Content uploaded by Jiesi Guo
Author content
All content in this area was uploaded by Jiesi Guo on Oct 16, 2018
Content may be subject to copyright.
Running head: EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
Extending Expectancy-Value Theory Predictions of Achievement and Aspirations in Science:
Dimensional Comparison Processes and Expectancy-by-Value Interactions
Revision (05 December 2016)
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
Abstract
Based on TIMSS data (18,047 Grade 8 students from the four OECD countries that collected
data for multiple science domains), this study integrated dimensional comparison theory and
expectancy-value theory and tested predictions about how self-concept and value are related to
achievement and coursework aspirations across four science domains (physics, chemistry, earth
science, and biology). First, strong support for social comparisons suggested that high
achievement in a particular domain enhance students’ motivation in the same domain, which in
turn predicted domain-specific aspirations. Particularly, self-concept significantly interacted with
value to predict aspirations. Second, in the processes underlying the formation of self-concept
and intrinsic value, students tended to engage in negative dimensional comparisons between
contrasting domains (physics vs. biology) but positive dimensional comparisons between
assimilating domains (physics vs. chemistry). Similar dimensional comparison processes were
evident for the effects of self-concept and intrinsic value on aspirations. The results generalized
well across all countries.
Keywords: self-concept, expectancy-value, science subjects, coursework aspirations,
latent interaction
2
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
The issue of talented and capable students opting out of the STEM (i.e., science,
technology, engineering, and mathematics) pipeline has been a topic of enduring interest in the
science education community. Given that dropping out of science coursework at high school
makes it very difficult to undertake STEM college majors and careers, growing attention in
research on science motivation has focused on disentangling the relationship between students’
motivational beliefs and achievement in science on one hand, and high-school science course
taking, aspirations, and persistence on the other (e.g., Guo, Parker, Marsh, & Morin, 2015; Nagy
et al., 2008; Parker et al., 2012).
These studies have demonstrated that motivation beliefs (e.g., academic self-concept and
value beliefs) represent important determinants of achievement-related decisions in STEM
subjects, net of individual’s actual ability and achievement (Wang & Degol, 2013). However,
much of this research has focused on motivational beliefs in general science, whereas science
choices and aspirations are often measured in specific science domains. Indeed, the process of
subject selection is inherently comparative. For example, let us consider the decision to major in
physics at college. Students will be most likely to select this major only if they hold high
confidence in their ability to do well in the course required by this major and place high value on
majoring in physics by comparing the physics major to other majors including other science
domains (see Eccles, 2009). Such intraindividual dimensional comparisons have been found to
be useful for predicting academic choices. Nevertheless, existing research has focused almost
exclusively on the dimensional comparison processes between math and verbal domains (e.g.,
Parker et al., 2012).
The aim of this study was to overcome the shortcomings of prior research, by testing the
relations between academic achievement, motivational beliefs, and coursework aspirations
taking into account several different science disciplines. In pursuing this overarching aim, we
integrated and extended two major theoretical models of academic motivation (i.e., dimensional
comparison theory [DCT], Möller & Marsh, 2013; expectancy-value theory [EVT], Eccles,
2009) in relation to four major science domains (physics, chemistry, biology, and earth science).
First, contrasting achievement and motivation, we tested how students’ subject-specific self-
concept and intrinsic and utility values in science were shaped by dimensional comparisons.
3
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
Second, extending theoretical developments based on DCT, we explored how such dimensional
comparison processes predicted coursework aspirations across different science domains. Third,
extending recent developments based on EVT, we tested how academic self-concept interacted
with value beliefs in predicting aspirations.
The present study drew on eight-grade students from the Trends in International
Mathematics and Science Study (TIMSS 2007). TIMSS has been a major basis of international
comparisons of countries in terms of educational motivation and achievement in the four major
science domains. Thus, it presents an unprecedented opportunity for researchers to investigate
students’ motivational pathways to different STEM-related fields. This study was among the first
to take advantage of the TIMSS data to address this substantive issue. In order to test the cross-
national generalizability of our results, we rely on a convenience sample of all OECD countries
who chose to conduct separate motivation assessments in physics, chemistry, biology and earth
science, including the Czech Republic, Hungary, Slovenia, and Sweden (Olson, Martin, &
Mullis, 2008). We note that the current approach, aiming to identify pan-human generalizations
rather than country-specific idiosyncratic effects, is well-aligned with the approach typically
taken in the study of similar educational phenomenon (e.g., the Internal-External frames of
reference [I/E] model, the Big-Fish Little-Pond effect) using large international data sets (Marsh
et al., 2014, 2015).
Focusing on motivational beliefs in general science or a single subject domain would
result in a very limited perspective in explaining achievement-related behavior choices in STEM
and may even be counterproductive in understanding coursework selection and aspirations in
particular science disciplines (Eccles, 2009). By evaluating the influence of the intraindividual
dimensional comparisons in relation to self-concept and value within science domains, this
investigation may shed some light on how achievement and motivational beliefs might affect the
decision students make to remain in or leave from the pathway toward different STEM-related
fields.
1 Dimensional Comparison Processes
Academic self-concept, the self-evaluation of a student’s ability in a given domain, has
been assumed to be a multifaceted, hierarchical construct including a number of self-perceptions
4
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
in different academic domains (Marsh, 2007). In order to evaluate their strengths and
weaknesses, students compare and contrast their own performances across different school
disciplines (Möller & Marsh, 2013). The I/E model were originally developed to explain the
apparently paradoxical relations among domain-specific self-concepts and achievement: near
zero-correlations between math and verbal self-concepts despite math and verbal achievement
being moderately to strongly correlated (Marsh, 2007). The I/E model posits that students form
their verbal and math self-concepts as a function of two underlying processes: social and
dimensional comparison. Using an external frame of reference, students conduct social
comparisons by comparing their self-perceived performance in a subject domain with that of
their peers in the same school or classroom. For instance, if students have higher math
achievement than do their classmates, their math self-concept is also likely to be higher. Thus,
the social comparison processes lead to a positive prediction from achievement and self-concept
within a subject domain. Employing a dimensional frame of reference, students conduct
dimensional comparisons by comparing their performances in one particular subject domain
against their performance in other subject domains. However, the dimensional comparison
processes are ipsative, so that high levels of math ability should lead to lower verbal self-concept
once the positive effect of verbal ability is controlled for.
Recently, the I/E model has been extended into DCT (Möller & Marsh, 2013) by
incorporating a wider variety of subject domains. DCT postulates that academic self-concepts are
formed by different dimensional comparisons. On the one hand, contrasting dimensional
comparison processes predict that good performance in one domain leads to lower self-concept
in other domains (i.e., contrast effects). On the other hand, assimilating dimensional comparison
processes are characterized by good performance in one domain leading to higher self-concept in
other domains (i.e., assimilation effects). Whether students engage in contrasting or assimilating
dimensional comparisons is related to their beliefs as to whether two abilities are negatively or
positively correlated (Möller et al., 2015). One of the critical assumptions of DCT is that
perceived subject similarity corresponds to the verbal-mathematical continuum of core academic
self-concept domains (Möller & Marsh, 2013). This assumption has been well supported in both
empirical and experimental studies. For example, Haag and Götz (2012) demonstrated that
5
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
subjects (far from each other on the continuum, e.g., math vs. German) with low self-concept
correlations were perceived as rather dissimilar and that subjects (close to each other, e.g., math
vs. physics) with high self-concept correlations are perceived as more similar. A recent empirical
study (Helm et al., 2016) also confirmed this assumption and addressed that contrast effects were
stronger when students focus on differences between two subject domains than when they
focused on similarities. Thus, according to the verbal-mathematical continuum of academic self-
concept, assimilation effects are assumed to occur between “near” domains, whereas contrast
effects are assumed to occur between “far” domains.
In relation to science domains, physics and chemistry are assumed to be located closer to
the math domain, whereas biology is assumed to be located in the middle of the continuum.
More recently, Jansen et al. (2014) contrasted achievement and self-concept in physics,
chemistry, and biology and found that associations of self-concept with achievement and grades
were substantial in the same domains. For cross-subject relations, they revealed slightly negative
contrast effects between biology and physics but assimilation effects between chemistry and
physics (for similar results, also see Jansen et al., 2015). However, these two previous studies
focus on German high school students, and the findings have yet to be replicated with other
populations across different science curricula. Moreover, these studies have not included earth
science and thus miss out on the opportunity to gain insight into dimensional comparison
processes between four major science disciplines.
More recently, based on DCT, the Generalized I/E (GI/E) Model (Möller et al., 2015) has
been developed by connecting dimensional comparison processes to broader cognitive, affective,
and motivational consequences. Dimensional comparisons are assumed to serve as a critical
source of information as to students’ strength and weakness across different domains. These self-
evaluations would help students to distinguish domains in which they can specialize, and for
which they could develop particular interests, emotions, and preferences. Thus, dimensional
comparisons are underlying mechanisms for the process of self-differentiation to serve
motivational needs (Möller et al., 2015). In this regard, the GI/E model assumption has been
tested with respect to emotions (Goetz, Frenzel, Hall, & Pekrun, 2008), intrinsic and utility
values (Nagy et al., 2008; Schurtz et al., 2014), and perceptions of the learning environment
6
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
(Arens & Möller, 2016). For example, Schurtz et al. (2014) found negative contrast effects from
grades to intrinsic value between math and English, following the typical I/E pattern. However,
the negative impact of dimensional comparisons on intrinsic value was totally mediated by self-
concepts (also see Nagy et al., 2008).
However, these studies mainly drew on math and verbal domains. Arens and Möller
(2016) argued that the scope of subject domains and outcome variables that are subject to
dimension comparison processes should be even broader. There is to our knowledge no study
examining the potential operation of dimensional comparisons in the formation of students’
values in “near” domains on the continuum, such as between science subdisciplines.
2 Integrating Dimensional Comparison into EVT
Dimensional comparison processes posited in DCT and the GI/E model have been
integrated into modern EVT, which has been widely used to explain students’ academic choice
behaviors (Eccles, 2009). EVT posits that a relative intraindividual’s hierarchy of competence
beliefs (e.g., academic self-concept) and task value are influenced as a function of previous
achievement across subject domains (Eccles, 2009). More importantly, these relative
motivational beliefs are postulated to play important roles to link between achievement and
behavioral choices and aspirations in EVT. All such behaviors are also assumed to be associated
with costs, as one choice often eliminates other options (an ipsative process), and thus trigger
dimensional comparison of achievement and motivation (Eccles, 2009). Put simply, individual
differences in relative self-concept and task value attached to a domain compared to other
domains influence course enrollment (Nagy et al., 2008). In this regard, the individual hierarchy
of self-concept and value across domains are not only the consequences of dimensional
comparisons but also the antecedents of behavioral choices.
In this study, we focus on two of these components: intrinsic and utility values. Intrinsic
value, referring to the extent to which the person gains enjoyment from performing an activity,
has been found to be a stronger predictor of academic engagement, effort exertion, and
coursework aspirations (e.g., Guo et al, 2015, 2016). Utility value refers to how useful a task is
for facilitating an individual’s long-range goals and helping an individual obtain long-range
7
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
external rewards. It has been found to more closed to educational and career aspirations,
particularly during the post-high school transition (Wigfield, Tonks, & Klauda; 2016)
Although the notion of dimensional comparison processes has been well integrated into
EVT, relatively little empirical work has applied such processes to predict achievement-related
choices. Nagy et al. (2008; Parker et al., 2012) presented one of the few exceptions and provided
an excellent example of these processes. By comparing their performance in math and English,
high school students who had better performance in math tended to become more confident and
interested in math but less in English. Subsequently, the positive motivation in math led these
students to choose an advanced math course but opt out of an advanced English course. Again,
these studies only focus on math and verbal domains, which leaves open the question as to
whether students engage in assimilating dimension comparisons between similar domains (e.g.,
physics and chemistry) during the decision-making process. Thus, this study integrates EVT with
new insights from DCT and draws on multiple, similar (science) domains to explore how
dimensional comparison processes predict coursework aspirations.
3 Interaction Between Self-Concept and Task Values
In addition to having the first-order effects, competence beliefs and value beliefs are
assumed to interact with each other in influencing achievement-related behaviors and choices in
early EVT (Atkinson, 1957). The expectancy-by-value interaction suggests that if students do not
have confidence in their abilities to succeed in a task, then even high value beliefs will not be
sufficient to motivate students to pursue the task. However, this multiplicative relation, which
was the central assumption of classic EVT, has not been widely studied in modern EVT.
Nagengast et al. (2011) attributed this to weak statistical methodology in testing interaction
effects and addressed that the expectancy-by-value interaction should be returned "to its rightful
place at the heart of EVT" (p. 1064).
