Measurement phase

The objective of the measurement phase is to isolate model misspecification and to verify that the measures adopted appropriately represent the latent constructs in the model. Syntax was written for the confirmatory model allowing covariances among all constructs and stand-alone variables (not intended as indicators). By allowing all factors to co-vary, the structural portion became just identified (thus with a perfect fit), and the measurement part of the model could be assessed.

The robust fit indices obtained for the measurement model were: χ2 =

1883.013 (df = 1279), CFI = .878, RMSEA = .045 and SRMR = .070. The χ2 statistic was statistically significant. It is noted that RMSEA and SRMR indices presented

good fits. The CFI index, however, was marginally significant (threshold is .90). The fit indices indicate that the data covariance matrix has a relatively good fit.

Convergent validity

Convergent validity refers to the extent that the items of the factor capture the content of the construct. Two standard means of assessing convergent validity are: 1) by examining whether the factor loadings of the measurement equations (that explain all variables as a function of the factor) are positive and statistically significant, and;

2) by calculating the “variance extracted” by the construct, which corresponds to the mean squared standardized loading. Ideally it should exceed .50 (Garver and Mentzer 1999).

Convergent validity was checked by both methods. By examining the software output, it was noted that all loadings were positive and statistically significant. It was thus inferred that convergent validity exists. In addition, the

“variance extracted” was calculated for all constructs (see Table 12). Out of 18 constructs, four fell significantly below the desired 0.50 threshold. Another four also fell below the threshold but were very close to 0.5. Given that the PCA results

showed that these items did load on a single factor, it was decided not to eliminate or rearrange the items used for these four constructs with low convergent validity.

Table 12 Variance extracted of the constructs

Construct Variance

extracted Logistics capabilities 0.685 Volatility product market 0.401 Diversity product market 0.582 Volatility 3PL market 0.342 Diversity 3PL market 0.651 Logistics complexity 0.498

Customer TSI 0.643

3PL TSI 0.451

3PL reputation 0.371

Experience with 3PL 1.000

Satisfaction 0.804

* The variance extracted for “Experience with 3PL”

and “Experience partnering” are 1 given that they were measured by a single indicator.

Discriminant validity

Another test conducted in the measurement phase consisted of examining the discriminant validity of the constructs; i.e., verifying that the items loaded on the construct of interest and not on other constructs. According to several authors (Shook et al 2005, Kline 2005, p. 182), achieving a good fit for the model in which each indicator loads on only one factor provides a precise test of discriminant validity.

The measurement model presented reasonable fit indices; thus it was inferred that discriminant validity existed. In addition, the factor covariances were fairly small in the vast majority of cases and non-significant in many cases as well. This fact also

diminished concerns that factors assumed as independent were in reality a single factor (i.e., not discriminant).

Shook et al (2005) indicate that an alternative method for testing for

discriminant validity is to calculate the shared variance between constructs and verify that it is lower than the average variance extracted for each individual construct. This procedure was conducted for all pairs of constructs. All but three pairs (TSI –

3PLTSI, TSI – DEP, 3PLTSI – DEP) did pass this test. Therefore, for these three pairs, a fit comparison of nested models was conducted. Models with correlations between the two factors set equal to 1 (i.e., where the two factors are considered a single, unique factor) were compared to models where the two factors were free to correlate. Given that the difference in χ²was statistically significant for all three pairs (see Table 13), the existence of discriminant validity was inferred.

Table 13. Test for discriminant validity for construct pairs with high covariance Single factor

Scale reliability refers to the internal consistency of a particular scale to measure a latent variable (Garver and Mentzer 1999); i.e., indicates whether a factor is expected to be stable and replicable. Garver and Mentzer (1999) point out that the coefficient alpha, the traditionally adopted measure of reliability, has some

limitations. In some cases, it tends to underestimate the scale reliability or become inflated when the construct has a larger number of items. They suggest the use of SEM reliability measures, such as the variance extraction measure and the SEM

“Reliability of the Construct” measure. Following their recommendations, SEM measures of reliability were taken into consideration.

The “variance extracted” was calculated for all constructs (Table 12 above) and most constructs had values above the recommended figure of 0.5. In addition, the coefficient “Maximal Reliability”, Coefficient H developed by Hancock and Mueller (2001), a measure of construct reliability, was calculated. Hancock and Mueller (2001) argue that the traditional “Reliability of the Construct,” RC, developed by Fornell and Larcker (1981) has some limitations: 1) its value is affected by loading signs; 2) it is decreased by additional indicators if those have small loadings; 3) it can be smaller than the reliability (squared loading) of the best indicator. Table 14, below, presents the coefficient H for each construct. All values were found to be above the 0.7 threshold.

Given that the measurement model has been assessed in terms of fit and convergent and discriminant validity, the next step was to test the structural model where the theoretical links are investigated.

Table 14. Construct reliability results

In the second phase, a new EQS program was written for the confirmatory model. All independent constructs were allowed to correlate. The disturbances of the construct pairs credibility/benevolence and dependence/3PL dependence were allowed to correlate as well.

The following steps were followed:

Check of goodness-of-fit information. There are a dozen fit indices that are used to assess the fit of structural equation models. Because there are so many options, different articles report different indices and reviewers may request different fit indices that they know or prefer (Kline 2005). Kline (2005) recommends the