The Relationship between Self-Concept and Brand Personality

Investigating The Fit of Research Structural Model (Inner Model Evaluation)

Once the reliability and validity of the outer models is established, several steps need to be taken to evaluate the hypothesized relationships within the inner model.

A. Structural Model Path Coefficients (significant coefficients)

In this section, all the paths shown in the model (hypotheses) and the relationships between the structures together or the relationships between each structure with its own measurements should be statistically significant. The PLS software tests the relationships by default at 95% confidence level and since the t-value of this confidence level is equal to 1.96, then each of the relationships whose t-value of it is outside the range of +1.96 to -1.96, is statistically approved at 95% confidence level. As shown in Fig.3, all the causal relations of the model are acceptable. The significance of relationships between variables indicates the appropriateness of the measurements and model structures.

B: Coefficient of Determination (R² value)

The R² is a measure of the model's predictive accuracy. Another way to view R² is that it represents the exogenous variable's combined effect on the endogenous variable(s). This effect ranges from 0 to 1 with 1 representing complete predictive accuracy. Because R² is embraced by a variety of disciplines, scholars must rely on a "rough" rule of thumb regarding an acceptable R², with 0.75, 0.50, 0.25, respectively, describing substantial, moderate, or weak levels of predictive accuracy. As shown in Table 3, the coefficient of determination for the endogenous structure of emotional attachment to brand is evaluated good and this result indicates the predictive power of the model. The values of the determination coefficient for the endogenous structure of the research model appears in Table 3.

C: Effect Size Coefficient (f²)

The effect size for each path model can be determined by calculating Cohen's f². Based on the f² value, the effect size of the omitted construct for a particular endogenous construct can be determined such that 0.02, 0.15 and 0.35 represent small, medium and large effects, respectively. That is, if an exogenous construct strongly contributes to explaining an endogenous construct, the difference between R² included and R² excluded will be high, leading to a high f² value. According to Table 3, the magnitude of the effect on the endogenous variable of emotional attachment to the brand has a large amount, indicating a high fit of this structure. The effect size of the endogenous variables appears in Table 3.

D: Root Mean Square Of Approximation (RMSEA)

The RMSEA is an index of the difference between the observed covariance matrix per degree of freedom and the hypothesized covariance matrix which denotes the model. Hu & Bentler remarked that RMSEA index smaller than 0.06 would be a criterion that will suffice. This measure appears in Table3.

E: Comparative Fit Index (CFI)

This index is incremental fit indices. CFI is a correlated version of the relative noncentrality index. The CFI produces values between 0-1 and high values are the indicators of a good fit. This measure is shown in Table 3.

F: The Goodness of Fit (GOF)

Tenenhaus et al. (2004) proposed a fitting goodness index as an operational solution to this problem, which could mean an indicator of the overall validity of the PLS model. Finally, after the computation of all the fitting criteria of the measurement models and the structural model of the research, the overall fitness of the model must be calculated. This measure, which is shown with GOF, is a number between zero and one and the closer it is to one, the higher the overall fit. The GOF criterion is derived from the root of the product by the mean values of the average determination coefficient and the mean values of the redundancy for the intrinsic models of the model. The formula for this benchmark and its calculations are shown below.