Recently empirical studies have successfully reintroduced examination of interaction
effects between expectancy and value in predicting educational outcomes based on the newer
approaches (e.g., the unconstrained approach; Nagengast et al., 2011). For example, Guo, Parker
et al. (2015) found that the interactions between high school math self-concept and values
significantly predicted math course selection, matriculation results, subsequent STEM major
8
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
choices and entry into university. However, most of this research only considered a single
domain (e.g., science), and the researchers did not test the domain specificity of the patterns of
results across different science domains. As a consequence, their research did not explore the
ipsative dimensional comparison processes; a matter that has been subsequently addressed with
the extension to DCT and its integration into EVT.
4 The present investigation
Drawing on DCT and EVT, the present investigation aims to examine the distinctiveness
of relationships between domain-specific achievement, motivational beliefs (self-concept,
intrinsic value, and utility value), and coursework aspirations across four major science subjects
(physics, chemistry, earth science, and biology). Importantly, we explore the roles of expectancy-
by-value interactions with dimensional comparison processes in predicting aspirations. Hence,
the present study is unique in that it takes multiple science disciplines into account and integrates
DCT and EVT to provide a greater understanding of the motivational dynamics leading students
to making academic choices within STEM-related fields. More specifically, self-concept,
intrinsic value, and utility value along with achievements and aspirations in the four science
domains are simultaneously included in the hypothesized model where all achievements are
linked to the domain-specific motivational beliefs that in turn predict coursework aspirations
(See Figure 1).
Hypotheses
4.1.1 Hypothesis 1: Relations between achievement and motivational beliefs
a. We predict matching paths from each of the four achievement domains to self-concept,
intrinsic value, and utility value in the same domain to be significantly positive.
b. For physics, chemistry, and biology, according to the verbal-math continuum of self-
concept (Marsh, 1990), we hypothesize non-matching paths (cross-paths) relating to “far”
domains (e.g., physics achievement predicts biology self-concept) to be negative (contrast
effects), whereas we hypothesize these cross-paths relating to “near” domains (e.g., physics
achievement predicts chemistry self-concept) to be positive (assimilation effects).
However, earth science has not been positioned in this continuum. According to TIMSS,
earth science is concerned with the study of earth and its place in the solar system and the
9
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
universe, covering the fields of geology, astronomy, meteorology, hydrology and oceanography
(Olson et al., 2008). For the four targeted countries, earth science is taught as a separate natural
science subject along with biology, chemistry, and physics in Czech Republic and Hungary;
although earth science is not taught separately, it is mainly represented in physics and chemistry
and only included as a small part of the social sciences subject of geography in Slovenia and
Sweden (Olson et al., 2008, see Table 1). Thus, we expect that earth science is more closely
related to the mathematical side than the verbal side of the verbal-mathematical continuum. More
precisely, we hypothesize that earth science is located in the middle of physics/chemistry and
biology on the continuum, given that topics covered in the teaching and learning of earth science
are largely intertwined with some concepts also covered in biology, physics, and chemistry.
However, given the absence of empirical evidence for this, we still leave cross-paths involving
earth science as a research question to be explored.
4.1.2 Hypothesis 2: Relations between motivational beliefs and coursework aspirations
a. We predict matching paths to be significantly positive from self-concept, intrinsic
value, and utility value in each domain to coursework aspirations in the same domain, even after
controlling for achievement. Based on previous research, in predicting coursework aspirations,
we hypothesize matching path coefficients for intrinsic value to be stronger than those for utility
value and self-concept.
b. We hypothesize cross-paths relating to “far” domain (e.g., biology self-concept
predicts physics aspirations) to be negative, whereas these cross-paths relating to “near domain”
(e.g., physics self-concept predicts chemistry aspirations) to be positive. Again, we leave the
pattern of the predictions in relation to earth science as a research question.
c. Consistent with the recent re-introduction of expectancy-by-value interactions into
EVT, we predict that latent interactions between self-concept and values (intrinsic value and
utility value) predict aspirations beyond the first-order (“main”) effects of these latent constructs.
4.1.3 Research question: Generalizability of results
Cross-cultural comparisons provide researchers with a heuristic basis to test the external
validity and generalizability of their measures, theories, and models. Typically, there are two
main approaches to cross-cultural comparisons: the etic and emic perspectives. The etic
10
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
perspective refers to the cultural universals with an emphasis on cross-cultural similarities of
theoretical predictions and replicability of results, whereas the emic perspective refers to
phenomena specific to a particular culture with an emphasis the uniqueness of an individual case
in its own terms. Marsh, Martin, & Hau (2006) addressed that one of the ongoing challenges in
cross-cultural research in education is to untangle the potentially confounding effects of
differences in participants representing different cultural groups and the appropriateness of
psychological measure in different cultural settings. To the extent that a strong theoretical model
generalizes well to heterogeneous samples drawn from a diverse set of countries, there is strong
support for the external validity and the robustness of the interpretations based on the theory.
Indeed, there is a strong basis for the etic approach based on Möller et al. (2009) meta-
analysis that found no significant differences across countries in support for the DCT predictions
in relation to verbal and math self-concept. More recently, Marsh et al. (2015) provided a more
critical evaluation of the cross-cultural generalizability of the I/E patterns. Their findings showed
the strong support for the generalizability of the DCT predictions in relation to math and general
science across 12 nations based on TIMSS2007 data. In this regard, one purpose of our study
was to expand the scope of tests of the generalizability of the DCT predictions beyond previous
studies that have been the primary basis of cross-cultural tests of the universality of support for
DCT predictions.
Therefore, we leave as an open research question whether the hypothesized associations
will generalize across the four OECD countries. Given that students were exposed in
substantially different cultural and educational contexts across countries (See Table 1), it would
provide a strong test of the external validity of our findings.
5 Method
Participants
Although standardized tests in four science domain-specific subjects (Physics, Chemistry,
Earth Science, and Biology) are administered to eighth-grade students in all participating
countries, TIMSS surveys in relation to the four subjects were only administered in countries
teaching some or all of these subjects separately, rather than as a single, general subject (Olson et
al., 2008). In TIMSS 2007 data, Czech Republic, Hungary, Slovenia, and Sweden are the only
11
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
OECD countries in which students completed surveys in relation to these four science domains
(Olson et al., 2008). Therefore, in the present study, the target population comprised eighth-grade
students who participated in TIMSS 2007 from the four OECD countries described above. In
total, we considered data from 18,047 students (51% boys) in 1,025 classes and 598 schools (see
Appendix A).
Measure
Motivational factors. The measures of expectancy-value constructs were selected from
the student-background questionnaire administered in TIMSS2007. All motivation items were
coded on a four-Likert scale. For the present purposes, responses were reverse-scored, so that
higher values represented more favorable responses and thus, higher levels of motivation.
A scale of students’ Self-confidence in Learning Science that assesses how students think
about their ability in specific domains was used to measure academic self-concept in TIMSS
studies (Marsh et al., 2013, See Table 2). The students’ Positive Affect Toward Science scale was
applied to assess the affect experienced by students when participating in domain-related
activities, in line with the notion of intrinsic value in the EVT. Likewise, the Students’ Valuing
Science scale was similar to utility value in the modern EVT, which assesses how well
achievement in specific domains relates to current and future goals. These three latent constructs
demonstrated satisfactory reliability across the four countries (see Appendix A).
Academic achievement. Participants’ academic abilities of science are assessed though a
range of questions in the four science subdomains. Two question formats were used in the
TIMSS assessment – multiple-choice and written-response questions that involved a mixture of
knowing, applying, and reasoning process (Olson et al., 2008).
Coursework aspirations. As there was only one item measuring students’ achievement-
related decisions in the TIMSS2007, following Marsh et al. (2013), this single item was used
students’ coursework aspirations in each subject area (“I would like to do more in
Biology/Physics/Earth science/Chemistry in school.”). The response scale ranged from 1,
indicating that the participants “disagree a lot” to 4, indicating “agree a lot”.
Data Analysis
In the present study, multi-group confirmatory factor analyses (CFAs) and structural
12
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
equation models (SEMs) were conducted with Mplus 7.11 using the robust maximum likelihood
estimator. The unconstrained approach (Nagengast et al., 2011) was utilized to model the latent
interactions between self-concept and task value in predicting coursework aspirations. The
classroom clustering and weighting variables were used to control for the clustering sample (see
Appendix B and C). We used full information maximum likelihood (FIML) estimation to handle
a relatively small amount of missing data on the remaining items (6.3% to 18.2% in Sweden and
less than 2% for other countries).
Preliminary Analyses
Preliminary analyses described in details Appendix D demonstrated: (a) there was good
support for the factor structures underlying the multiple domains of self-concept, intrinsic value,
and utility value; (b) rigorous tests of factorial invariance showed that factor loadings, variances
and covariances for motivational beliefs, achievement, and aspirations were invariant over the
four OECD countries (Models MG1–MG4, See Table 3), and (c) there was good support for the
convergent and discriminant validity of motivation beliefs in relation to achievement and
aspirations, particularly for self-concept and intrinsic value, to a lesser extent, but also for utility
value.
6 Results
Tests of Predictions Relating Achievement to Motivation Beliefs: Hypothesis 1
Matching paths. In this SEM model, we included one set of 16 (4 x 4; 1 matching path +
3 non-matching paths for each domain) paths from achievement in each science domain to each
of the four self-concepts with two additional sets of 16 paths from achievement to each of the
four intrinsic values and each of the four utility values (Models MG5–MG7, See Table 1). Of
particular importance were the substantial path coefficients between paths from achievement to
motivation constructs in matching domains compared to those in non-matching domains. To
clarify these critical path coefficients, we computed summary statistics for matching paths, non-
matching paths, and their difference (see Appendix E). As seen in Figures 2 based on Model
MG7b where factor loadings and factor variances and covariances, and path coefficients were
invariant across countries (see subsequent discussion), the matching paths from achievement to
matching self-concept (Mean [M] = .19, SE = .01) and intrinsic value (M = .14, SE = .01) factors
13
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
were positive across the four science disciplines. However, the matching paths for utility value
were relatively small (M = .05, SE = .01).
Non-matching paths. The means across the 12 remaining non-matching path
coefficients from achievement in each domain to non-matching motivational beliefs were
substantially smaller than the corresponding matching coefficients (self-concept:
[mean of
matching paths – mean of non-matching paths] M = .16, SE = .01; intrinsic value:
M = .16, SE
= .01; utility value:
M = .07, SE = .01). More specifically, consistent with predictions from
Hypothesis 1b, cross-paths between physics and biology were negative, whereas those between
physics and chemistry were positive. We also found that cross-paths between chemistry and
biology were slightly positive but significantly weaker than those between physics and chemistry
(see Appendix E). Cross-paths between earth science and the other science domains were slightly
positive or non-significant. It should be noted these patterns of results were only evident in
relation to self-concept and intrinsic value.
Mediating role of self-concept. Following Nagy et al., (2008), we evaluated whether
effects of achievements on task and intrinsic value could be explained by self-concept. In the
mediation model (MG10) achievements in the four science domains predicted self-concepts,
which in turn predicted intrinsic and utility values. In this model, the four domain-specific self-
concepts and values along with achievements were also allowed to predict coursework
aspirations. However, it is important to emphasize that the goodness of fit of this mediation
model (MG10) is necessarily the same as the original non-mediation model (MG7b), as are the
total (direct + indirect) effects of achievement; that is some of the effects interpreted as direct
effects in MG7b are now are now interpreted as mediated effects in MG10, but the total effects
are the same. The results revealed that all 32 direct paths from the four science achievements to
each of the intrinsic and utility values were relatively small (from -.05 to .05; M = .01) in the
mediation model. Subsequently, we evaluated a nested model where these 32 direct paths were
constrained to be 0. There was a negligible decrease in model fit (
CFI = .002,
TLI = .001,
RMSEA = .001) when compared to the fully mediated model. Consistent with previous
research these results can be interpreted to mean that the statistically significant total effects of
14
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
achievements on intrinsic and task value are largely mediated by self-concept. Although the
cross-sectional nature of our data dictate caution in the interpretation of the mediation model, the
total effects in the mediation model (MG10) are the same as the direct effects in the original non-
mediation model (MG7b). In this sense, the interpretations of total effects in the mediation model
are the same as those of the direct effects in the non-mediation model.
Tests of Predictions Relating Motivational Beliefs to Aspirations: Hypothesis 2
Matching paths. We began with an evaluation of models without latent interactions.
Consistent with predictions from Hypothesis 2a, matching paths from self-concept, intrinsic
value and utility value in each domain to coursework aspirations, were substantially positive,
controlling for achievement (see Figure 2). The mean across the four matching path coefficients
for intrinsic value (M = .67, SE = .01) was substantially larger than that for self-concept (M = .
10, SE = .01) and utility value (M = .06, SE = .01).
Non-matching paths. Non-matching paths (cross-path) from motivational beliefs to
aspirations smaller than the corresponding matching paths (self-concept:
M = .09, SE = .02;
intrinsic value:
M = .66, SE = .01; utility value:
M = .05, SE = .01). In line with predictions
from Hypothesis 2b, cross-paths between physics and biology were significantly negative. Again,
the pattern of results was found for self-concept and intrinsic value but not utility value.
