A Structural Equation Modelling of the Academic Self-Concept Scale

Abstract

The study aimed at validating the academic self-concept scale by Liu and Wang (2005) in measuring academic self-concept among university students. Structural equation modelling was used to validate the scale which was composed of two subscales; academic confidence and academic effort. The study was conducted on university students; males and females from different levels of study and faculties. In this study the influence of academic self-concept on academic achievement was assessed, tested whether the hypothesised model fitted the data, analysed the invariance of the path coefficients among the moderating variables, and also, highlighted whether academic confidence and academic effort measured academic selfconcept. The results from the model revealed that academic self-concept influenced academic achievement and the hypothesised model fitted the data. The results also supported the model as the causal structure was not sensitive to gender, levels of study, and faculties of students; hence, applicable to all the groups taken as moderating variables. It was also noted that academic confidence and academic effort are a measure of academic self-concept. According to the results the academic self-concept scale by Liu and Wang (2005) was deemed adequate in collecting information about academic self-concept among university students.

Full text

International Electronic Journal of Elementary Education, 2014, 6(2), 185-198.
A Structural Equation Modelling of the
Academic Self-Concept Scale
Musa MATOVU
∗
∗∗
∗
International Islamic University, Malaysia
Received: 14 August 2013 / Revised: 28 January 2014 / Accepted: 08 February 2014
Abstract
The study aimed at validating the academic self-concept scale by Liu and Wang (2005) in
measuring academic self-concept among university students. Structural equation modelling was
used to validate the scale which was composed of two subscales; academic confidence and
academic effort. The study was conducted on university students; males and females from
different levels of study and faculties. In this study the influence of academic self-concept on
academic achievement was assessed, tested whether the hypothesised model fitted the data,
analysed the invariance of the path coefficients among the moderating variables, and also,
highlighted whether academic confidence and academic effort measured academic self-
concept. The results from the model revealed that academic self-concept influenced academic
achievement and the hypothesised model fitted the data. The results also supported the model
as the causal structure was not sensitive to gender, levels of study, and faculties of students;
hence, applicable to all the groups taken as moderating variables. It was also noted that
academic confidence and academic effort are a measure of academic self-concept. According
to the results the academic self-concept scale by Liu and Wang (2005) was deemed adequate
in collecting information about academic self-concept among university students.
Keywords: Academic Self-Concept Scale, Structural Equation Modelling, University Students,
Malaysia.
Introduction
Academic self-concept is referred to as students’ perceptions about their levels of
competencies within the academic realm (Ferla et al., 2009; Lips, 2004; Wigfield &
Eccles, 2000; Wigfield & Karpathian, 1991). Broadly academic self-concept is the way
how students feel about themselves as learners (Guay et al., 2003). Specifically,
academic self-concept is a composite view of oneself across various sets of specific
academic domains, abilities, and perceptions (Trautwein et al., 2006). This is based on
∗
Musa Matovu, Institute of Education, International Islamic University Malaysia, Jalan
Gombak, Selangor, Kuala Lumpur, Malaysia. Phone: +60108931380 E-mail:
matovumousa@yahoo.com

