Planned missing data is controlled by
the researcher and thus missing completely at random (MCAR). Survey versions were equally
distributed across age, gender, ethnicity, parent education, and site (all chi-square tests were not
significant). The Principal Components Method was used to incorporate principal components as
auxiliary variables in the FIML missing data model (Howard, Rhemtulla, & Little, 2015).
Measures
Civic measures were drawn from existing sources and heavily adapted (Flanagan et al.,
2007; Kahne, Middaugh, & Schutjer-Mance, 2005) or newly written but conceptually based on
extant work (see Syvertsen et al., 2015). Items were examined in an iterative process involving
multi-phase interviews, cognitive interviews, and a pilot survey study of 213 elementary, middle,
and high school youth to ensure the developmental appropriateness of measures of youth across
ages. Items were identically worded across age groups, with careful attention for easy readability
and interpretation by the youngest participants. Omega coefficients are reported for elementary
(E), middle (M), and high school (H) ages in the measure descriptions below.
Multidimensional Measurement of Civic Engagement by Age 15
Social responsibility values were measured with 4 items: It is important to me to:”:
“consider the needs of other people,” “help those who are less fortunate,” “make sure that all
people are treated fairly,” “think about how my actions affect people in the future.” Responses
ranged from Not at all important (1) to Extremely important (5), ω = .63 (E), .79 (M), .77 (H).
Informal helping was measured with 6 items assessing the frequency of everyday forms
of helping, including: standing up for a classmate that was being picked on; helping a classmate
with homework; doing household chores such as cleaning, cooking, or yard work; sharing school
supplies with peers; helping a neighbor with projects for no pay; and, babysitting for no pay.
Responses ranged from Never (1) to Very often (5), ω = .52 (E), .65 (M), .64 (H).
Political beliefs were measured with 2 items assessing beliefs about actions: “People
should keep up with current events and politics,” “People should take part in a protest or rally to
help change a law that they disagree with.” Response options were: Doesn’t matter (1), Maybe
should (2), Probably should (3), Mostly should (4), Definitely should (5), r = .34 (E), .45 (M),
and .49 (H), all ps < .001.
Youth self-rated their ability to perform six civic skills: create a plan to address a
problem,” “get other people to care about a problem,” “express my views to others in-person or
in writing,” “contact someone in a leadership position about a problem,” “listen to conflicting
viewpoints and identify where they agree and disagree,” and, “summarize what another person
said to make sure I understood.” Response options were: I definitely can’t (1), Probably can’t
(2), Unsure if I can (3), Probably can (4), and Definitely can (5), ω = .72 (E), .84 (M), .84 (H).
Three items gauged environmental behaviors: “I turn off electronics when I’m not using
them,” “I try to limit how much paper I use,” and “I conserve water by taking shorter showers.”
Response options ranged from Never (1) to Very often (5), ω = .66 (E), .69 (M), .69 (H).
Multidimensional Measurement of Civic Engagement by Age 16
Volunteering was measured with a single item: “In a typical MONTH, about how many
hours do you spend volunteering (not part of a class project, graduation requirement, or court-
ordered requirement) to help other people or to help make your community a better place?”
Response options ranged from 0 hours (0) to 5+ hours (6).
Voting intentions were measured by asking: “Have you ever done or plan to do the
following? Vote in national elections.” Response options were: I wouldn’t do this (1), Probably
wouldn’t do this (2), Unsure (3), Probably will do this (4), Will do or have already done this (5).
News consumption was measured by a single item measuring how often participants
“access information about politics and current events on TV, the radio, in the newspaper, or on
news websites” in a typical week. Response options ranged from Never (1) to Very often (5).
Three items measured purpose, or commitment to a future goal that is larger than the self,
adapted from Benson and Scales (2009): “I believe I am going to make a difference in the
world,” “I feel a sense of purpose in life,” and “I have plans for my future.” Response options
ranged from Not at all like me (1) to Very much like me (5), ω = .66 (E), .69 (M), .74 (H).
For multigroup age models, the sample was divided into elementary (4-5th graders, n =
512), middle (6-8th graders, n = 813), and high school-aged youth (9-12th graders, n = 1,135).
Grade and age were highly correlated (r = .81, p < .001). Although we are most interested in age
developmentally, we chose school level as a proxy for age group because this offered a
straightforward grouping that was preferable to selecting an arbitrary age cut-offs.