However, the majority of cross-paths involving self-concept, intrinsic value, and utility value
were non-significant or slightly positive.
Latent interactions. We added two sets of domain-specific latent product variables to the
Model MG7b: one based on product indicators for the self-concept and intrinsic value (MG8a-
MG8b), and one based on those for self-concept and utility value (MG9a-MG9b). It should be
noted that all path coefficients in the model with interactions are similar to those without
interactions (see Appendix E). The mean of matching paths involving self-concept-by-intrinsic
value and self-concept-by-utility value interactions were significantly positive (M = .12, SE = .
01; M = .09, SE = .01, respectively). Given that the sizes of matching interaction path
coefficients for different domains were similar, a simple-slopes plot was constructed, based on
the mean of matching interaction path coefficients (see Figure 3). Tests of the simple slopes
15
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
indicated that the slope for the effect of self-concept on aspirations for intrinsic and utility values
of -1 SD below the mean (M = -.02, SE = .02, p = .211; M = -.01, SE = .01, p = .346,
respectively) was non-significant. However, the slopes at average intrinsic and utility values
became statistically significant (M = .10, SE = .01, p < .001; M = .08, SE = .01, p < .001,
respectively), which was smaller than those for intrinsic and utility values of +1 SD above the
mean (M = .22, SE = .02, p < .001; M = .17, SE = .02, p < .001, respectively). Figure 3 clearly
shows the interactive relations of domain-specific self-concept and task value in predicting
coursework aspirations: high self-concept only contributes to high aspirations when intrinsic and
utility values are moderately elevated. However, when either utility value or intrinsic value are
low, the contribution of self-concept in the prediction of aspirations is absent, which implies that
high self-concept cannot compensate for low value (and vice versa). Supplemental analyses
suggest that both types of domain-specific interactions (self-concept-by-intrinsic value and self-
concept-by-utility value) make similar contributions to the prediction of aspirations when both
product variables are considered simultaneously (see Appendix G).
Tests of Predictive Relations Over Countries
In order to test the generalizability of our results, we estimated a series of multiple-group
SEMs testing whether path coefficients were invariant across the four countries (Models MG5–
MG9b, see Table 3). We conducted pair comparisons for the models where the same
measurement invariance was imposed (i.e., factor loadings, factor variances, and factor
covariances) and the only difference was whether or not structural coefficients were freely
estimated (e.g., MG7a vs. MG7b). Although the imposition of the additional constraints on
structural coefficients resulted in some decreases in model fit, these decreases were negligible,
and all models provided a satisfactory level of fit to the data. To more directly compare the
similarity of country-specific path coefficients, we also calculated a profile similarity index
(PSI). The PSI is an estimate of the correlations between path coefficients obtained from
different countries. For all path coefficients based on Model 7a, the PSI indicated the very high
level of similarity across the four countries (range from to .861 to .957, see Appendix H for
country-specific path coefficients). Thus, there was strong support for the invariance of path
coefficients over the four countries.
16
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
7 Discussion
In this study we adopted a multidimensional perspective on self-concept and intrinsic and
utility values in science domains, and examined associations among achievement, motivational
beliefs and coursework aspirations. Our findings suggest that outcomes in any one domain
depend not only on accomplishments, self-concept beliefs, and value perceptions in that domain,
but also on how these constructs compare to those in other, contrasting domains.
The Relations between Achievement and Motivational beliefs
Our findings supported DCT to confirm that students receive information from two main
sources to form their self-concept: (a) they engage in social comparison with others as a way to
judge their own abilities as evident by strong domain-specific relations between achievement and
motivational beliefs; (b) students systematically evaluate their abilities by comparing difference
subject domains (dimensional comparison processes). More importantly, our findings supported
the crucial assumption of DCT that student tend to make both assimilating or contrasting
dimensional comparisons, which is related to perceived subject similarity. Specifically, students
are likely to engage in contrasting dimensional comparison between physics and biology which
are separated by the greatest distance on the continuum of academic self-concepts (relative to
other science domains). However, most previous support for such contrasting comparison is
based on studies of math and verbal domains that are at opposite ends of the academic self-
concept continuum. Simultaneously, students are likely to engage in assimilating dimensional
comparison between physics and chemistry. This indicates that students apparently perceive
physics and chemistry to be similar and complementary subjects, such that skills acquired in one
subject will help success in the other subject, and achievement feedback in one subject may
provide an additional source of positive information to help evaluate abilities in the other subject.
The assimilating dimensional comparisons are also evident between chemistry and
biology, but they are significantly smaller than those between physics and chemistry. This result
is in line with the verbal-math continuum, suggesting that chemistry and physics would be
perceived as more similar to each other than chemistry and biology. However, these assimilation
effects are not contradictory to the contrasting dimensional comparisons between physics and
biology. Students who have high ability in chemistry tend to have high self-concept in both
17
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
physics and biology, while highly able students in biology tend to have low self-concept in
physics (and vice versa) given the same ability in chemistry.
With respect to earth science, the contrasting dimensional comparison processes
apparently were not triggered in relation to other science domains. Instead, students are likely to
engage in assimilating dimensional comparisons between earth science and other science
domains in similar size. This indicated that students perceive earth science to be relatively
similar to other science domains, implying that earth science would be located between
physics/chemistry and biology in the verbal-math continuum. Note that this study is among the
first to incorporate earth science and explore perceived similarity in relation to other domains.
Thus, the results provide new theoretical and substantive insights into I/E model and DCT.
By integrating DCT into EVT, the results suggested that the two main sources involving
achievement/ability comparison also significantly influence the development of students’
intrinsic value. This finding suggests that when students perceive school subjects to be similar
(e.g., physics and biology), intrinsic motivation in one is likely to generalize to the other,
whereas when they perceive those subjects to be distinct (physics vs. biology), liking of one
subject domain tends to wane if students have high achievement in the other domain. However,
the pattern of results for utility value was somewhat weaker than that for intrinsic value. A
theoretical reason may be that utility value is more related to an individual’s personal and
collective identities, whereas intrinsic value is more related to performance-based experiences.
The formation of utility value may rely on other sources, such as cultural and parent subjective
norms (Wigfield et al., 2016). Put simply, parents who value math are likely to communicate
these beliefs to children as a way for children to understand that math is important and useful,
which can influence students’ own valuing of math. Another reason might be that students are
not able to distinguish utility value in different science subjects at Grade 9, as evident by the low
degree of domain specificity of utility value (see Appendix D). The domain specificity of the
construct is one of the bases underlying dimensional comparison mechanisms. The pattern of
relations between the motivational factors and achievement is largely a function of the domain-
specific nature of this factor. Previous research has suggested that a lower degree of domain
18
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
specificity for the motivational constructs is associated with weaker support for the I/E model
(Marsh et al., 2013).
The follow-up analyses indicated that the influence of dimensional comparison on the
development of students’ task values was largely mediated by self-concept. This result reinforces
the central role of self-concept in terms of DCT, but the cross-sectional nature of our data dictate
caution in the interpretation of the results. Hence, pursuit of this issue is a potentially important
direction for further research based on longitudinal data where stronger tests of the causal
ordering implicit in the mediation model are possible.
The Relations between Motivational beliefs and Aspirations
Consistent with a prior prediction, this study found that self-concept and intrinsic and
utility values are positively associated with coursework aspirations in the same domain.
Importantly, this study is among the first to test latent expectancy-by-value interactions for
multiple science domains within the same model. There is strong evidence of the high domain
specificity of interactive relations in predicting coursework aspirations. The interactive roles of
self-concept and value suggest that students with both high science self-concept and task value
are more likely to aspire to engage in science. However, students with high self-concept are
unlikely to desire to pursue science in the future, if they ascribe a low level of intrinsic value to
science. Similarly, students who value math are also unlikely to desire to enter a scientific career,
if their science self-concept remains low. Therefore, this study provides strong support for the
theoretical claim that self-concept and value interact in predicting achievement-related outcomes.
Dimensional comparison processes involving self-concept and value. This study
extends prior research by integrating EVT and DCT and exploring predictions from motivational
beliefs to educational aspirations. Contrasting dimensional comparison between physics and
biology is evident for self-concept and intrinsic value. This means that for example, students who
have high self-concept and interest in physics but even higher self-concept and interest in
biology are likely to have lower aspirations in physics compared to students who have the same
level of self-concept and interest in physics but lower self-concept and interest in biology. Thus,
aspirations in one science domain depend not only on abilities, self-concept, and intrinsic value
in that domain, but also on relative abilities and motivation in other science domains. These
19
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
findings shed further light on the important roles played by dimensional comparison processes in
shaping academic pathways to different STEM fields, and underline the importance of
differentiating motivational beliefs across science domains.
However, it should be noted that all cross-paths (dimensional comparisons) between
achievement, motivational beliefs and coursework aspirations were relatively weak, particularly
for the assimilation effects. These results are consistent with recent self-concept research on
science domains (Jansen et al., 2014). This may be because the four science subjects considered
here are all relatively similar, compared to the more obviously contrasted academic continuum,
ranging from relatively pure verbal subjects to relatively pure mathematical subjects (Marsh,
1990). Nevertheless, mathematics and verbal skills are posited as the endpoints of the academic
continuum were not considered in this study.
Generalizability of the results
How science subjects are taught in a given learning environment varies as a function of
the country, state or school system, and this is particularly true for earth science. Based on
TIMSS data, the present study evaluated the only four available participating OECD countries
that assessed students’ motivational beliefs in the four science domains. Despite substantial
variations in the sociocultural and educational background (see Table 1), the pattern of results is
invariant across the four countries, supporting the external validity of our findings. Particularly,
the cross-cultural support for the generalizability of DCT predictions reflects a broader tendency
of students to engage in both assimilating and contrasting dimensional comparisons to develop
their self-concept, task values, and aspirations in science. Our results indicate that even students
who excel at science, particularly in physics, might have high self-concept and values in both
physics and chemistry; however, they might have an average or below average self-concept and
values in biology, which may seem paradoxical in relation to their good achievement (better
compared to other students but not compared to their own performance in other science
domains). This indication is inconsistent with teachers’ perception of formation of students’
motivation. Previous studies have shown that teachers tend to believe that students who are
capable in one academic domain tend to be seen as having high self-concept and values in all
domains, while students who are not capable in one area are seen as having low self-concept and
20
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
values in all domains (Marsh, 2007). Thus, the generalized pattern has fundamental implications
about the way teachers give feedback to students in different academic domains (see further
discussion below). However, it should be noted that generalizability over only four countries is
not sufficient to provide strong support for cross-cultural generalizability. But it sheds light on
the generalized motivational mechanism by the integration of EVT and DCT and offers a good
starting point for further research.
Implications for Instructional Practices
With respect to instructional practices, the high domain specificity of self-concept and
intrinsic value suggests that interventions targeting general academic, or even a general science
self-concept and intrinsic value, may not be beneficial in promoting students’ motivation in
STEM areas. Rather, interventions targeting a specific academic self-concept domain, with the
integration of self-enhancement (self-concept enhances ability) and skill development (ability
improves self-concept) strategies, have been shown to be much more effective than those solely
targeting a global or skill-based self-concept (Marsh, 2007). Interventions designed to increase
students’ perceptions of the relevance of academic subjects to their lives through teachers and
parents have been found to be effective in triggering students’ interest and to promote academic
performance in STEM topics (Harackiewicz, Rozek, Hulleman, & Hyde, 2012).
Furthermore, we recommend that teachers should be aware not only of the dimensional
comparison processes underlying the formation of students’ self-concept and intrinsic value, but
also of the comparison processes leading students to different levels of coursework engagement
and aspirations. Particularly the contrasting comparisons between physics and biology may help
to explain the gender imbalance in STEM careers with girls’ underrepresentation in physics-
related careers but slightly overrepresentation in biology-related careers (Wang & Degol, 2013).
Understanding such comparison processes would also help teachers provide effective feedback to
students. In particular, attributional feedback, goal feedback, and contingent praise, as forms of
constructive feedback, have been identified as effective methods of boosting self-concept
(O’Mara et al., 2006). Thus, our findings would help educational policymakers and practitioners
to improve retention in STEM classes through high school and could be particularly beneficial in
supporting girls to pursue physics-related careers.
21
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
In addition, the distinctiveness of the interactive relations between self-concept and value
beliefs across science domains, suggests that interventions targeting the promotion of aspirations
to STEM majors should seek to enhance both domain-specific self-concept and task value. This
suggests that multicomponent interventions (Gläser-Zikuda, Fuß, Laukenmann, Metz & Randler,
2005) might be more effective in promoting students’ motivation than those based on self-
concept and value interventions considered separately.
Limitations and Directions for Future Research
Several limitations to this study, and some caveats, must be noted. First, in the present
cross-sectional study, the issue of the temporal or causal ordering among achievement,
motivational beliefs and aspirations could not be addressed on the basis of a single measurement
point. Thus, a longitudinal replication would enable us to draw stronger conclusions about the
directional influences of self-concept and value and the importance of their interactions.