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self-knowledge and evaluation of values formed through experiences with the
interpretation of one’s academic environment (Eccles, 2005; Bong & Skaalvik, 2003).
Academic self-concept has been noted of its tendency to decline among students from
early to mid adolescence, and also, it can extend to adulthood (Liu & Wang, 2005).
Marsh (1989) explained that academic self-concept reaches its lowest point in middle
adolescence, but, also found out that academic self-concept increased through early
adulthood. In other findings it has been noted that as students grow older their
academic self-concept becomes relatively stable (Guay et al., 2003). Academic self-
concept has been noted to vary as students move through grades in which their
academic self-concept tends to rise in the direction of their academic achievement (Liu
& Wang, 2005; Jacob et al., 2002), while others studies found out that it tends to
become weaker (Marsh & Yeung, 1997; Marsh et al., 2002). Generally, it has been
highlighted that academic self-concept influences students’ academic achievement
(Awad, 2007; Marsh, 2006; Cokley, 2000; Marsh et al., 2002, 1999). However,
although various researchers concur with the academic self-concept changes, only a
few studies have tackled changes in the instruments of measure of academic self-
concept across various groups of students they measure (Matovu, 2012).
In another issue, several studies have tested the validity of academic self-concept
instruments across age (Marsh, 1990; Marsh et al., 1988), gender (Byrne & Shavelson,
1987; Marsh, 1993), and other groups. There are no documented studies that have
validated the Liu and Wang (2005) academic self-concept scale across gender, levels
of study, and faculties among university students using structural equation modelling.
Validation of an instrument is one way of improving its performance over time.
Academic self-concept instruments which have been validated over time have become
better and more effective in measuring academic self-concept (Byrne, 2002; Marsh et
al., 1999). The validation of the academic self-concept scale in this study was done
because it had been noted that weak theoretical bases, poor quality of measurement
instruments, methodological shortcomings, and lack of consistent findings had merged
academic self-concept instruments (Byrne, 1984; Shavelson et al., 1976).
The third issues is that gender differences in academic self-concept have been
reported in some studies; males and females possessing different conceptions about
their competencies in academic abilities (Ireson et al., 2001; Wigfield et al., 2001;
Marsh, 1989). Studies have postulated that males show higher academic self-concept
than females (Kling et al., 1999). In other studies it has been posited that males tend to
exhibit higher academic self-concept in science courses while females in non-science
courses (Harter, 1999; Marsh, 1989). Jacob et al. (2002) articulated that gender
differences start as early as elementary school and remains stable throughout
adolescence to adulthood. With such existing differences this called for the validation of
the academic self concept scale to find out whether it was invariant across the groups it
was measuring. In another study it was highlighted that small stereotypic gender
differences linearly declined in mean levels of academic self-concept with age, and
modest differentiation between academic competencies among students (Marsh,
2006). This can also be the same situation in other groups defined by self-concept and
academic achievement (Worrell et al., 1999).
Fourth, Byrne (1996) and Hattie (1992) cited two major issues in which any research
concerning the self-concept should focus; (a) the development of instruments affording
to collect valid and reliable scores and (b) attention to cross-cutting concerns in the
development of academic self-concept measures which have also been addressed in
this study. Specifically, lack of the above cited issues reported in the literature have led
to the validation of the academic self-concept scale and further studies on academic
self-concept (Marsh, 1990; Marsh et al., 1988; Marsh et al., 1991).

A Structural Equation Modelling of the Academic Self-Concept Scale / Matovu
187
According to developed theories and models that explain academic self-concept and
academic achievement, there has been no much proof on whether prior academic self-
concept influences academic achievement or, prior academic achievement causes
subsequent academic self-concept (Marsh et al., 2002; Matovu, 2012). In the self-
enhancement model academic achievement is due to the consequence of academic
self-concept (Bong, 2001; Skaalvik & Skaalvik, 2005). Secondly, the skill-development
model highlights that academic achievement determines academic self-concept
(Marsh, 2006; Marsh et al., 2005, 2002, 1999). Third, academic self-concept and
academic achievement are reciprocal (Guay et al., 2003). The extensive debate among
researchers concerning whether prior academic self-concept influences academic
achievement, or, prior academic achievement causes subsequent academic self-
concept has been considered an egg-chicken question (Marsh et al., 2002). This also
calls for more understanding of the influence of academic self-concept on academic
achievement, and to validate further the instruments that measure academic self
concept (Byrne, 1996; Shavelson et al., 1976).
Figure 1. Academic self-concept - Academic achievement hypothesised model
ACHIEVE = Academic Achievement, ASC = Academic Self-Concept, AC = Academic
Confidence, AE = Academic Effort
Measure
The aim of the study was to validate the academic self-concept scale developed by Liu
and Wang (2005) to test for its variability and reliability in measuring academic self-
concept among university students. The academic self-concept scale was developed in
reference to the general academic status scale (Piers & Harris, 1964), the academic
esteem subscale (Battle, 1981), and the school subjects self-concept (Marsh et al.,
1983). The original academic self-concept scale by Liu and Wang (2005) had to two
sub scales; (a) academic confidence, and (b) academic effort each with 10 items. The
20 item questionnaire which utilised a 7 point likert scale with designated end points of
strongly agree and strongly disagree was used in this study. The items included both
negatively and positively worded items to avoid the same answers from the students.
Both academic confidence and academic effort items were mixed in the scale;
academic confidence items taking odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, 19), while
academic effort items taking even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20). For the
first validation the Liu and Wang (2005) academic self-concept scale item 13 was
removed, and in the second validation by Tan and Yates (2007) using Rasch modelling
three items (4, 13, and 18) were removed because of their poor in-fit statistics (see the