Analytic Plan
A series of structural equation models tested the factor structure of civic engagement. To
account for the nested nature of individuals in schools, all models included school as a cluster
variable (n = 17). Due to analysis of clustered data, analyses employed maximum likelihood
Multidimensional Measurement of Civic Engagement by Age 17
estimation with robust standard errors (i.e., MLR). Separate confirmatory factor analyses (CFAs)
were run to model dimensions of civic engagement as: a unidimensional model (Model 0),
correlated unidimensional factors (Model 1), a higher-order factor model (Model 2), and as a
bifactor model (Model 3). Scaling was done using the effects coding method, so that latent
means could be reported (Little, Slegers, & Card, 2006; see Table 2). The two-item political
beliefs construct was additionally scaled by constraining factor loadings to be equal. Standard
model fit criteria were used, including chi-square tests, root mean square error of approximation
(RMSEA), standardized root mean square residual (SRMR), and the Comparative Fit Index
(CFI). Acceptable model fit values are .05 or lower for RMSEA and SRMR and .90 or higher for
CFI, with .95 and higher preferred (Kline, 2015). Models were statistically compared based on
chi-square difference tests using the Satorra-Bentler scaled method (required when using MLR
estimation) to evaluate their relative fit (Satorra & Bentler, 1999). To establish validity of civic
measures and compare models, we next included purpose as a dependent variable in each model.
For each model that showed acceptable model fit, multiple group analysis was utilized to
assess measurement invariance across three age groups (elementary, middle school, high school).
Across multiple group models, we scaled latent variables using the fixed factor method (i.e.,
latent variable variances fixed to 1) to facilitate comparison of factor loadings and means (Little,
2013). Elementary was the reference group. In conducting these tests, we primarily relied on CFI
change to evaluate invariance, as chi-square difference tests have been found to be too liberal in
assessment of invariance for large samples. Aligned with current recommendations, a CFI
difference of .01 or greater was interpreted as substantively important and has also been
considered a measure of effect size for invariance tests (Cheung & Rensvold, 2002; Little, 2013).
To test metric invariance (i.e., equivalence of factor loadings), we compared a configural model
Multidimensional Measurement of Civic Engagement by Age 18
where factor loadings freely varied across groups to a model with factor loadings constrained to
be equal. Using the fixed factor scaling method, latent variable variances were fixed in
Elementary and freely estimated in Middle and High groups. To test scalar invariance (i.e.,
equivalence of intercepts), we compared the metric invariance model from the previous step (in
which factor loadings were fixed and intercepts were freed) to a model where intercepts were
constrained to be equal across groups. In this step, latent variable means were fixed at 0 in
Elementary and freely estimated in Middle and High Groups. In the higher-order factor model,
tests of metric and scalar invariance were conducted separately at the first-order and higher-order
levels (Chen et al., 2005). In the higher-order and bifactor models, we additionally tested for
invariance of first-order factor disturbances (Chen et al., 2005). When the CFI change was
greater than .01, models were considered non-invariant and modification indices were used to
identify sources of differences and parameters were freed until partial invariance was reached.
Satorra-Bentler scaled chi-square difference tests were used to evaluate individually freed
parameters using a Bonferroni correction of p = .002 (Little, 2013). In the final step, we
interpreted latent mean differences. The latent mean of the referent group (Elementary) was fixed
to zero and latent means for Middle and High groups represented deviations from the Elementary
mean. Latent mean differences were evaluated by examining significance of parameter estimates
and significant chi square difference if parameters were constrained (using p < .002).
Results for each model are presented in the following sequence: (a) CFA for the full
sample, (b) links from the civic engagement model to purpose, (c) tests of measurement
invariance, and (d) interpretation of latent means by age.
RESULTS
Bivariate correlations among all study variables are presented in Table 2. Associations
Multidimensional Measurement of Civic Engagement by Age 19
among variables were stronger between items from the same construct than across constructs.
Model 0: Unidimensional Model
The unidimensional model was estimated by loading all 24 items onto a single latent
variable. Based on multiple fit indices, this model was a poor fit to the data, MLR
χ
2(252) =
3659.01, p < .001, CFI = .69, RMSEA = .074 (90% CI: .072 - .076), SRMR = .080 and fit
significantly worse than the multidimensional models (Table 3). Standardized factor loadings
ranged from .23 to .72, with five loadings below .4 (Table 4). Thus, results indicated that a single
unidimensional construct of civic engagement was not viable in our data. Given the poor fit, no
further analyses were conducted with this model.
Model 1: Correlated Unidimensional Factors
A first step to modeling correlated unidimensional factors was verifying that each
dimension of civic engagement was distinct. In an exploratory factor analysis estimating 1 to 13
factors, results showed that an 8-factor model was better fitting than models with fewer factors
and models with 9 or more factors did not offer meaningful improvements.