Second, as our study is limited to the four OECD countries where science is taught as
separate subjects, it is also important to replicate the results in settings where students are taught
science as an interdisciplinary, unified subject. Relatedly, the strengths of DCT and EVT
predictions in science is likely to vary as a function of age, as the further students go in school
the more differentiated the coursework is likely to be. This is particularly the case as students
move into higher education. Thus, research across different international samples covering
multiple age groups, school subjects and schooling systems would be useful, to clarify the
generalizability of our findings.
Third, our findings support the assumption that students make assimilating or contrasting
dimensional comparisons are related to how they perceive similarity of two or more domains
These results are also consistent with the experimental studies suggesting that lower perceived
subject similarity would lead to stronger self-concept differences than did higher perceived
similarity (Helm et al., 2016). However, such experimental study focusing on the effect of
perceived subject similarity and dimensional comparisons on task value has been sparse. It,
therefore, would be another avenue for future research.
Finally, given that the present investigation only focuses on two out of four major value
components and single-item coursework aspirations, future research should consider
22
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
psychometrically stronger, multi-item measures of the four value components and coursework
aspirations.
23
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
References
Arens, A.K., & Möller, J. (2016). Dimensional comparisons in students' perceptions of the
learning environment. Learning and Instruction, 42, 22-30
Atkinson, J. W. (1957). Motivational determinants of risk-taking behavior. Psychological review,
64, 359–372.
Eccles, J. S. (2009). Who am I and what am I going to do with my life? Personal and collective
identities as motivators of action. Educational Psychologist, 44, 78–89.
Gläser-Zikuda, M., Fuß, S., Laukenmann, M., Metz, K., & Randler, C. (2005). Promoting
students’ emotions and achievement—Instructional design and evaluation of the ECOLE-
approach. Learning and Instruction, 15, 481–495.
Goetz, T., Frenzel, A. C., Hall, N. C., & Pekrun, R. (2008). Antecedents of academic emotions:
Testing the internal/external frame of reference model for academic enjoyment.
Contemporary Educational Psychology, 33(1), 9–33.
Guo, J., Parker, P. D., Marsh, H. W., & Morin, A. J. S. (2015). Achievement, motivation, and
educational choices: A longitudinal study of expectancy and value using a multiplicative
perspective. Developmental Psychology, 51, 1163–1176.
Guthrie, J. T., Wigfield, A., & VonSecker, C. (2000). Effects of integrated instruction on
motivation. Journal of Educational Psychology, 92, 331-341.
Haag, L., & Götz, T. (2012). Mathe ist schwierig und Deutsch aktuell: Vergleichende Studie zur
Charakterisierung von Schulfächern aus Schülersicht [Math is difficult and German up-
to-date: Comparative study of characterizations of school subjects from students’ points-
of-view]. Psychologie in Erziehung und Unterricht, 59, 32–46.
Harackiewicz, J. M., Rozek, C. S., Hulleman, C. S., & Hyde, J. S. (2012). Helping Parents to
Motivate Adolescents in Mathematics and Science: An Experimental Test of a Utility-
Value Intervention. Psychological Science, 23, 899–906.
Helm, F., Mueller-Kalthoff, H., Nagy, N., & Mo ller, J. (2016). Dimensional Comparison
Theory: Perceived Subject Similarity Impacts on Students Self-Concepts. AERA Open,
2(2), 1–9.
Jansen, M., Schroeders, U., & Lüdtke, O. (2014). Academic self-concept in science:
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
Multidimensionality, relations to achievement measures, and gender differences.
Learning and Individual Differences, 30, 11–21.
Jansen, M., Schroeders, U., Lüdtke, O., & Marsh, H. W. (2015). Contrast and Assimilation
Effects of Dimensional Comparisons in Five Subjects: An Extension of the I/E Model.
Journal of Educational Psychology.
Marsh, H. W. (2007). Self-concept theory, measurement and research into practice: The role of
self-concept in educational psychology. Leicester, UK: British Psychological Society.
Marsh, H. W., Abduljabbar, A. S., Abu-Hilal, M. M., Morin, A. J. S., Abdelfattah, F., Leung, K.
C., … Parker, P. D. (2013). Factorial, convergent, and discriminant validity of TIMSS
math and science motivation measures: A comparison of Arab and Anglo-Saxon
countries. Journal of Educational Psychology, 105, 108–128.
Marsh, H. W., Lüdtke, O., Nagengast, B., Trautwein, U., & Abduljabbar, A. S. (2015).
Dimensional Comparison Theory: Paradoxical relations between self-beliefs and
achievements in multiple domains. Learning and Instruction, 35, 16–32.
Marsh, H. W., Martin, A. J., & Hau, K-T. (2006). A multiple method perspective on self-concept
research in educational psychology: A construct validity approach. In M. Eid & E. Diener
(Eds.), Handbook of multimethod measurement in psychology (pp. 441–456).
Washington, DC: APA
Möller, J., Helm, F., Müller-Kalthoff, H., Nagy, N., & Marsh, H. W. (2015). Dimensional
comparisons and their consequences for self-concept, motivation, and emotion.
International Encyclopedia of the Social & Behavioral Sciences, 26, 430–436.
Möller, J., & Marsh, H. W. (2013). Dimensional comparison theory. Psychological Review, 120,
544–60.
Möller, J., Pohlmann, B., Köller, O., & Marsh, H. W. (2009). A meta-analytic path analysis of the
internal/external frame of reference model of academic achievement and academic self-
concept. Review of Educational Research, 79, 1129–1167.
Nagengast, B., Marsh, H. W., Scalas, L. F., Xu, M. K., Hau, K.-T., & Trautwein, U. (2011). Who
took the “x” out of expectancy-value theory? A psychological mystery, a substantive-
methodological synergy, and a cross-national generalization. Psychological Science, 22,
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
1058–1066.
Nagy, G., Garrett, J., Trautwein, U., Cortina, K., Baumert, J., & Eccles, J. S. (2008). Gendered
high school course selection as a precursor of gendered careers: The mediating role of
self-concept and intrinsic value. In H. M. G. Watt & J. S. Eccles (Eds.), Gender and
occupational outcomes: Longitudinal assessments of individual, social, and cultural
influences (pp. 115–143). Washington, DC, US: APA.
Olson, J. F., Martin, M. O., & Mullis, I. V. S. (2008). TIMSS 2007 technical report. Chestnut
Hill, MA: TIMSS & PIRLS.
Parker, P. D., Schoon, I., Tsai, Y.-M., Nagy, G., Trautwein, U., & Eccles, J. S. (2012).
Achievement, agency, gender, and socioeconomic background as predictors of postschool
choices: a multicontext study. Developmental Psychology, 48, 1629–42.
Schurtz, I. M., Pfost, M., Nagengast, B., & Artelt, C. (2014). Impact of social and dimensional
comparisons on student’s mathematical and English subject-interest at the beginning of
secondary school. Learning and Instruction, 34, 32–41.
Wang, M. T., & Degol, J. (2013). Motivational pathways to STEM career choices: Using
expectancy-value perspective to understand individual and gender differences in STEM
fields. Developmental Review, 33, 304–340.
Wigfield, A., Tonks, S., & Klauda, S. L. (2016). Expectancy-value theory. In K. R. Wentzel & D.
B. Miele (Eds.), Handbook of motivation at school (pp. 55–74). New York: Routledge.
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
EXPECTANCY VALUE IN SCIENCE SUBDISCIPLINES
-1.0 -0.5 0.0 0.5 1.0
-1.0 -0.5 0.0 0.5 1.0
Self-concept (SD)
Coursework Aspirations (SD)
IV = +1SD
IV = Mean
IV = -1SD
-1.0 -0.5 0.0 0.5 1.0
-0.5 0.0 0.5
Self-concept (SD)
Coursework Aspirations (SD)
UV = +1SD
UV = Mean
UV = -1SD
Figure 3. Simple-slopes depicting the effects of latent interactions (self-concept by intrinsic value and self-concept by utility value) on coursework aspirations.
Note. IV = intrinsic value; UV = utility value.
EXPECTANCY-VALUE INTERACTION AND UNIQUE PREDICTION
Table 1.
30
EXPECTANCY-VALUE INTERACTION AND UNIQUE PREDICTION
Table 2
31
EXPECTANCY-VALUE INTERACTION AND UNIQUE PREDICTION
Table 3
Model Fit Statistics for the Multi-group CFA and SEM Models Used in the Present Study
32
Online Supplemental Materials for:
Extending Expectancy-Value Theory Predictions of Achievement and Aspirations in
Science: Dimensional Comparison Processes and Expectancy-by-Value Interactions
Note: These appendices are intended to appear only on a website hot-linked to the article, and are not intended for the
printed article.
Table of Contents
External Appendix A: Sample Size and Reliabilities of The TIMSS Motivation Constructs..34
External Appendix B: Unconstrained Approach, Standardization, and Annotated Mplus
Syntax.......................................................................................................................................35
Unconstrained Approach......................................................................................................35
Standardization.....................................................................................................................35
The Annotated Mplus Syntax for Model..............................................................................36
External Appendix C: Weight and Goodness of Fit.................................................................40
Weighting.............................................................................................................................40
Goodness of Fit....................................................................................................................40
External Appendix D: Preliminary Analyses Tests..................................................................41
Factor Structure: Preliminary CFA......................................................................................42
Tests of Invariance of Factorial Structure Over Countries: Multi-group CFA....................42
Domain specificity of Motivation Responses, Achievement, and Aspirations....................42
External Appendix E: Full Results for the Path Invariance Model (Model 7b).......................45
External Appendix F: Supplemental Analyses for the Mediating Role of Academic Self-
concept.....................................................................................................................................49
External Appendix G: Supplemental Analyses for Interaction Effect between Self-Concept
and Value..................................................................................................................................50
External Appendix H: Full Results for country-specific path coefficients (Model MG7a).....54
References for Online Supplemental Materials.......................................................................57
External Appendix A:
Sample Size and Reliabilities of The TIMSS Motivation Constructs
Table A1
Sample Size and Reliabilities of The TIMSS Motivation Constructs Based on Four Science Domains for Four OECD Countries
Country
Sample Size Reliability Estimates
Studen
t
Class School %boys PSC CSC ESC BSC PIV CI
V
EIV BIV PUV CUV EUV BUV Mean
Czech Republic 4842 212 147 52% .84 .85 .83 .82 .84 .86 .86 .85 .84 .86 .86 .85 .83
Hungary 4108 246 144 50% .83 .82 .83 .82 .84 .85 .87 .88 .84 .85 .87 .88 .83
Slovenia 4029 260 148 50% .77 .80 .79 .80 .83 .87 .87 .87 .83 .87 .87 .87 .82
Sweden 5068 307 159 52% .79 .79 .79 .79 .87 .88 .88 .88 .87 .88 .88 .88 .84
Total 18047 1025 598 51% .81 .82 .81 .81 .85 .87 .87 .87 .84 .84 .80 .79 .83
Note. The column headed Mean is the mean of the eight reliability estimates. The wording of the items was rigorously parallel for the corresponding science domain-specific
scales. Reliability estimates are Cronbach’s alpha estimates. P = physics; C = chemistry; E = earth science; B = biology; SC = self-concept; IV = intrinsic value; UV = utility value.
Say
External Appendix B:
Unconstrained Approach, Standardization, and Annotated Mplus Syntax
Unconstrained Approach
In comparison to the traditional constrained approach (e.g., Jöreskog & Yang, 1996;) and the
Standardization
First, all individual indicators (rating item, test scores and coursework aspirations) were standardized
in relation to the total sample mean and standard deviation, as recommended by Marsh and his colleagues
(Marsh et al., 2004; Marsh, Hau et al., 2013). Second, for total group analysis, product indicators for the
latent interactions were formed using the match-pair strategy according to Marsh, Hau et al.(2013)’s guiding
principles (also see Marsh et al., 2004 for more discuss about the product predictors selection procedure).