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instrument in Appendix A). These studies were done in secondary schools and primary
schools respectively in Singapore.
Research Questions
This study was based on two research questions; (a) whether the Liu and Wang (2005)
academic self-concept scale was appropriate to measure academic self-concept
among university students, and (b) whether university students’ academic self-concept
influenced their academic achievement.
Hypotheses
The study was conducted on four hypotheses which included; (a) academic self-
concept directly influences academic achievement, (b) the hypothesised model will fit
the data collected using the Liu and Wang (2005) academic self-concept scale, (c) the
path coefficients of the hypothesised model vary significantly among groups (gender,
levels of study, and faculties) as moderating variables, and (d) academic confidence
and academic effort are a measure of academic self-concept.
Methods
Sample
The data was collected from a total of 280 students in a public university in Malaysia.
The sample composition was of males (50.4%) and females (49.6%) for gender, non
science (61.8%) and science (38.2%) for faculties, and undergraduates (50.7%) and
postgraduates (49.3%) for levels of study. All the students were randomly selected
from their respective groups. For science and non science faculties, the students were
selected from the different departments in their respective faculties. The sample was
appropriate because it considered the proportions of the different groups in its
selection.
Instrument
The data was collected using the original academic self-concept scale by Liu &Wang
(2005) which measured academic confidence and academic effort on the general
academic self-concept. Academic confidence and academic effort served as
endogenous variables to the general academic self-concept. The instrument had 20
items on a 7 point scale on which students responded to indicate their agreement or
disagreement with the items. The 20 item original Liu and Wang (2005) academic self-
concept scale was validated because there was no literature that it had ever been
validated on measuring academic self concept among university students using
structural equation modelling.
Structural Equation Modelling
The study applied four stages structural equation modelling using AMOS 18 to test the
hypotheses. The study validated the measurement model, confirmatory factor analysis
was done to the hypothesised model, metric invariance were calculated, and then later,
good fit of the fully fledged academic self-concept and academic achievement model
was tested. All these processes allowed the relation to be tested only after ensuring
that the latent variables were measured adequately (Barry & Stewart, 1997). In cross
validation of the model, moderating effects of gender, levels of study, and faculties
were considered. In estimating the hypothesised model using covariance matrix the
estimations satisfied the underlying statistical distribution theory by giving appropriate
estimates for the properties. This was due to having adopted a maximum likelihood in
estimating the full-fledged model. After the model had been estimated a set of criteria
were applied to evaluate the model goodness-of-fit. The measures were based on the

A Structural Equation Modelling of the Academic Self-Concept Scale / Matovu
189
conventionally accepted criteria for deciding what constitutes a good fit model, that is,
(a) reasonableness of the estimates, (b) consistence of the model that collected data,
and (c) proportions of variance of the dependent variables that accounted for by the
exogenous variables.
Table 1. Measurement of the variables of the hypothesised model
Construct
Items
Measure
M
SD
CR
Academic
Confidence
C1
I can follow the lectures easily.
4.35
1.81
.853
C2
I am able to help my course mates
in their school work.
4.66
1.73
C3
If I work hard, I think I can get
better grades.
5.31
1.64
C10
I am able to do better than my
friends in most courses.
4.58
1.77
Academic
Effort
E2
I often do my course work without
thinking.
5.67
1.36
.861
E3
I pay attention to the lecturers
during lectures.
6.39
1.12
E4
I study hard for my tests.
6.49
.97
E5
I am usually interested in my
course work.
6.48
1.03
E6
I will do my best to pass all the
courses this semester.
6.84
.46
E9
I do not give up easily when I am
faced with a difficult question in my
course work.
5.80
1.22
Note: M = Mean, SD = Standard Deviation, CR = Composite Reliability
Results
In this section, the results of the structural equation modelling that addressed the
hypotheses of the study are presented.
Measurement model
Confirmatory Factor Analysis using AMOS 18 was used to determine the psychometric
properties of the academic self-concept scale and the academic achievement among
university students. The results got using the maximum likelihood estimation of
confirmatory factor analysis tested the validity of the model which indicated that the
hypothesised model fitted the data. In the first run of the data some items had poor
loading on their respective factors. The items with poor fit were removed from the
model. In the subsequent run, the overall fit of the measurement model was adequate
with Relative Chi- Square = 2.386, CFI = .943, RMSEA = .070, SRMR = .048, and p =
.000 (see figure 2). All measures were within acceptable values indicating good model