A CFA estimated 5 latent variables (social responsibility values, informal helping,
political beliefs, civic skills, and environmental behaviors) and 3 manifest single-item variables
(volunteering, voting intentions, and news consumption). The model provided a good fit to the
data, MLR
χ
2(228) = 831.29, p < .001, CFI = .95, RMSEA = .033 (90% CI: .030 - .035), SRMR
= .033 (Table 3). Standardized factor loadings ranging from .43 to .76 (ps < .001; Table 4).
Covariances among dimensions of civic engagement were positive and significant, ranging from
.09 to .59. The smallest correlations were with environmental behaviors and volunteering (r =
.10), voting intentions (r = .09), and news consumption (r = .15). The largest correlations were
between social responsibility values and informal helping (r = .59) and between informal helping
Multidimensional Measurement of Civic Engagement by Age 20
and civic skills (r = .57). The majority of other correlations ranged from .2 to .4 (Table 5).
Next, we linked the unidimensional factors to purpose to examine validity. As expected,
social responsibility values, informal helping, political beliefs, civic skills, and voting intentions
were positively associated with youth purpose. However, environmental behavior, volunteering,
and news consumption were not associated with purpose (Table 6).
To test metric invariance by age, the configural model with all parameters free to vary
across groups was compared to a model with factor loading constrained to be equal (Table 7).
Based on a CFI of .002, we concluded that factor loadings did not significantly differ by age.
Likewise, the test for scalar invariance was non-significant, CFI = .005.
We next examined mean differences by age in the 8 civic engagement constructs (see
Table 8). Elementary youth were lower on informal helping compared to middle and high school
youth; the latter groups did not differ. High school youth were higher on political beliefs and
civic skills compared to elementary and middle school youth; the latter groups did not differ. An
unexpected pattern for environmental behavior showed that elementary youth were highest,
followed by middle and then high school youth (all three groups differed). There were no age
differences in social responsibility values, volunteering, voting, or news consumption.
Model 2: Higher-Order Factor Model
A second-order CFA included the 5 latent and 3 manifest civic variables from Model 1 as
indicators of a second-order civic engagement factor. Model fit was acceptable, MLR
χ
2(248) =
1012.24 p < .001, CFI = .93, RMSEA = .035 (90% CI: .033 - .038), SRMR = .039, although this
model fit the data worse than Model 1, indicating the correlated unidimensional factors model fit
better than the second-order model (Table 3). First-order loadings ranged from .43 to .76, and
second-order factor loadings ranged from .33 to .76 (all ps < .001; Table 4).
Multidimensional Measurement of Civic Engagement by Age 21
The higher-order civic engagement latent variable was strongly positively associated with
youth purpose (Table 5).
Metric invariance was tested separately for lower- and higher-order factor loadings.
Based on ∆CFIs of .005, and .001, respectively, we concluded factor loadings were equivalent
across groups. Regarding scalar invariance at the item level, intercepts were determined to be
invariant based on ∆CFI of .003. In examining the intercepts of the first-order latent variables, a
significant CFI change (∆CFI=.018) revealed non-invariance. Based on modification indices, 4
first-order latent factor intercepts were freed across groups (Table 7). The environmental
behavior intercept was freed for middle and high school youth, indicating again that elementary
youth were highest on environmental behavior, followed by middle and then high school youth
(Table 8). Social responsibility values were freed for high school, indicating that these values
were lower for high school youth compared to elementary and middle school youth. Informal
helping was freed for middle and high school youth, whose means were constrained to be equal:
Elementary youth reported lower informal helping than middle and high school youth.
For the higher-order model, invariance of disturbances of first-order factors was tested.
Disturbances were determined invariant, based on a non-significant chi square and CFI of 0.
The higher-order civic engagement factor was highest in high school compared to
elementary and middle school-aged youth; the latter two groups did not differ (Table 8).
Model 3: Bifactor Model
In Model 3, we estimated a bifactor model that included the 8 specific civic engagement
constructs (5 latent, 3 manifest as described above) and a general civic engagement factor
comprised of loadings from the 24 items. The model fit the data acceptably well, MLR
χ
2(232) =
870.35, p < .001, CFI = .942, RMSEA = .033 (90% CI: .031 - .036), SRMR = .036. Standardized
Multidimensional Measurement of Civic Engagement by Age 22
factor loadings for the general civic engagement factor ranged from .18 to .58, with 8 loadings
below .40 (ps < .001, Table 4). Bifactor models assess both shared and unique variance, which
typically leads to specific factor loadings being lower than in Models 1 and 2 (Chen et al., 2012).
The bifactor model showed fit better than the higher-order model, but fit worse than the
correlated unidimensional factors model (Table 3).
The general civic engagement factor was again strongly positively associated with
purpose. Social responsibility values, informal helping, civic skills, and voting intentions were
positively associated with purpose, but political beliefs, environmental behavior, volunteering,
and news consumption were not (Table 6).
