Validating the University Student Engagement Model through Structural Equation Modeling

The main purpose of this study is to investigate whether emotional, cognitive and behavioral engagements, represents three conceptually and empirically distinct psychological constructs when studied within the same domain. This paper reports part of the findings from a major study entitled “Predictors of Self-Handicapping Behavior among Muslim Students”. Testing for factorial equivalence of scores from a measuring instrument was carried-out through structural equation modeling by using AMOS version 16. Results of Confirmatory Factor Analysis of responses from 790 undergraduates prove that the SEM three factor model of University Student Engagement (USE) is empirically fit and reliable, which also supports the argument that emotion, behavior and cognition are the student engagement manifestations of an interrelated constellation of academic student engagement.

The general purpose of this study is to add to the existing knowledge about student engagement. Many educators have become dissatisfied with student engagement, whereby an engaged student is expected to show sustained behavioral involvement in learning activities accompanied by a positive emotional tone (Finlay, 2006). Unfortunately, many changes experienced among students have been found to have a negative influence on their efficacy, which includes practicing academic self-handicapping behavior, decline in academic self-concept and decline of academic motivation and engagement. The main purpose of this study however, is to develop the measurement model of student engagement (USE) on the data derived from undergraduate students in an ongoing co-curriculum compulsory course. The result of which can be utilized by Researchers, Counselors, Psychologists and Students in studying issues pertaining to student engagement.
In this study, student engagement is defined according to the definition from the study of research report written by Finlay (2006) on "Quantifying School Engagement" at the center for School Engagement in Colorado, USA. Students are expected to show sustained behavioral involvement in learning activities accompanied by a positive emotional tone, select tasks at the border of their competencies, initiate action when given opportunities and make intense effort and concentration in the implementation of learning tasks. They are also expected to show positive emotions during ongoing actions including curiosity, interest, enthusiasm and optimism. Thus the three categories of engagement in this study are defined as:


Emotional Engagement: relationships with lecturers, colleagues, academics, faculty, university as well as willingness to work.
 Behavioral Engagement: participation in the university related activities, academic and learning tasks, positive conduct and absence of disruptive behaviors.

Methodology
This is a theoretical study which deals with model building, assessment and evaluation through structural equation modeling. It involves a confirmatory two-step approach theory testing and development using Maximum Likelihood Estimation method which is the method of testing the parameters of a statistical model. MLE has been selected because it corresponds with many statistical estimation methods wherewith it selects the set of values of the model parameters which maximizes the likelihood function.

SPSS (Statistical Package for Social Science) version 16 and AMOS (Analysis of Moment Structures)
Version 16 has been applied in conducting individual construct analysis group analysis and invariance analysis. In the first step, the three constructs of the measurement model of University Student Engagement model were assessed through PCA and CFA, whereby all three student engagement constructs (emotion, behavior and cognitive) proved to be fit and reliable. In the second step, the individual constructs were assessed as a group of constructs by embedding the three university student engagement constructs together as a measurement model of USE before assessing its fitness in the form of first and second order measurement models.

Sample
From our target population of 1,032 undergraduate students of International Islamic University Malaysia (IIUM), only 832 responded and only 790 students followed the instructions and filled in the survey report correctly and completely thus, 42 samples were discarded due to either incorrectly filled in questionnaire or partially filled or unfilled. Therefore, the total sample included in the final analysis is  & Presser, 1986).
To be precise, the dimensions of the original instrument have been maintained but the researcher modified some of the phrases and also changed all the negatively worded items to positive items. The reason for making all items positively worded is to avoid leading the respondents in identifying and correcting the statement before answering which would lead to unclear presupposition (Foddy, 1993). In addition, the researcher added the demographic section which included the respondent's age, nationality, Gender. The scale of SEQ (2011) is between 1 and 7, i.e., from disagreeing very much to agreeing very much. The middle category has been avoided according to the suggestion of Converse and Presser (1986) who argues that the by adding the middle point, the real direction which the respondents lean on, will be lost. In the main study, the SEQ (2011) has been applied as dependent variables and predictors of self-handicapping behaviors whereby a negative influence is assumed.
This study applies the multivariate method of analysis which is Structural Equation forty four in order to ensure higher reliability.