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190
fit (Byrne, 2001, 2006, 2010; Arbuckle & Wothke, 1999; Masrom & Hussein, 2008;
Brown, 2006). In other words, measuring academic self-concept did generate the
observed covariance matrix; that is to say, there was no evidence to reject the
measurement model at this level. From the measurement model the factor loading
were substantial and statistically significant at p = .000, and the model was free from
offending estimates. The composite reliability for the first order factors was .85 for
academic confidence and .86 for academic effort (see table 1). A composite reliability
above .70 for a model is adequate (Hair et al., 1998). Also, both convergent and
discriminant validity were examined. The convergent validity which is the extent to
which indicators of a specific construct converge or share proportion of variance in
common was examined using composite reliability and Average Variance Extracted
(AVE). Discriminant validity which is the extent to which a construct is truly distinct from
other constructs (Bagozzi & Lee, 2002; Shen et al., 2009) was examined as well. The
data supported the measurement adequacy with the Average Variance Extracted
(AVE) of .68 to academic confidence and .62 to academic effort which were above the
threshold (.50) and an evidence of convergent validity (Fornell & larker, 1981; Shittu et
al., 2011). Also the AVE for both academic confidence and academic effort were
greater than the squared correlation (.42) which was an evidence for discriminant
validity that is, supporting the evidence of construct validity of the model. This indicated
that the measured variables were more in common with the construct they were
associated with than they did with the other constructs (Byrne, 2010).
Figure 2. Measurement model of Academic Self-Concept
AC = Academic Confidence, AE = Academic Effort
From the measurement model in figure 2, six items (7, 9, 11, 13, 15 and 17) were
removed from the academic confidence subscale, while four items (2, 14, 16 and 20)
were also removed from the academic effort subscale (see items in appendix A). This
was because the items had poor loadings onto their factors.

A Structural Equation Modelling of the Academic Self-Concept Scale / Matovu
191
Full- fledge model of academic self-concept and academic achievement
Figure 3 shows results of structural equation modelling of the influence of academic
self-concept on academic achievement in the full-fledged model. According to the
goodness-of-fit statistics, confirmatory modelling yielded consistence in the causal
relationship with the data, with Relative Chi-Square = 2.272; CFI = .937, RMSEA =
.068, SRMR = .050, and p = .000. All the results got indicated that the indices satisfied
their critical cut off scores; that is, the model fitted the data.
Figure 3. Standardised coefficients of the Academic Self-concept - Academic Achievement
hypothesised Model
According to the model in figure 3, the parameter estimates of the derived model
were good and free from offending values. According to the coefficients of the causal
structure, all path coefficients were statistically significant at .005 levels, showing the
practical importance of the model. From the model in figure 3 it can be highlighted that
students’ academic confidence (β = .88, p < .05) and academic effort (β = .68, p < .05)
contributed to their academic self-concept. Also, academic self-concept was influential
to the students’ academic achievement (β = .41, p < .001). The two endogenous
variables explained 61% of the variability in academic self-concept. From the findings,
the four hypotheses were supported by the results got in the study.
Gender, levels of study, and faculties’ invariance of the model
It was also in the interest of the research to examine the structure invariance of the
model among the moderating variables. The model had three moderating variables
which included gender (males and females), levels of study (Postgraduate or
undergraduate), and faculties (science or non-science). In testing the invariance
simultaneous analysis was done on the males (n
1
= 141) and females (n
2
=139). Later,

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an analysis of the constrained model for the males and females was done whose Chi-
Square values were tested against the baseline Chi-Square values for the statistical
significance difference. The same procedure was done to test for the invariance in the
levels of study (undergraduates; n
1
= 142 and postgraduates; n
2
= 138), and faculties
(science; n
1
= 107 and non-science; n
2
= 173) of the university students (see table 2).
The invariance tests across male and female groups resulted in a statistically
insignificant change in the Chi-Square value, χ² (df = 8) = 16.84, p > .005. Also for
undergraduates and postgraduates, χ² (df = 8) = 8.76, p > .005, and non science and
science faculties, χ² (df = 8) = 5.918, p > .005 had also a statistically insignificant
change in the Chi-Square value. According to the results, the difference in the Chi-
Square values of the constrained and unrestricted model did not produce poor fit. It can
be concluded from the results of the invariance tests, that is; gender, levels of study,
and faculties in which the students study did not interact with the students’ academic
achievement. It can also be drawn from the results that the path coefficients did not
vary significantly across the three groups (gender, levels of study and faculties). Hence
gender, levels of study, and faculties of the students were not invariant on the
academic self concept scale among university students.
Table 2. Results of multiple groups modelling of the hypothesised model
Chi-Square
df
Critical
value
Chi-Square
Change
Gender
Unrestricted
150.18
86
21.95
16.84
Constrained
167.02
94
Level
Unrestricted
142.67
86
21.95
8.76
Constrained
151.43
94
Faculty
Unrestricted
150.88
86
21.95
5.92
Constrained
156.80
94
df = degrees of freedom
Discussion
In this study, several findings have been got and have expanded on the knowledge in
the area of academic self-concept and academic achievement at large. The results got
can explain related issues on students’ achievement in relation to their academic self-
concept with the studied moderating variables. The results showed that academic self-
concept directly influenced academic achievement. These results are similar to those
found by Awad (2007), Cokley (2000), Cokley (2002) & Lent et al. (1997) who
highlighted that academic self-concept had a relationship with academic achievement.
It can also be derived from the results of this study that the higher the academic self-
concept the students have the more they will achieve academically. Or, the avoidance
of repeated failure can produce good academic achievement (Martin et al., 2004).
It can also be highlighted that academic self-concept through gender, levels of
study, and faculties does not influence academic achievement. So, in the current
situation where studies are being done on academic self-concept as an influencer to
academic achievement, gender, levels of study, and faculties do not moderate