The metric invariance test showed that factor loadings were equivalent across age groups,
CFI = .007. The test of scalar variance showed that intercepts were equivalent, ∆CFI = .006.
First-order factor disturbances were also equivalent across groups, ∆CFI = .001 (Table 7).
Similar to the higher-order model, high school-aged youth were higher on general civic
engagement than middle and elementary school-aged youth (Table 8). No age differences
emerged for informal helping, political beliefs, or civic skills. As in other models, environmental
behaviors were lower at successive ages. Social responsibility values were lowest in high school,
followed by middle school, and then elementary school (all three groups differed).
DISCUSSION
Our results demonstrate that youth civic engagement is a multidimensional construct,
supporting contemporary conceptual thinking (e.g., Sherrod & Lauckhardt, 2009). In comparing
three distinct multidimensional models, the correlated unidimensional factors model best fit our
data. However, notably, higher-order and bifactor models also provided good fit to the data.
Evidence for metric and scalar measurement invariance by age and convergent validity (although
Multidimensional Measurement of Civic Engagement by Age 23
it varied by model) provided evidence that our measures are well-positioned for further
examining developmental questions related to civic engagement. Our study offers new evidence
of cross-sectional age differences in civic engagement, but divergent findings across models also
illustrate that model selection should be guided by both theory and empirical tests.
Evaluating Models
Comparing three multidimensional models of civic engagement to a unidimensional
single latent variable provided strong evidence for the multidimensional structure of civic
engagement. Scholars from across disciplines have described the multidimensional nature of
civic engagement among youth and adults (Amnå, 2012; Haste & Hogan, 2006; Sherrod &
Lauckhardt, 2009), and our work provides empirical support for these conceptual claims. In
comparing the other three multidimensional models, the best-fitting model was the correlated
unidimensional factors model, with the bifactor model the second-best fitting and the higher-
order factor model fitting least well of the multidimensional models. The implications of these
model comparisons extend to developmental science broadly and to research on civic
engagement specifically.
Based on model fit criteria, each model fit the data acceptably well and thus could be
empirically justified, which is common across studies of multidimensional constructs (Brunner et
al., 2012; Reise, 2012). Our results align with similar model comparisons of internalizing
symptoms by Reise (2012), who concluded that empirical differences were small between
models, and thus in practice, model choice should be guided by theory and study goals. Thus, an
important take-away point for scholars interested in multidimensional constructs is to prioritize
conceptual rationale in model selection, carefully considering study purpose and goals for theory
and practice along with empirical advantages and disadvantages (see Table 1). Moreover, given
Multidimensional Measurement of Civic Engagement by Age 24
the relevance of model comparisons for clarifying definitions and conceptualizations of a
construct, multiple models should be explicitly empirically compared (Wang et al., 2015). For
example, our results favor the correlated unidimensional factors model and conflict with the
model presented by Zaff and colleagues (2010), who found evidence for a higher-order factor
model of civic engagement using a smaller set of civic constructs and data from the 4-H
longitudinal study of mostly White, mostly middle class youth ages 14 to 16. Notably, if we had
not empirically compared models, our findings could have aligned with Zaff et al.’s (2010)
results based on a reasonably good fitting higher-order model. Thus, we underscore the need to
replicate measurement model findings by conducting rigorous measurement work in other
samples in order to best inform theory and practice.
Regarding implications of model comparisons for research on civic engagement, the best-
fitting correlated unidimensional factors model implies that civic engagement is a conceptual
idea measured by individual constructs that capture distinct dimensions of civic engagement. The
magnitude of correlations among the individual latent variables varied substantially, explaining
why the higher-order and bifactor models were not adequately capturing these covariances with a
latent civic factor. Substantively, the correlated unidimensional factors model is well-poised to
spur greater specificity in understanding civic engagement and related developmental processes.
Recent work is already advancing our understanding of specificity in correlates of youth civic
engagement (Crochetti et al.; Duke et al., 2009; Metzger & Ferris, 2013; Wray-Lake & Sloper,
2015). Greater use of the correlated unidimensional factors approach will advance civic
engagement theory that articulates different precursors and outcomes of distinct dimensions of
civic engagement (Metzger & Smetana, 2009). In turn, nuanced recommendations will likely
emerge for practitioners in applied settings and civic education curricula. Practitioners tend to
Multidimensional Measurement of Civic Engagement by Age 25
crave specificity in recommendations; the utility of the correlated unidimensional factors model
lies in illuminating specific levers of change for each dimension of civic engagement.