Data Screening of SEQ
Descriptive statistics of all 44 items of SEQ (Student Engagement Questionnaire) was done from the whole sample (790). The score of means were noted from 7-points Likert scale ranging from 3.88 to    According to the results of component matrix (Tables 2-4 Tables 2 to 5 highlights retained and deleted items from the three scales of student engagement. The results indicate emotional (Table 5) and cognitive scales (2.7) maintained their items but, behaviour engagement scale ( Table 6) lost one of its item, i.e., BE 7 = I stay at home after the lecture hours.
However, according to this result as well as the proposed theory of reciprocal interaction between EE, BE and CE, the researcher restricted all three scales into single components. Note. The alpha reliability = 0.87.

Confirmatory Factor Analysis of Single Constructs
After validating the instruments, basic model was proposed and examined with SEM techniques. The researchers examined the three student engagements separately for the entire population (N=790).

2010).
During the initial individual construct analysis (according to Byrne 2010), we found that each scale among the three scales of SEQ (2012), had some extremely problematic items and therefore removed.
Sixteen out of forty four items have been retained as indicated in the Table 8. The overall fit indices of individual constructs and component fit measures were examined to check whether any construct would be rejected, but none was rejected. All the factor loadings were above 0.5 and all the three constructs were fit and accepted. The accepted constructs in terms of overall fit and component fit were then knitted together to form the measurement model of USE.

Descriptive Statistics of the Final Items of the Measurement Model of USE
The reliability statistics of the 15 items of the model of USE indicate a standard Cronbach's Alpha of 0.87.
From a scale of 1-7 the mean is 5.28; the minimum and maximum scores range from 3.88 to 6.784; and the Standard deviation is from .591 to 1.96. The statistical values (z) of skewness fell below the threshold point of -3 to +3 (Kline 2011), and kurtosis fell below -10 and +10 thus, all are within the acceptable limits (Table 9), except for item CE11 with kurtosis of 14.63 which has been eliminated for further analysis.  (Kline, 2011).

CFA and Results of the Second Order Measurement Model of USE
By using the maximum likelihood procedure of the confirmatory factor analysis the validity of second order factor was tested after the first order factor of the model of USE. The hypothesis for second order measurement model of USE are: Responses to the Student Engagement can be explained by three first order-factors (emotional engagement, behavioural engagement and cognitive engagement); each item has a nonzero loading on the first-order factor it was designed to measure, and a zero loadings on the other two first-order factors; error terms associated with each item are uncorrelated; co-variation among the three firs-order factors is explained fully by their regression on the second order factor.  loadings define their respective factors, and the co-variation among the three first-order factors is explained fully by their regression on the second order factor. Figure 3 depicts two of the first order factors which are measured by three items and the third factor is measured by five items and each item is loading on its own factor only. Results indicate that the hypothesized first and second order measurement models provide a good explanation of the model of USE in the current study. With its three inter-related factors (emotional engagement, behavior engagement and cognitive engagement) and eleven measured variables, this model supports the hypothesis that the measurement model of USE is a multidimensional construct consisting of emotional engagement, behavior engagement and cognitive engagement. The overall fit of the model is adequate as depicted in the model and as explained in the results of the first and second order measurement models.
All factor loadings define their respective factors, and factor correlations are of moderate size while representing their distinct constructs. Therefore, this result affirms the two hypothesis of research question firstly, it affirms that each factor substantially influences its target indicators; each of which accounts for more than 50% of the variance explained and secondly, it affirms that the hypothesized measurement model of USE adequately fits the data. Moreover, it affirms the single hypotheses of research question two which claims for the occurrence of a significant inter-relationship between emotional, cognitive, and behavioural, engagement of undergraduate students.
In summary, the hypothesized measurement model (Figure 3)  representing their distinct constructs. Therefore this result affirms the hypothesis of this study firstly, each factor substantially influences its target indicators, each of which accounts for more than 50% of the variance explained and secondly, the hypothesized measurement model of USE adequately fits the data.