A Structural Equation Modelling of the Academic Self-Concept Scale / Matovu
193
academic achievement. This refutes the findings of Ireson et al. (2001), Wigfield et al.
(2001), Marsh & Yeung (1998), Pajares & Miller (1994) who articulated that males and
females possess different conceptions about their competence in academic abilities.
This was by males having a higher academic self-concept than females (Kling et al.,
1999). Basing this on gender this may discourage a particular gender from certain
academic choices view themselves as poorly fitting into certain academic areas (Eagly,
1987; Eccles, 1987). This was evidenced in male dominated course where females
reported higher levels of academic discrimination than females in female dominated
course (Steele et al., 2002). Also the results reject that there is a difference in self-
concept of students offering either science based or non-science courses (Harter,
1999; Marsh, 1989). Again the results of this study have differed from the findings of
Trautwein et al. (2006) who suggested that academic self-concept may differ as a
function of the students’ achievement on their reference group. At the same time
findings of this study are similar to those of Bong and Skaalvik (2003) that revealed that
academic self concept directly influences how students perform at academic tasks.
Conclusion
In analysis of the findings of the study they have applicable implications in the teaching
and learning process among university students. In the teaching and learning situation
targeted on academic self-concept instructors should be aware that students’ academic
confidence and academic effort are great contributors to their academic self-concept
which determines their academic achievement. Teaching instructors should go an extra
mile to develop students’ academic confidence and also encourage them to put in more
effort in order to achieve highly academically. Secondly, researchers to us the
academic self-concept scale by Liu and Wang (2005) in future to find out the academic
self concept of university students they should know that it is valid and invariant across
students’ gender, levels of study and faculties.
• • •
Musa MATOVU is a doctoral student at Institute of Education, International Islamic University
Malaysia. He holds a Masters degree in Educational Psychology, a Postgraduate Diploma in
Education, and a Bachelor of Arts degree from Makerere University, Uganda. He is a lecturer in
the Department of Educational Psychology, Islamic University in Uganda. His areas of research
interest include educational psychology, educational assessment, assessment practices,
assessment conceptions, educational psychometric measurement and instrument validation,
and school guidance and counselling.
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APPENDIX A
1= strongly Disagree, 2 = Disagree, 3 = Disagree some-what, 4 = neither agree nor disagree,
5 = Agree some-what, 6 = Agree, 7 = Strongly Agree
1.
I can follow the lectures easily.
1
2
3
4
5
6
7
2.
I day-dream a lot in lectures.
1
2
3
4
5
6
7
3.
I am able to help my course mates in their school work.
1
2
3
4
5
6
7
4.
I often do my course work without thinking.
1
2
3
4
5
6
7
5.
If I work hard, I think I can get better grades.
1
2
3
4
5
6
7
6.
I pay attention to the lecturers during lectures.
1
2
3
4
5
6
7
7.
Most of my course mates are smarter than I am.
1
2
3
4
5
6
7
8.
I study hard for my tests.
1
2
3
4
5
6
7
9.
My lecturers feel that I am poor in my studies.
1
2
3
4
5
6
7
10.
I am usually interested in my course work.
1
2
3
4
5
6
7
11.
I often forget what I have learned.
1
2
3
4
5
6
7
12.
I will do my best to pass all the courses this semester.
1
2
3
4
5
6
7
13.
I get frightened when I am asked a question by the
lecturers.
1
2
3
4
5
6
7
14.
I often feel like quitting the degree course.
1
2
3
4
5
6
7
15.
I am good in most of my courses.
1
2
3
4
5
6
7
16.
I am always waiting for the lecture to end and go home.
1
2
3
4
5
6
7
17.
I always do poorly in course works and tests.
1
2
3
4
5
6
7
18.
I do not give up easily when I am faced with a difficult
question in my course work.
1
2
3
4
5
6
7
19.
I am able to do better than my friends in most courses.
1
2
3
4
5
6
7
20.
I am not willing to put in more effort in my course work.
1
2
3
4
5
6
7

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