Given other viable models, researchers should consider the limitations of the correlated
unidimensional factors approach alongside its strengths. The large number of estimated
parameters means greater model complexity and including covariates could easily lead to testing
a dizzying number of model parameters, causing problems with model convergence and
increasing probability of Type-I error. Complex and unexpected results could emerge from
models with multiple dependent variables, heightening the potential for researchers to generate
post-hoc, atheoretical explanations for findings. In areas such as youth civic engagement where
theorizing about specific pathways is lacking, complicated and contradictory results could lead to
more confusion than clarity about developmental processes.
The higher-order factor model revealed age differences in the civic engagement factor
that align with the normative growth hypothesis that civic engagement increases with age; this
idea has received only partial support in previous work (Wray-Lake et al., 2015) and has not
been examined to a great extent. It would be difficult to ascertain this sort of holistic
understanding of civic engagement with the correlated unidimensional factors model. Often,
research starts with broad, general understanding and then proceeds to specific nuances
(Metzger, Oosterhoff, Palmer, & Ferris, 2014). For a complex construct such as civic
engagement, results related to a higher-order factor provide a straightforward and simpler way to
discuss a phenomenon that policymakers and the public may more easily digest. This higher-
order conception of civic engagement may be too general for practitioners, however, as it can be
hard to know how to promote such as a diffuse construct. A reason to be cautious about higher-
order approaches is that they can mask important variations occurring among specific
Multidimensional Measurement of Civic Engagement by Age 26
dimensions of a construct. If theory suggests that specific dimensions of a construct should show
different age patterns, aggregating across dimensions could wash out unique variance and
preclude understanding of specific developmental changes. In this study, we would likely not use
a higher-order factor model due to its poor relative fit compared to the other multidimensional
models. However, particularly given Zaff et al.’s (2010) previous work, it is worth considering
this model in further work on civic engagement and for other multidimensional constructs.
A bifactor model has not been examined with youth civic engagement to our knowledge,
and in our study, the bifactor model offered a better fit than the higher-order factor model.
Unlike a higher-order factor model, a bifactor model can be useful in cases, like in our study,
where each dimension contributes differently to the general factor (Chen et al., 2012). The
bifactor model offers an ideal circumstance in conferring advantages of both general and specific
approaches, increasing broad understanding of civic engagement and illuminating specificity.
Despite their conceptual and empirical appeal, bifactor models are uncommon in the
literature. Perhaps bifactor models are difficult to estimate, given high model complexity and
possible instability of model structure over time. In bifactor models, alternative explanations
could easily apply to the general factor, which may represent unwelcomed sources of shared
variance such as social desirability or positivity bias. A consistent and expected pattern of results
gave us confidence in the interpretation of our general factor as civic engagement. For example,
the pattern of associations linking specific and general factors to purpose replicated across
correlated unidimensional and higher-order models. Also, the same age pattern emerged for the
civic engagement factor in the bifactor and higher-order models. More broadly, interpretations of
specific dimensions in a bifactor model must acknowledge that these dimensions represent
unique variance only. Thus, results with specific dimensions in bifactor models may not always
Multidimensional Measurement of Civic Engagement by Age 27
align with models that do not remove shared variance. Our divergent age findings across models
for social responsibility values, described further below, are a good example of this. Our bifactor
model included several low loadings, which can be substantively interesting in illustrating the
amount of variance an item contributes to a general versus specific factor (Gignac, 2016).
However, when a latent variable such as informal helping has several low factor loadings, this
pattern may suggest lower reliability of the specific construct. In summary, bifactor models
should be further explored for use with youth civic engagement and other constructs. We would
feel confident using the bifactor model in our data, particularly in situations where the research
questions and study goals necessitate use of specific and general civic engagement constructs.
Evaluating Measures
After accounting for clustering by school, assumptions of metric and scalar invariance
were largely met across models. Measurement invariance tests are essential to advancing
developmental research. In our case, finding invariance gave us confidence to proceed with
examining age differences in levels of constructs and suggests a path forward for future work to
examine developmental change longitudinally using these measures. Our work contributes to
youth civic engagement research by identifying reliable, valid, and developmentally appropriate
civic engagement measures for youth from late childhood through late adolescence.