For the multi-group analysis, the standardized indicators were centered (but not re-standardized the product
term) within country-specific mean before forming the product indictors for the latent interaction variable
(Nagengast et al., 2011). In order to obtain appropriate standardized results (Wen, Marsh, & Hau, 2010), for
total group analysis all latent factors (including the latent product variables) were then standardize in
relation to the total sample. For multi-group analyses, the critical assumption of test whether the pattern of
results generalizes across groups is invariance of factor structure. To provide parameter estimates
standardized to a common metric over the multiple groups, factor loadings and factor variances are needed
to be invariant across the four countries. More specifically, we conducted a preliminary CFA model in which
factor loadings and factor variances were constrained to be invariant over the multiple groups, and the
metric was identified by fixing the factor variances of constructs to be 1.0 across the four groups, instead of
fixing the first factor loading to 1.0. In subsequent SEMs these standardized factor loadings were used to
define the latent factors, fixing the first factor loading for each factor to the value obtained in the CFA, in
which the factor variances were fixed to be 1.0. In this way, all parameter estimates were estimated in
relation to a standardized metric that was common across the four countries, providing appropriate
standardized results (see Wen et al., 2010 for more details; also see below for the Mplus syntax). As showed
in the main text, we also conducted a series of invariance tests with respect to factor covarances and path
coefficient for multi-group measurement and structural models As the assumption of invariance was tenable,
all results reported in this study were based on multi-group SEM with factor loading, path coefficients and
factor variances and covariance invariances
The Annotated Mplus Syntax for Model
DATA: FILE = "Multi_Sci_ExT_fix_MG.csv";
VARIABLE:
NAMES = IDCNTRY IDSCHOOL
!domain-specific self-concept; P = physics; C = chemistry; E = earth science; B = biology;
PSCP1 PSCP2 PSCN1 PSCN2 CSCP1 CSCP2 CSCN1 CSCN2
ESCP1 ESCP2 ESCN1 ESCN2 BSCP1 BSCP2 BSCN1 BSCN2
!domain-specific intrinsic value;
PIVP1 PIVN1 PIVP CIVP1 CIVN1 CIVP2 EIVP1 EIVN1 EIVP2 BIVP1 BIVN1 BIVP2
!domain-specific utility value;
PVAL1 PVAL2 PVAL3 PVAL4 CVAL1 CVAL2 CVAL3 CVAL4
EVAL1 EVAL2 EVAL3 EVAL4 BVAL1 BVAL2 BVAL3 BVAL4
!domain-specific self-concept-by- intrinsic-value product terms
! three product terms for
Pmsciv1 Pmsciv2 Pmsciv3 Cmsciv1 Cmsciv2 Cmsciv3
Emsciv1 Emsciv2 Emsciv3 Bmsciv1 Bmsciv2 Bmsciv3
!domain-specific achievement
PACH CACH EACH BACH
!domain-specific coursework aspirations
PCW CCW ECW BCW
HOUWGT CONTSCHL;
MISSING=.;
CLUSTER= CONTSCHL;
! cluster variable is the classroom;
!We note that the classroom is the critical clustering variable for TIMSS data because class was the !sampling
unit used in the TIMSS sampling design, which was based on sampling all stu dents within intact !classes; most
schools are represented by a single class, and a given class might not be representative of the !school from which it
came.
WEIGHT = HOUWGT;
! HOUWGT is the weighting variable in the TIMSS database; incorporates six components; ! three have to !
do with sampling of the school, class and student, and adjustment factors ! associated with non-!participation at the
level of the school, class and student.
grouping is IDCNTRY (203=CZE 348=HUN 705=SVN 752=SWE); ! identify the four OECD countries
ANALYSIS: ESTIMATOR = MLR; TYPE = COMPLEX;
H1ITERATIONS = 20000;
ITERATIONS = 100000;
processors =2;
define : CONTSCHL=(IDCNTRY*1000000)+IDCLASS; # define cluster variable
standardize PACH CACH EACH BACH PCW CCW ECW BCW;
MODEL:
PSC by PSCP1@.818 PSCP2-PSCN2; CSC by CSCP1@.823 CSCP2-CSCN2;
ESC by ESCP1@.814 ESCP2-ESCN2; BSC by BSCP1@.791 BSCP2-BSCN2;
PIV by PIVP1@.867 PIVN1 PIVP2; CIV by CIVP1@.879 CIVN1 CIVP2;
EIV by EIVP1@.858 EIVN1 EIVP2;BIV by BIVP1@.841 BIVN1 BIVP2;
PVAL by PVAL1@.662 PVAL2-PVAL4; CVAL by CVAL1@.664 CVAL2-CVAL4;
EVAL by EVAL1@.531 EVAL2-EVAL4; BVAL by BVAL1@.566 BVAL2-BVAL4;
PmscXiv by Pmsciv1@.812 Pmsciv2 Pmsciv3 ;CmscXiv by Cmsciv1@.798 Cmsciv2 Cmsciv3;
EmscXiv by Emsciv1@.797 Emsciv2 Emsciv3 ;BmscXiv by Bmsciv1@.789 Bmsciv2 Bmsciv3;
!fixed factor loading of first indicator of each factor to provide common metric standardization;
!Correlated uniquenesses for negative worded items
BSCN1 BSCN2 ESCN1 ESCN2 CSCN1 CSCN2 PSCN1 PSCN2 WITH
BSCN1 BSCN2 ESCN1 ESCN2 CSCN1 CSCN2 PSCN1 PSCN2 ;
EIVN1 BIVN1 CIVN1 PIVN1 WITH EIVN1 BIVN1 CIVN1 PIVN1 ;
BSCN1 BSCN2 ESCN1 ESCN2 CSCN1 CSCN2 PSCN1 PSCN2 WITH
EIVN1 BIVN1 CIVN1 PIVN1 ;
! Correlated uniquenesses for parallel items
BSCP1 ESCP1 CSCP1 PSCP1 WITH BSCP1 ESCP1 CSCP1 PSCP1;
BSCP2 ESCP2 CSCP2 PSCP2 WITH BSCP2 ESCP2 CSCP2 PSCP2;
EVAL1 BVAL1 CVAL1 PVAL1 WITH EVAL1 BVAL1 CVAL1 PVAL1 ;
EVAL2 BVAL2 CVAL2 PVAL2 WITH EVAL2 BVAL2 CVAL2 PVAL2 ;
EVAL3 BVAL3 CVAL3 PVAL3 WITH EVAL3 BVAL3 CVAL3 PVAL3 ;
EVAL4 BVAL4 CVAL4 PVAL4 WITH EVAL4 BVAL4 CVAL4 PVAL4 ;
EIVP1 BIVP1 CIVP1 PIVP1 WITH EIVP1 BIVP1 CIVP1 PIVP1 ;
EIVP2 BIVP2 CIVP2 PIVP2 WITH EIVP2 BIVP2 CIVP2 PIVP2 ;
! Correlated uniquenesses for parallel worded product terms
Pmsciv1 Cmsciv1 Emsciv1 Bmsciv1 with Pmsciv1 Cmsciv1 Emsciv1 Bmsciv1;
Pmsciv2 Cmsciv2 Emsciv2 Bmsciv2 with Pmsciv2 Cmsciv2 Emsciv2 Bmsciv2;
Pmsciv3 Cmsciv3 Emsciv3 Bmsciv3 with Pmsciv3 Cmsciv3 Emsciv3 Bmsciv3;
! paths from achievement to self-concept
PSC on physi (pscVphy); PSC on chems (pscVche); PSC on earth (pscVear); PSC on biolo (pscVbio);
CSC on physi (cscVphy);CSC on chems (cscVche);CSC on earth (cscVear);CSC on biolo (cscVbio);
ESC on physi (escVphy);ESC on chems (escVche);ESC on earth (escVear);ESC on biolo (escVbio);
BSC on physi (bscVphy);BSC on chems (bscVche);BSC on earth (bscVear);BSC on biolo (bscVbio);
! paths from achievement to intrinsic value
PIV on physi (pivVphy);PIV on chems (pivVche);PIV on earth (pivVear);PIV on biolo (pivVbio);
CIV on physi (civVphy);CIV on chems (civVche);CIV on earth (civVear);CIV on biolo (civVbio);
EIV on physi (eivVphy);EIV on chems (eivVche);EIV on earth (eivVear);EIV on biolo (eivVbio);
BIV on physi (bivVphy);BIV on chems (bivVche);BIV on earth (bivVear);BIV on biolo (bivVbio);
! paths from achievement to utility value
PVAL on physi (pvaVphy);PVAL on chems (pvaVche);PVAL on earth (pvaVear);PVAL on biolo (pvaVbio);
CVAL on physi (cvaVphy);CVAL on chems (cvaVche);CVAL on earth (cvaVear);CVAL on biolo (cvaVbio);
EVAL on physi (evaVphy);EVAL on chems (evaVche);EVAL on earth (evaVear);EVAL on biolo (evaVbio);
BVAL on physi (bvaVphy);BVAL on chems (bvaVche);BVAL on earth (bvaVear);BVAL on biolo (bvaVbio);
PmscXiv-BmscXiv on physi-biolo; ! paths from achievement to product variables
phyCours- bioCours on PSC-BVAL; !paths from motivational factors to coursework aspirations
phyCours- bioCours on physi-biolo; ! product variables to coursework aspirations
phyCours- bioCours on physi-bioCours ! achievement to coursework aspirations
! factor variances invariances
PSC-BmscXiv (fa1-fa16); physi-bioCours (fa21-fa28); ! constrain factor variance to be equal
factor covariances invariances
PSC with CSC-BIV(p1-p11);CSC with ESC-BIV (c1-c10);ESC with BSC-BIV (e1-e9);
BSC with PVAL-BIV (b1-b8);PVAL with CVAL-BIV (pv1-pv7);CVAL with EVAL-BIV (cv1-cv6);
EVAL with BVAL-BIV (ev1-ev5);BVAL with PIV-BIV (bv1-bv4);PIV with CIV-BIV(pi1-pi3);
CIV with EIV BIV (ci1-ci2);EIV with BIV (ei1);
PSC with PmscXiv-BmscXiv (pscx1-pscx4);CSC with PmscXiv-BmscXiv (cscx1-cscx4);
ESC with PmscXiv-BmscXiv (escx1-escx4);BSC with PmscXiv-BmscXiv (bscx1-bscx4);
PIV with PmscXiv-BmscXiv (pivx1-pivx4);CIV with PmscXiv-BmscXiv (civx1-civx4);
EIV with PmscXiv-BmscXiv (eivx1-eivx4);BIV with PmscXiv-BmscXiv (bivx1-bivx4);
PVAL with PmscXiv-BmscXiv (pslx1-pslx4);CVAL with PmscXiv-BmscXiv (cslx1-cslx4);
EVAL with PmscXiv-BmscXiv (eslx1-eslx4);BVAL with PmscXiv-BmscXiv (bslx1-bslx4);
PmscXiv with CmscXiv EmscXiv BmscXiv (x23-x25);CmscXiv with EmscXiv BmscXiv (x26-x27);
EmscXiv with BmscXiv (x28);
physi with chems earth biolo (l1-l3);chems with earth biolo (l4-l5);earth with biolo (l6);
phyCours with cheCours earCours bioCours (l7-l9);cheCours with earCours bioCours (l10-l11);earCours with
bioCours (l12);
Model HUN:
[PSCP1-Bmsciv3]; [PSC-BmscXiv@0]; !freely estimate items intercepts for each group
[PACH-BBORE];[physi-bioCours@0];
MODEL SVN:
[PSCP1-Bmsciv3]; [PSC-BmscXiv@0];
[PACH-BBORE];[physi-bioCours@0];
MODEL SWE:
[PSCP1-Bmsciv3]; [PSC-BmscXiv@0];
[PACH-BBORE];[physi-bioCours@0];
!!! create the summary for match and non-matching cross-paths from achievement to motivational factors (see
Table E1-E3 in Appendix E in the supplemental materials)
MODEL CONSTRAINT:
!mean of 16 match and non-matching cross-paths involving self-concept
NEW(Mn_scVah,Mn_ivVah,Mn_vaVah,Mn_siVah);
Mn_scVah=(pscVphy+pscVche+pscVear+pscVbio+cscVphy+cscVche+cscVear+cscVbio+escVphy+
escVche+escVear+escVbio+bscVphy+bscVche+bscVear+bscVbio)/16;
!mean of 16 match and non-matching cross-paths involving intrinsic value
Mn_ivVah=(pivVphy+pivVche+pivVear+pivVbio+civVphy+civVche+civVear+civVbio+eivVphy+
eivVche+eivVear+eivVbio+bivVphy+bivVche+bivVear+bivVbio)/16;
!mean of 16 match and non-matching cross-paths involving utility value
Mn_vaVah=(pvaVphy+pvaVche+pvaVear+pvaVbio+cvaVphy+cvaVche+cvaVear+cvaVbio+evaVphy+
evaVche+evaVear+evaVbio+bvaVphy+bvaVche+bvaVear+bvaVbio)/16;
NEW(Mm_scVah,Mm_ivVah,Mm_vaVah,Mm_siVah);
Mm_scVah=(pscVphy+cscVche+escVear+bscVbio)/4; !mean of 4 matching cross-paths involving self-
concept
Mm_ivVah=(pivVphy+civVche+eivVear+bivVbio)/4; !mean of 4 matching cross-paths involving intrinsic
value
Mm_vaVah=(pvaVphy+cvaVche+evaVear+bvaVbio)/4; !mean of 4 matching cross-paths involving utility
value
!NoMath
NEW(No_scVah,No_ivVah, No_vaVah,No_siVah);
No_scVah=(pscVche+pscVear+pscVbio+cscVphy+cscVear+cscVbio+escVphy+escVche+escVbio+bscVphy+
bscVche+bscVear)/12; !mean of 12 non-matching cross-paths involving self-concept
No_ivVah=(pivVche+pivVear+pivVbio+civVphy+civVear+civVbio+eivVphy+eivVche+eivVbio+bivVph+bi
vVche+bivVear)/12; !mean of 12 non-matching cross-paths involving intrinsic value
No_vaVah=(pvaVche+pvaVear+pvaVbio+cvaVphy+cvaVear+cvaVbio+evaVphy+evaVche+evaVbio+bvaVp
hy+bvaVche+bvaVear)/12; !mean of 12 non-matching cross-paths involving utility value
External Appendix C:
Weight and Goodness of Fit
Weighting
Consistent with its two-stage stratified sampling design, TIMSS provides the HOUWGT weighting
variable that has six components, one each for school, class and student level, and one each for adjustment
factors associated with non-participation at these three levels (See Marsh, Abduljabbar et al., 2013 for
additional detail on the development of this weighting variable). HOUWGT is based on the actual number of
students in each participating countries that is appropriate for correct computation of standard errors and
tests of statistical significance. Thus, the HOUWGT weighting variable was taken into account in the data
analysis.