Discussion
This paper reports first part of the findings of the major study written by the Authors of this study, entitled "Predictors of Self Handicapping Behavior among Muslim Students", therefore, the main goal of this study is to share the study which is on edge of methodological development. However, the aims for this part of the study are to assess construct validity of the student engagement questionnaire (SEQ, 2011) and to examine the factorial structure of the Measurement model of the University Student Engagement. In summary, the hypothesized measurement model of USE provides a good explanation of the model of the current study. With its three inter-correlated factors (emotional engagement, behavior engagement and cognitive engagement) and eleven measured variables, this model supports the hypothesis that the measurement model of USE is a multidimensional construct consisting of emotional engagement, behavior engagement and cognitive engagement. Thus, the three constructs of emotional, behavioral and cognitive engagement, managed to fulfill the assumptions of construct validity, i.e., convergent validity (Factors loadings and variance extracted of ≥ 0.5) which also proves discriminant validity (AVE's are more than the sum of square correlation between the items within each factor). All the factor loadings define their respective factors, and factor correlations are of moderate size while representing their distinct constructs. Reliability is also very good with the Cronbach Alpha = 0.87. Therefore, this result affirms the hypothesis of this study firstly, each factor substantially influences its target indicators, each of which accounts for more than 50% of the variance explained and secondly, the hypothesized measurement model of USE adequately fits the data.
Findings of the present study have expanded the existing body of knowledge on the reciprocal interaction theory of emotion, behavior and cognition. Firstly, it substantiated the psychometric adequacy of the measure of university student engagement model, the measures seems to be sufficient to represent the measurement tools of assessing student engagement. Secondly, it validated the good fit of the measurement model of USE. Fourthly, it supported the efficacy of the original model of reciprocal interaction of emotion, behavior and cognition of (Elis, 1955) which posits that cognitions, emotions, and behaviors interact significantly and have a reciprocal cause and effect relationship. In addition the results are congruent with the results of (Ellis, 2001a(Ellis, , 2001b(Ellis, , 2002(Ellis, , 2011Wolfe, 2007) which also found the significant relationship of emotion, cognition and behavior.

Conclusion
The strength of this study is the ability to examine the hypothesized USE model and to validate the results through structure equation modeling for the three instruments that are measuring emotional engagement, behavioral engagement and cognitive engagement of undergraduate students. Adequate fit indices for the USE model is indicated within the model. All items are reliable with standardized loadings ≥ 0.5. Thus all three tools are considered valid and can be used by School counselors in studying the students' behavior.
In conclusion, finding of this study proves Albert Elis's theory of reciprocal interaction between emotion, behavior and cognition. The SEQ (2011) provides means by which researchers can investigate students' engagement towards emotion, behavior, and cognition. Hence, it has proved its usefulness in predicting students' engagement or disengagement as well as self-handicapping behavior which is detrimental to successful achievement. Therefore, the next plan of the authors of this study is to proceed with the study of predictors of self-handicapping behavior by utilizing the present SEQ (2011) and correlate with the self-handicapping behavior scale. We take the advantage of latest analytical approaches and new computer software development which allows us to apply new methods of analysis thus, contribute to the solutions of educational, psychological and counseling issues as well as improved analysis. Hence, the results of this study will not only contribute to the literature and researches done on student engagement, but might also allow the introduction of valid instrument that can be used by School Counselors and counseling undergraduate students in identifying and rectifying issues on student disengagement especially from Islamic universities.