However, our measures are not a panacea, and limitations should be noted. Political
activism is an important aspect of civic engagement (Kirshner, 2015), but these kinds of political
behaviors are expected to be relatively rare, particularly among younger children, and due to
concerns about survey length and item complexity, we asked political activism measures of
middle and high school youth but not elementary. At a more basic level, each specific dimension
of a construct has to load strongly and positively onto a broad construct before a higher-order
Multidimensional Measurement of Civic Engagement by Age 28
approach can be viable. Dimensions of civic engagement that we did not examine – such as
political activism may negatively correlate with other dimensions and invalidate a higher-order
model. Reliability coefficients were lower on most dimensions for elementary youth. This
pattern is not surprising, as developmental research has long shown that measurement reliability
for multiple constructs increases with age, and differences are attributed to cognitive
development such as growth in abstract thinking, memory, and language (e.g., Edelbrock,
Costello, Dulcan, Kalas, & Conover, 1985). We do not view this pattern as problematic in our
data, given that reliabilities for younger youth were approaching acceptable standards of .70 and
measurement invariance tests suggested equivalence across age groups. However, there may be
room to further improve the measurement of these constructs for our youngest participants.
Finally, with respect to convergent validity tests, not all dimensions of civic engagement
were positive associated with purpose. Purpose may only be related to certain dimensions of
civic engagement such as social responsibility, informal helping, civic skills, and voting
intentions. Civic engagement as a general factor was consistently linked to purpose, and
likewise, scholarship conceptually linking civic engagement to purpose conceives of civic
engagement broadly (Damon et al., 2003; Malin et al., 2015). Overall, validity tests may need to
become more refined for civic engagement as theory and research get more specific and if the
correlated unidimensional model is used. Currently, few papers on civic measurement conduct
validity tests and much more work is needed in this area (Torney-Purta et al., 2015).
Evaluating Age Differences
The correlated unidimensional factors model, identified as best-fitting, also showed the
greatest specificity in age differences for dimensions of civic engagement. Higher-order and
bifactor models showed that their broad civic engagement factor was higher in high school
Multidimensional Measurement of Civic Engagement by Age 29
compared to younger ages. Thus, results from these two models provide some support for the
normative growth hypothesis that civic engagement increases across adolescence (Wray-Lake et
al., 2015). Since the shared variance for civic engagement was captured in a general civic
engagement factor for these two models, age differences in specific dimensions mostly reflect
deviations from this general pattern. On the other hand, the correlated unidimensional factors
model provides the most direct test of which civic dimensions follow this pattern: Informal
helping, political beliefs, and civic skills are higher for high school youth in this model. Not
surprisingly, these findings largely disappear in the other two models because this shared
variance is moved to the general/higher-order civic engagement factor (with the exception of
civic skills that remain higher). Thus, age differences across models mostly tell a similar story.
In some cases, age findings were inconsistent across models, most notably for social
responsibility values. Previous research has found declines in social responsibility values across
adolescence (Wray-Lake et al., 2016). Our results show that social responsibility values follow
this pattern of being lower at older ages only when shared variance with other dimensions of
civic engagement are factored out (i.e., in the higher-order and bifactor models). In the correlated
unidimensional factors model, social responsibility values were highly correlated with informal
helping and civic skills. It is likely that factoring out this shared variance leaves meaningful
unique variance for social responsibility; alternatively, factoring out shared variance could
substantially change the construct. Clearly, removing shared variance changes the association
between age and social responsibility values. Given the notable differences in interpretation and
alignment with previous work, the social responsibility findings illustrate the importance of
using conceptual rationale to guide selection of multidimensional models to avoid cherry-picking
findings. On the other hand, consistent results across models for the other civic constructs we
Multidimensional Measurement of Civic Engagement by Age 30
measured in this study are encouraging and increase confidence in interpretation of findings. For
instance, the consistent finding that environmental behaviors were lower in each successive age
group is informative in suggesting that older adolescents may be less inclined toward everyday
environmental conservation. This finding merits replication in other studies and with other
measures, given that this pattern was unexpected based on the normative growth hypothesis. This
pattern could be due to our measure’s narrow focus on conservation.
Limitations and Future Directions
Strengths of our study include the large socioeconomically, racially, ethnic, and
geographically diverse sample that spanned a wide age range. Our study is primarily limited by
its cross-sectional design. Cross-sectional age comparisons offer a useful starting point, yet
longitudinal data are necessary for examining developmental change. Three broad age groups are
likely insufficiently nuanced to capture complex (e.g., non-linear) age patterns. Model selection
criteria certainly influence conclusions drawn. We evaluated invariance tests using a change in
CFI rule, which is conservative in reducing Type-I error (Cheung & Rensvold, 2002). More
differences would have emerged on factor loadings and on intercepts had we used different
criteria, such as the chi-square difference tests or a more sensitive CFI rule (Meade, Johnson, &
Braddy, 2008). Furthermore, Gignac (2016) argues that fit indices that add a penalty for model
complexity can better determine differences between higher-order and bifactor models. More
uniformity in applying model evaluation criteria in the field would better facilitate ability to draw
conclusions across studies. Other models may offer different ways to think about
multidimensionality, such as mixture models that recognize individual variability in response
patterns and can determine that facets work together in different ways for different people. This
kind of idiographic approach to multidimensionality is important to consider and can offer a
Multidimensional Measurement of Civic Engagement by Age 31
nuanced look at civic engagement (e.g., Voight & Torney-Purta, 2013). Finally, it was beyond
the scope of this paper to test for measurement invariance across other key subgroups (e.g.,
gender, ethnicity), but future work should conduct these important tests to better understand the
viability of these measures for assessing civic engagement across groups.