Goodness of Fit
A number of traditional indices that are relatively independent of sample size were utilized to assess
model fit (Hu & Bentler, 1999): the comparative fit index (CFI), the root-mean-square error of
approximation (RMSEA) and the Tucker-Lewis Index (TLI). To explore how well the hypothesized relations
generalize across the four OECD countries, we conducted multiple-group analyses (Bollen, 1989) and tested
a series of increasingly stringent invariance constraints on the parameters of measurement and structural
parts of the model, in which little or no change in goodness of fit supported invariance of the factor structure
and parameter estimates (Millsap, 2011; see Appendix D in the supplemental materials for more details). We
note that to compare differences in patterns of relations among multiple groups, it is only necessary to have
factor loadings invariant for latent variable models (Millsap, 2011; Nagengast et al., 2011). Nevertheless, to
facilitate interpretation of the parameter estimates in relation to a common metric over the multiple groups,
we also tested invariance models of factor variances/covariances and path coefficients over the four
countries (see Appendix C in the supplemental materials for the standardization procedure).
Values greater than .95 and .90 for CFI and TLI typically indicate excellent and acceptable levels of
fit to the data. RMSEA values of less than .06 and .08 are considered to reflect good and acceptable levels of
fit to the data. To explore how well the hypothesized relations generalize across the four OECD countries,
we conducted multiple-group analyses (Bollen, 1989) and tested a series of increasingly stringent invariance
constraints on the parameters of measurement and structural parts of the model, in which little or no change
in goodness of fit supported invariance of the factor structure (Marsh, Hau et al., 2013). Chen (2007) have
suggested that if the decrease in CFI is not more than .01 and the RMSEA increases by less than .015 for the
more parsimonious model, then invariance assumptions are tenable. To facilitate interpretation of parameter
estimates in relation to a common metric over the multiple groups, factor variances and covariances are also
constrained to be invariant over the four countries in this study (see Appendix E in the supplemental
materials for the standardization procedure). Other more stringent tests would have been necessary in order
to support the test of latent mean differences over time or models based on the use of manifest, rather than
latent, scale scores, which is not the case in the present study.
External Appendix D:
Preliminary Analyses Tests
Table D1
Model Fit Statistics for the CFA Models Used in the Present Study
Model Description χ2df CFI TLI RMSEA
Total group (TG) analysis
CFA
TG1 SC + IV + UV 10757 722 .963 .952 .028
TG2 SC + IV + UV + SCxIV + SCxUV 16766 2090 .953 .942 .020
TG3 SC + IV + UV + SCxIV + SCxUV + ACH + ASP 19406 2506 .957 .946 .019
Second-order CFA model
TG4 SO(SC + IV +UV) 40918 773 .852 .820 .054
Multi-group (MG) analysis
CFA
MG1 SC + IV + UV + ACH + ASP, CUs, Configural 18038 3912 .964 .951 .028
MG2 SC + IV + UV + ACH + ASP, CUs, IN = FL 19416 4008 .961 .948 .029
MG3 SC + IV + UV + ACH + ASP, CUs, IN = FL, FV 20138 4068 ,959 .947 .030
MG4 SC + IV + UV + ACH + ASP, CUs, IN = FL, FV, CV 23961 4638 .951 .944 .030
Note. CFA = confirmatory factor analysis; SEM = Structural equation modelling; PC = path coefficients; SC = self-concept; IV= intrinsic value; UV = utility value; ASP = coursework
aspirations; SCxIV = the product term of self-concept by intrinsic value interaction; SCxUV = the product term of self-concept by utility value interaction; IN = invariant; CUs = correlated
uniquenesses; UCUs = uncorrelated uniquenesses; FL = factor loading; FV = factor variances; CV = factor covariances; INT= item intercepts; Unq = item uniquenesses; FMn = factor latent
mean.
Factor Structure: Preliminary CFA
Total group CFA. In the preliminary analyses, we evaluated a series of CFAs of the
factor structures underlying the multiple domains of self-concept, intrinsic value and utility
value, and their relations to parallel measures of achievement and coursework aspirations. We
began with an evaluation of the results based on the total group. A critical feature of the TIMSS
data is that each motivation construct was measured by a mixture of positively and negatively
worded items, with parallel wording across the four science domains. This requires the inclusion
of a priori correlated uniquenesses, relating responses to negatively worded items and parallel
worded items, to obtain unbiased parameter estimates (see Marsh, Abduljabbar et al., 2013,
2015). Following previous TIMSS research (Marsh, Abduljabbar et al., 2013), these a priori
correlated uniquenesses were included in all CFA and SEM models. The goodness of fit for the
CFA models with proper methodological control for item wordings was good (e.g., CFI &TLI > .
942; see models TG1–TG3 in Table D1).
We also tested a second-order CFA model where global science self-concept, intrinsic
value and utility value were formed by the four corresponding first-order constructs from each
science domain. However, the second-order CFA model was highly unsatisfactory in terms of
model fits (e.g., CFI & TLI < .852; Model TG4), thus providing support for the domain
specificity and discriminant validity of these factors. This result indicates that it is important to
distinguish the patterns of theoretical predictions in relation to each of the four science domains.
Tests of Invariance of Factorial Structure Over Countries: Multi-group CFA
A key interest of the present study is to evaluate the degree to which the results generalize
across the four OECD countries included in our sample. We began with an evaluation of
invariance of the factor structure over multiple groups (four OECD countries) based on CFAs.
The fit indices for the baseline model with no invariance constraints were very good (e.g., CFI
= .964, Model MG1 in Table 2). There was a negligible decrease in fit (
CFI = .003,
TLI = .
003) for Model MG2, in which the factor loadings were constrained to be equal across groups,
suggesting that the invariance of factor loadings was supported by the data. Similarly, adding
equality constraints on the factor variances (MG3) and covariances (MG4) resulted in a
satisfactory level of fit to the data, and only a negligible change in fit (
CFI = .008,
TLI = .
003). These results support the generalizability of the factor structure of the five constructs
across the four countries.
Domain specificity of Motivation Responses, Achievement, and Aspirations
We examined relations among the five constructs to evaluate the expected domain
specificity of the motivation responses. Latent correlations among the 20 constructs (4 domains x
5 constructs) based on Model MG4 with invariant factor loadings, variances, and covariances for
motivational beliefs, achievement, and aspirations over the four OECD countries, are presented
in Table D2(below). The latent correlations among the four self-concept factors (r = .28 to .42)
and among the four intrinsic value factors (r = .23 to .40) in different science domains were
modest. These correlations were smaller than those among utility value factors (r = .46 to .65).
Of particular relevance, correlations among the four coursework aspirations (r = .21 to .38) were
much smaller than those among the four achievement scores (r = .77 to .81). In summary, there
was good support for the high domain specificity of self-concept and intrinsic value, but the
support for utility value was much weaker. Our findings also provided good support for the
domain specificity of coursework aspirations but relatively weak support for the domain
specificity of achievement scores.
Latent correlations among all the constructs (4 latent factors for each self-concept,
intrinsic value and utility value, and 4 corresponding measure of achievement and coursework
aspirations) are presented in Table 2 based on Model MG4. In support of the convergent validity
of latent constructs, correlations between each self-concept and the matching intrinsic value were
consistently substantial (rs vary from .74 - .79). Also, convergent validity correlations involving
utility value were consistently moderate for matching domains of self-concept and intrinsic value
(rs vary from .41 to .34 and from .45 to .51 respectively). Both self-concept and intrinsic value
were highly correlated with the matching area of coursework aspirations (convergent validities,
rs vary from .57 - .62 and from .75 to .78 respectively), whereas the correlations between each
utility value and matching domains of aspirations were moderate (rs vary from .40 to .45).
However, the convergent validity correlations involving self-concept and intrinsic value were
somewhat weaker for the corresponding measure of achievement scores (rs vary from .24 to .32
and from .09 to .16 respectively). The sizes of convergent validities of utility value in relation to
achievement scores were substantially small and even non-significant (rs vary from -.03 to .09).
Achievement scores also have relatively weak convergent validity in relation to coursework
aspirations (rs vary from .05 to .08).
In support of the discriminant validities of self-concept and intrinsic value, the
convergent validities were substantially larger than correlations among self-concept factors (rs
vary from .31 to .42) and among intrinsic value factors (rs vary from .21 to .40) and correlations
between each self-concept factor and non-matching domains of intrinsic value (rs vary from .14
to .90). In support of the discriminant validities of self-concept and aspirations, the convergent
validities were much larger than correlations between each self-concept and non-matching
measure of coursework aspirations (rs vary from .09 to .22) and correlations among domain-
specific aspirations (rs vary from .21 to .38). Similar patterns were also found for the convergent
validities of intrinsic value in relation to aspirations. Although the convergent validities involving
utility value were higher than correlations of utility value to non-matching domains of self-
concept, intrinsic value and aspirations, these convergent validities were weaker than correlations
among utility value factors (rs vary from .46 to .65). Likewise, whilst the convergent validities
involving achievement were slightly larger than correlations of achievement to non-matching
area of self-concept, intrinsic value and aspirations, they were much smaller than correlations
among science domain-specific achievement scores (rs vary from .77 - .81).
In summary, consistent with previous research (e.g., Marsh, Abduljabbar et al., 2013),
self-concept was more highly correlated with achievement scores, whereas intrinsic value was
more highly correlated with coursework aspirations. The results provided good support for the
convergent and discriminant validity of self-concept, intrinsic value and coursework aspirations
in relation to each other. Whereas there was good support for the convergent validity of utility
value, utility value only had limited discriminant validity in relation to self-concept, intrinsic
value and coursework aspirations. Achievement scores had weak convergent validity and
discriminant validity in relation to self-concept, intrinsic value and aspirations but not utility
value.
Table D2
Latent Correlations Among Self-Concept, Intrinsic Value, Utility Value, Achievement Scores and Coursework Aspirations Based on Four Science Domains
Science self-concept Science intrinsic value Science utility value Science achievement Science aspirations
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Science self-concept
1.PSC −
2.CSC .42 −
3.ESC .34 .28 −
4.BSC .31 .41 .35 −
Science intrinsic value
5.PIV .79 .27 .20 .18 −
6.CIV .27 .79 .15 .30 .38 −
7.EIV .20 .14 .77 .19 .28 .23 −
8.BIV .13 .25 .15 .74 .25 .40 .28 −
Science utility value
9.PUV .41 .23 .14 .14 .50 .28 .19 .18 −
10.CUV .19 .40 .11 .22 .25 .49 .16 .29 .
65 −
11.EUV .13 .14 .34 .13 .18 .19 .45 .19 .
50 .53 −
12.BUV .13 .21 .11 .39 .18 .30 .19 .51 .
46 .63 .56 −
Science achievement
13.PACH .32 .25 .21 .20 .16 .12 .07 .02 .
09
-.0
1
-.0
5-.02 −
14.CACH .31 .25 .21 .26 .16 .13 .07 .08 .
09 .02 -.0
2.03 .77 −
15.ECAH .29 .23 .24 .25 .13 .09 .09 .06 .
07
-.0
2
-.0
3-.02 .77 .78 −
16.BACH .28 .25 .23 .30 .12 .12 .08 .11 .
04
-.0
1
-.0
5.00 .80 .80 .81 −
Science coursework aspirations
17.PAPS .57 .20 .12 .11 .75 .30 .21 .18 . .25 .18 .18 .08 .05 .04 .03 −
44
18.CAPS .21 .62 .09 .22 .30 .78 .16 .31 .
26 .44 .19 .27 .07 .05 .04 .06 .38 −
19.EAPS .14 .09 .60 .13 .21 .16 .76 .19 .
18 .15 .40 .17 .03 .02 .06 .04 .26 .21 −
20.BAPS .09 .19 .11 .57 .18 .31 .20 .75 .
17 .27 .19 .45 .01 .03 .04 .06 .22 .35 .25 −
Note. P = physics; C = chemistry; E = earth science; B = biology; SC = self-concept; IV= intrinsic value; UV = utility value; Standardized errors for all correlation coefficients are approximately .
01. All correlations greater than .023 or less than -.023 are statistically significant (p < .05); shaded correlations are convergent validity coefficients involving two constructs in matching domains.
