Structural Equation Modeling (SEM)

Structural Equation Modeling (SEM) through AMOS version 18.0 is applied to analyze the mediating roles of the study. SEM is considered an influential compound of multiple regression, paths and factor analysis. It is symbolized by two stages of validating measurement models and fitting structural models (Hoyle, 1995).

The measurement model explained before is to generate methods of calculating concepts in a reliable and valid manner. Measurement model is a vital step in building up a SEM model, and this procedure was achieved as has been explained in the validity section. The subsequent stage in SEM is to identify the structural model by allocating associations from one construct to another based on the projected theoretical model.

Thus, this method allows the analysis of clusters of independent variables and dependent variables concurrently (Hair et al., 2006; Hoyle, 1995).

SEM, like other statistical methods, is seriously persuaded by sample size. In terms of an appropriate sample size, Hair et al. (2006) suggest a delegate of five responses for every observed variable. In this study, there are four constructs (all of them latent with 10, 3, 9, and 1 dimensions) consisting of almost 134 items. Further, the sample size is 1852, such that a hypothesized model containing adequate parameters is to be estimated by a full structural model (Hair et al., 2006).

SEM offers information on the model fit and variance explain (R²) assists in clarifying or forecasting the variance in variables. The standardized regression coefficient () generated also clarifies the association as direct, indirect and total effect.

Figure 4.1 displays a diagrammatic rationalization of the outcomes.

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1 = Direct effect; Indirect Effect = 2*3; Total Effect = 1+ 2 * 3

Figure 6.1

Direct and Indirect Effects

Direct effects signify the direct effect of one variable on another variable. It demonstrates a direct tie between an independent variable to a dependent variable. This direct association is calculated by a structure coefficient or path coefficient. Path coefficient is the calculated association between independent variables and dependent variables. Indirect effects are those associations that engage a succession of associations with at least one intervening construct concerned. Indirect effects are consistent with mediation (Hair et al., 2006; Kenny, 2006; Bagozzi, 1980). The importance of the indirect effects is specified by the product of the standardized coefficients of the path linking the two variables (Bentler, 1995). Total effects are the total of all direct effects and indirect effects of one variable on another.

Indirect effect or a mediating effect helps the researchers to clarify how and why the effects or associations takes place (Hair et al., 2006). Any model that contains a mediated relationship of the form A  B  C (e.g. full mediation, Baron & Kenny, 1986) can, and ought to be checked against the partial mediated model which as well comprises a path from A to C (Kelloway, 1995; Bagozzi & Dholakia, 2006).

Mediational analyses can be executed with either multiple regression or SEM.

Conversely, SEM is regarded as the favored technique (Baron & Kenny, 1986; Kenny,

A B

C







342 2006) as SEM can manage measurement fault, gives information on the level of fit of the whole model, and is much more flexible than regression (Frazier, Tix, & Barron, 2004). Effectively, SEM permits the application of multiple predictor variables, and multiple mediators (MacKinnon, 2000) which are appropriate for the model of this study.

Baron and Kenny (1986) clarify the methods for mediation and set out the four stages to set up mediation:

1) The independent variable influences the dependent variable.

2) The independent variable influences the mediator 3) The mediator influences the dependent variable

4) To ascertain that the mediator fully mediates the independent-dependent relationship.

Full mediation happens if the independent variable has no noteworthy influence when the mediator is in the equation and partial mediation happens if the influence of the independent variable is smaller but significant when the mediator is in the equation. In other words, in investigating the mediation, the spotlight ought to be on the chi-square differences assessment, then the indices of the fit statistics and the assessment of the statistical significance of the paths (Baron & Kenny, 1986).

In this study, the mediation effect involved is with country image through perceived quality to intention to study and university reputation through perceived quality to intention to study. The explanation on mediation analysis is offered in the results and discussion section.

343 6.10.4 Stages of Structural Equation Modeling

Path and full structural SEM are judged to discover a model that parsimoniously matched the data and is proficient to offer the best rationalization on the relationship of the model.

a. Model specification

The relationship in the hypothesized model was originated from an extensive literature investigation at the start of the research. These methods are very essential as they help the development of hypotheses that are used to identify the theoretical relationships in the structural equation modelling.

b. Assessment of Model Fit

Absolute fit, model parsimonious and incremental fit are the goodness of fit measures applied to analyze the model fit. The goodness of fit has been clarified noticeably in chapter five (Research methodology) in which Table 5.42 clarifies in detail the features of the goodness of fit measure.

c. Model Re-specification and Modification

Scholars might desire to scrutinize likely modifications to advance the theoretical rationalization or to progress the goodness-of-fit. If the measurement model holds an improper fit, standardized residual and modification indices can assist the researcher resolve why the model is improper. On the other hand, when investigating standardized residuals and modification indices, theoretical thoughtfulness must always be applied as the primary concern in constructing model modifications (Garver & Mentzer, 1999).

In investigating standardized residuals, prototypes of big residuals ought to be taken into judgement. A big residual will be over 2.00 and 2.58, and are judged as a statistical significant at the 0.05 level (Garver & Mentzer, 1999). Significant residual specifies a substantial prediction fault for a pair of indicators. Those items with cross-loading or

344 matching to more than one factor will demonstrate large residuals with diverse items from different factors and ought to be removed from the model. If the modification is executed, the model has to be re-stated and re-assessed after each modification (Schumacker & Lomax, 1996). Modification indices (hereinafter MI) are incredibly useful in deciding how to adjust the measurement model. A considerable modification index value of 7.88 is believed to be a noteworthy model development (Garver &

Mentzer, 1999), but Hair et al. (2006) suggested that modification indices of around four or larger will develop the model considerably by freeing that specific corresponding path. The biggest MI signifies the most development in fit and these items have to be considered for modification first, if and only if, the modification is consistent with a priori theory or can be deduced substantively (Bryne, 2001).

Comparable to standardized residual modification, the model ought to be re-assessed after each re-specification through MI (Garver & Mentzer, 1999).