In a complex world with complex constructs, it is critical for researchers to consider the
implications of different approaches for modeling multidimensional phenomena. Our illustration
demonstrates the utility of empirical tests for model comparisons but also shows that model
selection should be driven by theoretical rationale. As a field, we should better recognize that the
findings of any single study should not constitute the basis for theory or practical solutions, given
that findings are sensitive to small nuances in model selection. Replication and accumulation of
evidence across studies and across methodological approaches is important for drawing firm
conclusions. Our paper offers a set of valid, reliable, and age invariant measures of civic
engagement that, particularly when modeled multidimensionally, can enhance understanding of
development in this domain. In studying multidimensional constructs, we urge scholars to take
comfort in the now classic statistical adage, “All models are wrong, but some are useful” (Box &
Draper, 1976, p. 424). There is room for both general and specific approaches to
multidimensional constructs, and different approaches advance theory in distinct ways and
produce different kinds of evidence of value for policy and practice.
Multidimensional Measurement of Civic Engagement by Age 32
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Measuring Multidimensional Developmental Constructs 47
Figures 1-4. Conceptual figures illustrating various multidimensional measurement model
approaches.
Model 0. Unidimensional Model
S1
S2
S3
S4
I1
I2
I3
I4
I5
I6
P1
P2
C1
C2
C3
C4
C5
C6
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E2
E3
Civic
Engagement
Model 1. Correlated Unidimensional Factors Model
S1
S2
S3
S4
I1
I2
I3
I4
I5
I6
P1
P2
C1
C2
C3
C4
C5
C6
E1
E2
E3
SocResp
Values
Volunteer
Informal
Helping
Vote
News
Political
Beliefs
Civic Skills
Enviro
Behavior
Measuring Multidimensional Developmental Constructs 48
Model 2. Higher-Order Model
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S2
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S4
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I4
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I6
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C2
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C4
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SocResp
Values
Volunteer
Informal
Helping
Vote
News
Political
Beliefs
Civic Skills
Enviro
Behavior
Civic
Engagement
Model 3. Bifactor Model
S1
S2
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S4
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I2
I3
I4
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I6
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Measuring Multidimensional Developmental Constructs 49
Online Appendix A
Description of Planned Missingness Design
Data collection for the Roots of Engaged Citizenship Project used a planned missingness
design. Planned missingness designs represent an efficient way to maximize the number of
survey questions asked in a fixed time frame. This design reduces cognitive demands on
participants, produces surveys that are developmentally responsive to participants’ abilities, and
increases likelihood of survey completion, thus minimizing less desirable forms of missing data
(Enders, 2010; Graham, 2012; Little & Rhemtulla, 2013). Our study assessed multiple individual
and contextual factors in relation to various dimensions of civic engagement. To achieve our
aims, we used a school-based survey design where students were surveyed for approximately 45
minutes during school hours. The planned missingness design allowed us to include a wider set
of constructs while keeping the survey length short enough to complete during a class period.
A three-form planned missing design was employed, such that survey items were divided
into one core set (X) and three additional item sets (A, B, C). Three survey forms were created
that included the core items (X) and two out of three other items sets (see Table A1). The X set
was presented first in all survey versions, and item sets A, B, and C were counterbalanced across
versions. Items in a scale were kept together in the same item set (Graham, 2012). The core X set
contained the primary dependent variables for the study (i.e., civic engagement), demographics,
and a few central predictors. A, B, and C sets were structured to include a balance of
competencies, character, and context variables across item sets. Consistent with
recommendations for planned missingness designs, constructs were grouped together within
version if we had specific hypotheses about how they were associated, which maximized power
to test these hypotheses (Graham, 2012).
Measuring Multidimensional Developmental Constructs 50
Table A1. Survey forms and item sets
Survey Form
Item Sets
Number of Items
Elementary
Middle
High
1
X + A + B
96
153
173
2
X + C + A
96
149
169
3
X + B + C
96
150
167
Total # of Items Measured
134
225
247
Another layer of our design was planned missingness by age. After creating the three
forms, we created age-specific versions of the survey such that elementary and middle school
versions were shorter than the high school version (see Table A1). Item wording was the same
across ages, but more complex and less central constructs were included at older ages only. This
resulted in 9 versions of the survey (3 forms X 3 age groups). The civic engagement
measurement models utilized items that were measured identically across all three age groups.