External Appendix E:
Full Results for the path invariance Model (Model 7b)
Table E1
The Predictive Effects of Achievement on Self-Concept, Intrinsic Value and Utility Value Based
on Four Science Domains
Predictors
Motivation outcome variables
Model MG7b
Self-concept Intrinsic value Utility value
Physics
Physics Ach .16 (.02)* .13 (.02)* .09 (.02)*
Chemistry Ach .17 (.02)* .11 (.02)* .11 (.02)*
Earth science Ach .06 (.02)* -.00 (.02) .01 (.02)
Biology Ach -.09 (.02)* -.08 (.02)* -.13 (.02)*
Chemistry
Physics Ach .09 (.02)* .03 (.02) .00 (.02)
Chemistry Ach .12 (.02)* .11 (.02)* .09 (.02)*
Earth science Ach .01 (.02) .06 (.02)* -.08 (.02)*
Biology Ach .07 (.02)* .04 (.02)* -.01 (.02)
Earth science
Physics Ach .00 (.02) -.03 (.02) -.07 (.02)*
Chemistry Ach .00 (.02) -.03 (.02) .08 (.02)*
Earth science Ach .15 (.02)* .10 (.02)* .02 (.02)
Biology Ach .11 (.02)* .04 (.02)* -.07 (.02)*
Biology
Physics Ach -.14 (.02)* -.18 (.02)* -.08 (.02)*
Chemistry Ach .08 (.02)* .05 (.02)* .13 (.02)*
Earth science Ach .04 (.02)* .03 (.02) -.07 (.02)*
Biology Ach .32 (.02)* .23 (.02)* .02 (.02)
Summary (Means across different sets of path coefficients based on 4 domains
Mn Total .07 (.00)* .03 (.00)* .00 (.00)
Mn Match .19 (.01)* .14 (.02)* .05 (.01)*
Mn NoMatch .03 (.01)* -.02 (.00)* -.02 (.00)*
Difference .16 (.01)* .16 (.01)* .07 (.01)*
Note. SC = self-concept; IV= intrinsic value; UV = utility value; Ach = Achievement; shaded estimates
are path coefficients from achievement to motivational constructs in the matching domain; * p < .05
Table E2
The Predictive Effects of Self-Concept, Intrinsic Value, Utility Value and Their Interactions on Coursework Aspiration Based on Four Science Domains
Motivation predictors
Model MG7b
SC IV UV
Physics
Coursework
Aspirations
Physics .07 (.03)* .68 (.03)* .06
(.01)*
Chemistry -.02 (.03) .04 (.03) .02 (.01)
Earth science .05 (.02)* .06 (.02)* .01 (.01)
Biology -.05
(.02)*
-.08
(.02)*
.03
(.01)*
Chemistry
Coursework
Aspirations
Physics -.01 (.03) .02 (.03) .02 (.01)
Chemistry .08 (.03)* .69 (.03)* .06
(.01)*
Earth science .06 (.02)* .02 (.02) .01 (.01)
Biology .02 (.02) -.02 (.02) .01 (.01)
Earth science
Coursework
Aspirations
Physics -.05 (.03) .06 (.03) .01 (.01)
Chemistry .03 (.02) -.04 (.02) .01 (.01)
Earth science .10 (.03)* .66 (.02)* .06
(.01)*
Biology -.03 (.02) .01(.02) .01 (.01)
Biology
Coursework
Aspirations
Physics -.05
(.02)*
.01 (.03) .02 (.01)
Chemistry -.02 (.03) .05 (.02)* -.01 (.01)
Earth science -.04 (.02) .02 (.02) .01 (.01)
Biology .13 (.02)* .63 (.02)* .07
(.01)*
Mn Total
Mn Match
Mn NoMatch
.03 (.01)* .17(.00)* .03
(.00)*
.10(.01)* .67 (.01)* .06
(.01)*
.01 (.01) .01 (.01) .02
(.00)*
Difference .09 (.02)* .66 (.01)* .05
(.01)*
Note. SC = self-concept; IV= intrinsic value; UV = utility value; SCxIV = self-concept by intrinsic value interaction; SCxUV = self-concept by utility value
interaction; shaded estimates are path coefficients from motivational constructs to coursework aspirations in the matching domain; * p < .05.
Table E3
The Predictive Effects of Self-Concept, Intrinsic Value, Utility Value and Their Interactions on Coursework Aspiration Based on Four Science Domains
Outcomes
Motivation predictors
Model MG8b Model MG9b
SC IV UV SCxIV SC IV UV SCxUV
Physics
Coursework
Aspirations
Physics .08 (.03)* .67 (.03)* .07 (.01)* .09 (.01)* .08 (.03)* .72 (.03)* .06 (.01)* .09 (.01)*
Chemistry -.02 (.03) .05 (.03) .02 (.01) -.02 (.01) -.02 (.02) .03 (.02) .02 (.01) -.01 (.01)
Earth science .05 (.02)* .06 (.02)* .01 (.01) -.02 (.01)* .05 (.02)* .04 (.02) .01 (.01) -.00 (.01)
Biology -.05 (.02)* -.07 (.02)* .03 (.01)* -.01 (.01) -.05 (.02)* -.06 (.02)* .02 (.01) -.00 (.01)
Chemistry
Coursework
Aspirations
Physics -.01 (.03) .03 (.03) .02 (.01) -.04 (.01)* .01 (.02) -.01 (.02) .02 (.01) .01 (.010)
Chemistry .10 (.03)* .66 (.03)* .05 (.01)* .12 (.01)* .07 (.03)* .71 (.03)* .06 (.01)* .08 (.01)*
Earth science .06 (.02)* .03 (.02) .01 (.01) -.03 (.01)* .06 (.02)* .01 (.02) .02 (.01) -.02 (.009)
Biology .02 (.02) -.03 (.02) .01 (.01) .01 (.01) .01 (.02) -.02 (.02) -.01 (.01) .05 (.010)
Earth science
Coursework
Aspirations
Physics -.05 (.03) .05 (.03) .01 (.01) -.02 (.01)* -.03 (.02) .02 (.02) .02 (.01) .01 (.01)
Chemistry .03 (.02) -.04 (.02) .01 (.01) .01 (.01) .02 (.02) -.04 (.02) -.01 (.01) .02 (.01)
Earth science .13 (.03)* .64 (.02)* .05 (.01)* .13 (.01)* .08 (.02)* .70 (.02)* .05 (.01)* .09(.01)*
Biology -.03 (.02) .01(.02) .01 (.01) -.02 (.01)* -.02 (.02) -.00 (.02) .01 (.01) -.02 (.01)*
Biology
Coursework
Aspirations
Physics -.05 (.02)* .01 (.03) .02 (.01) -.03 (.01)* -.05 (.02)* -.02 (.02) .02 (.01) .00 (.01)
Chemistry -.02 (.03) .05 (.02)* -.01 (.01) -.01 (.01) -.01 (.02) .05 (.02)* -.01 (.01) -.02 (.01)
Earth science -.04 (.02) .02 (.02) .01 (.01) -.03 (.01)* -.04 (.02) .01 (.02) .01 (.01) -.01 (.01)
Biology .14 (.02)* .62 (.02)* .08 (.01)* .15 (.01)* .09 (.02)* .64 (.02)* .07 (.01)* .09 (.01)*
Summary (Means across different sets of path coefficients based on 4 domains
Mn Total
Mn Match
Mn NoMatch
.03 (.01)* .17(.00)* .03 (.00)* .02 (.00)* .01 (.01) .18 (.00)* .02 (.00)* .02 (.00)*
.10(.01)* .64 (.01)* .06 (.01)* .12 (.01)* .08 (.01)* .70 (.01)* .06 (.01)* .09 (.01)*
.01 (.01) .01 (.01) .02 (.00)* -.02 (.00)* -.01 (.01) .00 (.00) .01 (.00)* -.00 (.00)
Difference .09 (.02)* .66 (.01)* .05 (.01)* .14 (.01)* .08 (.02)* .70 (.02)* .06 (.01)* .08 (.01)*
Note. SC = self-concept; IV= intrinsic value; UV = utility value; SCxIV = self-concept by intrinsic value interaction; SCxUV = self-concept by utility value interaction;
shaded estimates are path coefficients from motivational constructs to coursework aspirations in the matching domain; * p < .05.
External Appendix F:
Supplemental Analyses for the mediating role of academic self-concept
Given that some previous studies suggested that the dimensional comparisons between achievements were likely to
indirectly affect value beliefs via the mediating role of self-concept (e.g., Nagy et al., 2008), we further tested whether the
effects of achievement on task value could be explained by the effects of self-concept. To this end, we evaluated a
mediation model in which the achievements in the four science domains predicted self-concepts, which in turn predicted
intrinsic and utility values. In this model, the four domain-specific self-concepts and values along with achievements
were also allowed to predict coursework aspirations. This mediation model provided an identical fit with original
hypothesized model (Model MG7b). The results revealed that all 32 direct paths from the four science achievements to
each of the intrinsic value and each of utility values were relatively small (from -.05 to .05; M = .01). Subsequently, we
evaluated a nested model where these 32 direct paths were constrained to be 0. There was a negligible decrease in model
fit (
CFI = .002,
TLI = .001,
RMSEA = .001) when compared to the fully mediated model, suggesting that self-
concept entirely mediated the effects of achievement on values.
External Appendix G:
Supplemental Analyses for Interaction Effect Between Self-Concept and Value
In the main text, latent interactions between self-concept and intrinsic value as well as between self-concept and utility value, when these two
multiplicative terms (self-concept x intrinsic value and self-concept x utility value) are considered separately.
Subsequently, we included the two sets of latent interactions into the same model (i.e, Model MG10a – MG10c in Table G1). All first-order effects and
interaction effects between self-concept and intrinsic value were significantly positive and similar in size with the pattern of results from Model MG8a-MG8b
(See Table 2 in the main text) where only self-concept and intrinsic value interactions were included (see Table G2). However, the interactions between self-
concept and utility value lost their predictive power on coursework aspirations. Given that correlations between matching domains of latent product variables
were substantial (r = .58 to .69, Table G3), we argue that the parameters involving interaction effects in this model should be interpreted with caution. In Model
MG11c, we constrained the paths leading from self-concept by intrinsic value interactions to aspirations and those from self-concept by utility value
interactions to be equal. The model fits the data as well, and there was a very small decrement in CFI (
.001) and RMSEA (
.001) but no difference in TLI in
comparison to Model MG10c. We also found a notable reduction in the size of the standard errors (from [.011 to .016] to [.004 to .006]) associated with the
paths from all domain-specific interactions to aspirations. The results for this model show that all domain-specific interactions positively predicted matching
measures of aspirations (M = .06, SE = .003). Thus, the results suggest that both types of domain-specific latent interaction (self-concept-by- intrinsic value,
and self-concept-by- utility value) may make similar contributions to the prediction of coursework aspirations (Marsh, Dowson, Pietsch & Walker, 2004).
