4.1.3. Motivation

This was also a new scale proposed for this research and consisted of seven reflexive items. Assessing the reliability, the Cronbach's alpha was high (0.886). Analyzing the dimensionality, we found that the scale was unidimensional, with an explained variance of 60.417 percent.

Results regarding the other constructs (external brand identity and brand reputation), the initial measures, the analysis of the dimensionality of reputation, and the final research measures are summarized in Tables 2 and 3. More information regarding the technical procedures can be provided on request.

*4.2. Guidelines and Criteria to Assess Model for Brand Relationships*

We used the following guidelines:


Following these guidelines, we applied the first-order measurement model to the brand relationships concept. A summary of the psychometric properties for the first-order constructs is provided in Table 4. Discriminant validity was tested, and after dropping item T4, no problems were reported, as can be seen in Table 5. Taking these results into account, we tested the second-order model for the brand relationships construct. The results showed robustness regarding the selected indicators (see Table 6).

We assessed the reliability and validity of the second-order factor for the brand relationships construct. Construct validity is demonstrated by plausible correlations of the second-order construct with first-order indicators, whereas convergent validity can be suggested by an AVE for the second-order construct that is greater than 0.5 (Bagozzi et al. 1991; Ping 2004).

The values of CR = 0.87 and AVE = 0.68 are greater than the recommended values, suggesting higher reliabilities and convergent validity for the second-order construct. In line with this, we can conclude that the results support the first hypothesis (H1) and state that the constructs of trust, commitment, and motivation are a part of a higher dimension construct of brand relationships.


<sup>a</sup> Sum of the factor loadings; <sup>b</sup> Delta is a measure that is used to calculate CR (construct reliability), and the formula to obtain it is 1 − λ2.


**Table 5.** Construct and discriminant validity for brand relationships.

Notes: Squared root of AVE on the diagonal; correlation estimates below the diagonal.

**Table 6.** Summary of second-order factors for brand relationships.


The theoretical propositions justifying the second-order model were assumed to directly estimate the empirical. Model; no further tests were used.

#### *4.3. Model Evaluation*

The first analysis of the proposed measurement model suggested that the item Rep2.4 (innovation) be dropped. We re-calculated the reliability and unidimensionality of the scale and found the following for the new three items. The brand reputation scale had a Cronbach's α of 0.777 (higher than the threshold of 0.7 defined by Bland and Altman 1997; DeVellis 2003; Nunnally 1978; Nunnally and Bernstein 1994) and a percentage of explained variance of 68.481 percent, which is highly acceptable. In line with these findings, we re-specified the model and conducted CFA again. The results are summarized in Table 7.

**Table 7.** Summary of the indices of fit of the measurement model.


These fit indices were satisfactory according to the selected guidelines. This means that the second-order construct named brand relationships was related to the second-order corporate brand identity construct (external part) and to the brand construct reputation formed by three measures.

An analysis of all loadings showed that all except one were higher than the threshold of 0.5. The "physical" dimension was the exception; it contributed poorly to the external part of the corporate brand identity construct (0.420 < 0.5). Even so, the model fit was satisfactory. We can conclude that, in contrast to what Kapferer (1986, 2008) suggests, the used sample did not greatly value the physical

dimension of corporate brand identity (external part). This is consistent with the sample, which was composed of goal-oriented engineering students. They demonstrated that they assign more value to the dimensions reflecting consumer (loading: 0.784) and relation (loading: 0.750), because they believe that these dimensions are more connected with their lives as students and future professionals. The reflected consumer dimension (the one with the highest loading) was strictly connected with the aspirations of students. However, this finding should be further investigated in other contexts, using other samples. The following standardized residual values also deserve further attention: 2.629 between F4 and Rep2.2; 2.731 between R5 and C3; and 2.716 between R5 and C2.

Rep2.4 (innovation), that was immediately deleted because it had a high standardized residual. Rep2.2 (network performance) also had a relatively high standardized residual, yet we had to maintain one of them because CFA demands at least three items to run an analysis. We considered Rep2.2 more in line with the theoretical background and the factor loadings gave us the same cue (Rep2.2 0.813 vs. Rep2.4 0.685). All the other standardized residuals were below the cut-off point of 2.58, as suggested by Jöreskog and Sörbom (2001). The other items were a part of other second-order constructs, which were previously analyzed and evaluated and revealed as valid (convergent, discriminant, and nomological). Therefore, considering that the mentioned values were far from the cut-off point of 4.0 (Hair et al. 2006) and required no further considerations and that the model fit was satisfactory, we decided to keep these items and test the structural model.

Regarding the modification indices, the one between R5 and C3 had a value of 11.588 (>11). This was expected, given the standardized residual value between both items. However, as mentioned above, the difference was very small, and it was decided to keep both items. All other modification indexes (Mis) had values below 11. No problems regarding multicollinearity were found, and no other indices required our attention; with these findings, we tested the structural model.