Given that this type of missing data is completely controlled by the researcher and thus
missing completely at random (MCAR), modern missing data approaches can easily
accommodate this form of missingness. The Principal Components Method was used to handle
planned and other types of missing data (Howard, Rhemtulla, & Little, 2015; Little, Howard,
McConnell, & Stump, 2008). PCA is conducted on all variables in the data and resulting
principal components are used as auxiliary variables in conjunction with full information
maximum likelihood (FIML) estimation. Auxiliary variables improve the performance of FIML
by making assumptions of missing at random (MAR) more reasonable and increasing FIML
efficiency by reducing uncertainty due to missingness (Collins, Schafer, & Kam, 2001). PCA
was conducted using the Quark package for R version 3.1.2. For each school level (elementary,
Measuring Multidimensional Developmental Constructs 51
middle, and high), variables were first standardized in Quark to ensure that all variables
contributed equally to PC scores. Following standardization, a single imputation was run so that
all variables were included in the PCA. After conducting the PCA on the imputed data, 10 of the
initial PCs were retained, accounting for 50% of the variance. Sensitivity analyses determined
the number of principal components to ensure that the number of retained PCs provided
consistent results across models. These PCs were merged with the original, non-imputed data
and used as auxiliary variables in FIML estimations in Mplus version 7.
A series of chi-square tests were conducted to determine whether survey versions were
distributed randomly across participants. We examined survey version in relation to site
(California, Minnesota, West Virginia), school level (elementary, middle, and high), grade (4th-
12th), gender (male, female), ethnicity (Black, Hispanic, White, Asian, Other), and immigrant
status (born in US, born outside of the US). As shown in Table A2, no chi-square tests were
significant, indicating that assignment to survey version did not vary by demographics. This
provides evidence that the planned missing design was successfully executed and randomly
distributed across participants.
Measuring Multidimensional Developmental Constructs 52
Table A2. Chi-square tests of independence with survey version and key demographics.
Pearson chi-square tests
χ2
df
p-value
Survey version (3) x Site (3)
1.60
4
.809
Survey version (3) x School level (3)
.947
4
.918
Survey version (3) x Grade (9)
2.50
16
1.00
Survey version (3) x Gender (2)
2.06
2
.357
Survey version (3) x Ethnicity (5)
11.08
12
.523
Survey version (3) x Immigrant status (2)
1.16
2
.559
Appendix References
Collins, L. M., Schafer, J. L., & Kam, C. M. (2001). A comparison of inclusive and restrictive
strategies in modern missing data procedures. Psychological Methods, 6(4), 330. doi:
10.1037//1082-989X.6.4.330
Enders, C. K. (2010). Applied missing data analysis. New York: Guilford Press.
Graham, J. W. (2012). Missing data: Analysis and design. New York: Springer Science &
Business Media.
Howard, W., Rhemtulla, M., & Little, T. D. (2015). Using principal components as auxiliary
variables in missing data estimation. Multivariate Behavioral Research, 50(3), 285-299.
doi: 10.1080/00273171.2014.999267.
Little, T. D., McConnell, E. K., Howard, W. J., & Stump, K. N. (2008). Missing Data in Large
Data Projects: Two methods of missing data imputation when working with large data
projects. (KUant Guides#11.3). Retrieved from the Center for Research and Data
Analysis Website: http://web.ku.edu/~quant/cgi-bin/mw0/index.php?title=KUant_Guides
Little, T. D., & Rhemtulla, M. (2013). Planned missing data designs for developmental
researchers. Child Development Perspectives, 7(4), 199-204. doi: 10.1111/cdep.12043
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There are many reasons for scholars to investigate empathy. Empathy plays a crucial role in human social interaction at all stages of life; it is thought to help motivate positive social behavior, inhibit aggression, and provide the affective and motivational bases for moral development; it is a necessary component of psychotherapy and patient-physician interactions. This volume covers a wide range of topics in empathy theory, research, and applications, helping to integrate perspectives as varied as anthropology and neuroscience. The contributors discuss the evolution of empathy within the mammalian brain and the development of empathy in infants and children; the relationships among empathy, social behavior, compassion, and altruism; the neural underpinnings of empathy; cognitive versus emotional empathy in clinical practice; and the cost of empathy. Taken together, the contributions significantly broaden the interdisciplinary scope of empathy studies, reporting on current knowledge of the evolutionary, social, developmental, cognitive, and neurobiological aspects of empathy and linking this capacity to human communication, including in clinical practice and medical education.