Table G1
Model Fit Statistics for CFA and SEM Models Used in The Present Study
Model Description χ2df CFI TLI RMSEA
SEM
MG10a SC + IV + UV + ACH + ASP, CUs, INV = FL, FV, PC; Free = PT(scXiv, scXuv) 33843 10516 .946 .936 .022
MG10b SC + IV + UV + PT(scXiv,scXuv) + ACH + ASP, CUs, INV = FL, FV, PC 34934 10792 .945 .935 .022
MG10c SC + IV + UV + PT(scXiv,scXuv) + ACH + ASP, CUs, INV = FL, FV, CV, PC 38453 11398 .939 .931 .023
MG11a SC + IV + UV + ACH + ASP, CUs, INV = FL, FV, PC; Free = PT(scXiv, scXuv), PC (scXiv = scXuv) 34039 10580 .946 .936 .022
MG11b SC + IV + UV + PT(scXiv,scXuv) + ACH + ASP, CUs, INV = FL, FV, PC (scXiv = scXuv) 35081 10808 .944 .935 .022
MG11c SC + IV + UV + PT(scXiv,scXuv) + ACH + ASP, CUs, INV = FL, FV, CV, PC (scXiv = scXuv) 38629 11414 .938 .931 .023
Note. SC = self-concept; IV= intrinsic value; UV = utility value; PT = product term; ASP = coursework aspirations; scXiv = the product term of self-concept by intrinsic value
interaction; scXuv = the product term of self-concept and utility value interaction; INV = invariant; CUs = correlated uniquenesses; UCUs = uncorrelated uniquenesses; FL =
factor loading; FV = factor variances; CV = factor covariances; Free = PT (scXiv): freely estimate factor loading, factor variances and covariance and path coefficients with
respect to scXiv; Free = PT (scXuv): freely estimate factor loading, factor variances and covariance and path coefficients with respect to scXuv; PC (scXiv = scXuv):
constrain the path coefficients from scXiv to ASP and from scXuv to ASP to be equal
Table G2
The Predictive Effects of Self-Concept, Intrinsic Value, Utility Value and Their Interactions on Coursework Aspiration Based on Four Science Domains
(Standardized Path Coefficients as A Ratio of Standard Errors)
OutcomeMotivation Predictors
Model MG10c Model MG11c
SC IV UV SCxIV SCxUV SC IV UV scXiv = scXuv
Physics
Coursework
Aspirations
Physics .064/.028 .686/.030 .083/.016 .063/.015 .045/.013 .060/.027 .696/.029 .078/.016 .053/.005
Chemistry -.026/.025 .040/.026 .016/.013 -.021/.013 .004/.013 -.019/.025 .032/.025 .018/.013 -.008/.005
Earth science -.071/.024 .054/.023 .004/.011 -.025/.012 .008/.013 -.062/.023 .044/.022 .007/.011 -.009/.005
Biology -.047/.023 -.065/.022 .022/.012 .002/.013 -.008/.015 -.047/.023 -.061/.022 .022/.012 -.002/.005
Chemistry
Coursework
Aspirations
Physics -.011/.027 .024/.027 .023/.015 -.048/.014 .024/.013 .017/.028 -.012/.027 .030/.015 -.008/.006
Chemistry .074/.027 .689/.027 .057/.013 .113/.013 .005/.014 .061/.028 .718/.028 .053/.013 .059/.006
Earth science -.061/.023 .019/.022 .017/.011 -.031/.013 .001/.013 -.061/.024 .019/.022 .017/.011 -.015/.005
Biology .018/.022 -.016/.021 -.002/.013 -.010/.013 .018/.014 .015/.022 -.013/.021 -.004/.013 .003/.005
Earth science
Coursework
Aspirations
Physics -.067/.027 .024/.028 .019/.014 -.051/.013 .029/.013 -.035/.027 .024/.027 .027/.015 -.009/.006
Chemistry .028/.024 -.043/.024 .006/.014 -.011/.012 .020/.013 .029/.025 -.045/.025 .007/.014 .006/.005
Earth science .101/.025 .662/.024 .060/.011 .130/.014 -.001/.013 .067/.025 .703/.024 .048/.011 .063/.005
Biology -.033/.022 .005/.021 .011/.013 -.021/.014 -.005/.014 -.024/.022 -.001/.021 .012/.013 -.015/.004
Biology
Coursework
Aspirations
Physics -.023/.027 .004/.028 .021/.016 -.036/.013 .017/.011 -.006/.026 -.019/.026 .020/.015 -.006/.005
Chemistry -.048/.024 .046/.024 -.001/.014 -.017/.012 .006/.012 -.054/.024 .052/.025 -.001/.014 -.010/.005
Earth science -.042/.023 .018/.022 .007/.012 -.030/.013 .007/.013 -.041/.023 .017/.021 .016/.012 -.014/.005
Biology .123/.023 .635/.022 .077/.012 .159/.015 -.019/.016 .110/.023 .644/.022 .063/.013 .073/.004
Summary (Means across different sets of path coefficients based on 4 domains)
Mn Total .003/.003 .174/.003 .027/.002 .010/.003 .010/.003 .003/.003 .175/.003 .027/.002 .010/.001
Mn Match .090/.012 .668/.013 .069/.006 .116/.007 .008/.007 .075/.013 .690/.013 .061/.006 .062/.003
Mn NoMacth -.032/.005 .011/.005 .013/.003 -.025/.003 .010/.003 -.024/.005 .003/.005 .015/.003 -.007/.001
Difference .122/.016 .657/.017 .056/.007 .141/.008 -.002/.008 .099/.017 .687/.017 .046/.007 .069/.004
Note. SC = self-concept; IV= intrinsic value; UV = utility value; scXiv = self-concept by intrinsic value interaction; scXuv = self-concept by utility value
interaction. Shaded estimates are path coefficients from motivational constructs to coursework aspirations in the matching domain
Table G3
Latent Correlation Among Product Variables Based on Four Science Domains
Self-concept by intrinsic value Self-concept by utility value
1 2 3 4 5 6 7 8
Science self-concept by intrinsic value
1.PSCxIV −
2.CSCxIV .38 −
3.ESCxIV .25 .21 −
4.BSCxIV .22 .33 .28 −
Science self-concept by utility value
5.PSCxUV .58 .20 .15 .14 −
6.CSCxU
V
.24 .59 .13 .20 .35 −
7.ESCxUV .14 .10 .57 .14 .23 .21 −
8.BSCxU
V
.13 .15 .14 .69 .19 .26 .21 −
Note. P = physics; C = chemistry; E = earth science; B = biology; SC = self-concept; IV = intrinsic value; UV = utility value; scXiv = self-concept by intrinsic
value interaction; scXuv = self-concept by utility value interaction.
External Appendix H:
Full Results for country-specific path coefficients (Model MG7a)
Table H1
The Predictive Effects of Achievement on Self-Concept, Intrinsic Value and Utility Value Based
on Four Science Domains (Czech Republic/Hungary/Slovenia/ Sweden)
Predictors
Motivation outcome variables
Model MG6
Self-concept Intrinsic value Utility value
Physics
Physics Ach .144/.170/.186/.236 .125/.097/.147/.082 .094/.078/.083/.106
Chemistry Ach .218/.151/.224/.154 .145/.119/.141/.085 .159/.085/.151/.094
Earth science Ach .069/.075/.080/.071 .016/-.001/-.013/.013 -.005/.024/-.024/.026
Biology Ach -.118/-.101/-.078/-.105 -.066/-.058/-.091/-.119 -.128/-.115/-.131/-.196
Chemistry
Physics Ach .112/.078/.086/.102 .034/.016/-.015/-.025 .016/-.014/.042/.041
Chemistry Ach .121/.104/.142/.119 .131/.088/.089/.143 .084/.132/.089/.061
Earth science Ach .008/.017/.010/.018 .049/.050/.062/.086 -.118/-.075/-.130/-.081
Biology Ach .079/.083/.082/.065 .039/.066/.085/.044 .024/.057/.017/-.017
Earth science
Physics Ach -.010/-.010/.020/.014 -.045/-.047/.019/.023 -.092/-.114/-.075/-.094
Chemistry Ach -.013/.020/.013/-.016 -.056/.011/.005/-.038 .111/.125/.053/.074
Earth science Ach .178/.187/.125/.114 .123/.148/.085/.096 -.026/.019/-.018/.035
Biology Ach .094/.074/.147/.073 .067/.053/.054/.040 -.088/-.094/-.053/-.097
Biology
Physics Ach -.122/-.114/-.067/-.082 -.212/-.164/-.156/-.197 -.062/-.112/-.077/-.069
Chemistry Ach .093/.079/.069/.094 .091/.061/.053/.068 .101/.172/.111/.141
Earth science Ach .037/.084/.044/.064 .017/.053/-.022/.047 -.106/-.071/-.092/-.062
Biology Ach .267/.271/.348/.252 .232/.232/.280/.175 .032/.017/.042/.024
Note. SC = self-concept; IV= intrinsic value; UV = utility value; Ach = Achievement; shaded estimates
are path coefficients from achievement to motivational constructs in the matching domain; * p < .0
EXPECTANCY-VALUE INTERACTION AND UNIQUE PREDICTION
Table H2
The Predictive Effects of Self-Concept, Intrinsic Value, Utility Value and Their Interactions on Coursework Aspiration Based on Four Science
Domains (Czech Republic/Hungary/Slovenia/ Sweden)
Motivation predictors
Model MG6b
SC IV UV
Physics
Coursework
Aspirations
Physics .064/.066/.116/.084 .810/.657/.787/.737 .074/.064/.114/.087
Chemistry -.030/-.015/-.009/-.00
3 .019/.056/.033/.060 .017/-.018/-.013/.039
Earth science .075/.061/.069/.058 .085/.084/.046/.065 -.018/.034/-.001/.007
Biology -.077/-.048/-.087/-.05
3 -.112/-.670/-.112/-.073 .035/.064/.059/.050
Chemistry
Coursework
Aspirations
Physics .017/.013/.013/-.019 .025/-.014/.038/.029 .032/.041/-.003/.045
Chemistry .072/.135/.128/.111 .775/.801/.676/.735 .054/.057/.071/.053
Earth science .059/.650/.083/.073 .036/.032/-.011/.038 .013/-.004/-.007/.020
Biology .036/.025/-.028/-.023 -.023/-.024/-.011/.004 .004/.034/-.013/.003
Earth science
Coursework
Aspirations
Physics -.010/-.002/-.048/-.05
8 .041/.040/.022/.061 .024/-.004/.012/.028
Chemistry .016/.038/.022/.012 -.011/-.013/-.044/-.016 -.019/-.015/.025/.010
Earth science .063/.076/.113/.092 .672/.572/.692/.747 .057/.058/.103/.067
Biology -.025/-.035/-.041/-.04
3 .011/.010/.005/-.016 .006/.020/.014/-.006
Biology
Coursework
Aspirations
Physics -.058/-.045/-.053/-.07
4 -.020/-.018/-.012/.016 .021/.003/.028/.038
Chemistry -.008/-.028/-.015/-.04
0 .047/.085/.053/.056 -.021/.011/-.008/-.002
Earth science -.052/-.018/-.015/-.01
0 .018/.007/-.020/-.037 .029/-.009/-.007/.033
Biology .116/.081/.117/.161 .627/.602/.710/.667 .126/.138/.090/.071
55
EXPECTANCY-VALUE INTERACTION AND UNIQUE PREDICTION
Note. SC = self-concept; IV= intrinsic value; UV = utility value; SCxIV = self-concept by intrinsic value interaction; SCxUV = self-concept by utility value
interaction; shaded estimates are path coefficients from motivational constructs to coursework aspirations in the matching domain; * p < .05
56
EXPECTANCY-VALUE INTERACTION AND UNIQUE PREDICTION
References for Online Supplemental Materials
Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
Chen, F. F. (2007). Sensitivity of Goodness of Fit Indexes to Lack of Measurement
Invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464–
504. doi:10.1080/10705510701301834
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure
analysis: Conventional criteria versus new alternatives. Structural Equation
Modeling: A Multidisciplinary Journal, 6(1), 1–55. doi:10.1080/10705519909540118
Jöreskog, K. G., & Yang, F. (1996). Nonlinear structural equation models: The Kenny–Judd
model with interaction effects. In G. A. Marcoulides & R. E. Schumacker (Eds.),
Advanced structural equation modeling: Issues and techniques (pp. 57–87).Mahwah,
NJ: Lawrence Erlbaum Associates.
Marsh, H. W., Abduljabbar, A. S., Abu-Hilal, M. M., Morin, A. J. S., Abdelfattah, F., Leung,
K. C., … Parker, P. D. (2013). Factorial, convergent, and discriminant validity of
TIMSS math and science motivation measures: A comparison of Arab and Anglo-
Saxon countries. Journal of Educational Psychology, 105(1), 108–128.
doi:10.1037/a0029907
Marsh, H. W., Abduljabbar, A. S., Parker, P. D., Morin, A. J. S., Abdelfattah, F., Nagengast,
B., … Abu-Hilal, M. M. (2015). The Internal/External Frame of Reference Model of
Self-Concept and Achievement Relations: Age-Cohort and Cross-Cultural
Differences. American Educational Research Journal, 52(1), 168–202.
doi:10.3102/0002831214549453
Marsh, H. W., Dowson, M., Pietsch, J., & Walker, R. (2004). Why Multicollinearity Matters:
A Reexamination of Relations Between Self-Efficacy, Self-Concept, and
Achievement. Journal of Educational Psychology, 96(3), 518–522. doi:10.1037/0022-
0663.96.3.518
Marsh, H. W., Hau, K-T.,Wen, Z., Nagengast, B. & Morin, A. J. S. (2013). Statistical Models
of Moderation. In Little, T. (Ed.), Oxford Handbook of Quantitative Methods. New
York: Oxford University Press.
Marsh, H. W., Wen, Z., & Hau, K.-T. (2004). Structural equation models of latent
interactions: evaluation of alternative estimation strategies and indicator construction.
Psychological Methods, 9(3), 275–300. doi:10.1037/1082-989X.9.3.275
Mullis, I. V. S., Martin, M. O., Olson, J. F., Berger, D. R., & Stanco, G. M. (Eds.). (2008).
TIMSS 2007 encyclopedia: A guide to mathematics and science education around the
world (Vols. 1 and 2). Chestnut Hill, MA: TIMSS & PIRLS International Study
Center, Lynch School of Education, Boston College.
Nagengast, B., Marsh, H. W., Scalas, L. F., Xu, M. K., Hau, K.-T., & Trautwein, U. (2011).
Who took the “x” out of expectancy-value theory? A psychological mystery, a
substantive-methodological synergy, and a cross-national generalization.
Psychological Science, 22(8), 1058–1066. doi: 10.1177/0956797611415540
Wen, Z., Marsh, H. W., & Hau, K.-T. (2010). Structural Equation Models of Latent
Interactions: An Appropriate Standardized Solution and Its Scale-Free Properties.
Structural Equation Modeling: A Multidisciplinary Journal, 17(1), 1–22.
