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Principal component analysis

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DATA PRESENTATION, ANALYSIS AND RESULTS

5.5 IDENTIFYING THE UNDERLYING DIMENSIONS OF THE RESEARCH VARIABLES

5.5.2 Principal component analysis

After establishing the appropriateness of the data collected through KMO MSA and Bartlett’s test of sphericity, the next step in identifying the underlying attributes of research constructs is component (factor) extraction which is the process of determining the variables that strongly load on the components indicating that such variables measure the construct (Field, 2013;

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Pallant, 2012). For this study, the intention is to conduct PCA on the Targeted Procurement strategy variables to confirm if each variable is a sub-construct on its own. On the other hand, PCA is conducted on relationship quality and SMC development variables to identify potential factors or components within the constructs and ascertain that the variables in the component retained for model validation measures the same construct (Pallant, 2012; Field, 2013).

Factor extraction was done via the principal component extraction method based on the criteria described in Section 4.10.2. Given that this study has a sample of 307, Kaiser’s eigenvalue-one criterion was used. A visual inspection of the scree plot was also conducted, as well as assessment of communality values. The interpretability criterion of achieving ‘simple structure’ (Thurstone, 1947) was also taken into consideration; this is a structure where you have a readily explainable division of variables onto components, with a component loading onto at least three variables (Laerd Statistics, 2015).

5.5.2.1 PCA: Targeted Procurement strategies

A PCA was run on the six Targeted Procurement strategy variables and the result presented in Table 5.9. PCA revealed that only one component had eigenvalues greater than one, explaining 39% of the total variance. A further visual inspection of the scree plot (Figure 5.3) confirmed that all six Targeted Procurement strategies loaded on one component (factor); hence, factor rotation was not done on the Targeted Procurement strategy variables. Furthermore, the one component solution meets the interpretability criterion of achieving simple structure (Laerd Statistics, 2015; Thurstone, 1947). The PCA results also show that all Targeted Procurement strategies loaded above 0.5 on component matrix; thus, they can be retained for hypothesis testing and model validation. However, communality values indicate that the Targeted Procurement strategies do not fit well into one component or construct with three strategies having communality values below the recommended minimum of 0.4 (Costello and Osborne, 2005). Moreover, the one component solution explaining only 39% of the total variance further confirm that each of the six Targeted Procurement strategies is more likely to be a sub-construct on its own rather than variables measuring a latent construct. Therefore, each Targeted Procurement strategy will be used as a formative indicator rather than reflective indicator for model validation.

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Table 5.9: PCA results for Targeted Procurement strategies Targeted Procurement strategies Component 1 Communalities

Preferencing .724 .377

Tendering Equity .644 .379

Accelerated Rotations .632 .524

Mandatory Subcontracting .616 .256

Unbundling of Contracts .614 .415

Third-party Management .506 .400

Total eigenvalues of variance 2.351

% of variance 39.183

Figure 5.3: Cattel’s scree plot test for Targeted Procurement strategies

5.5.2.2 PCA: Supply chain relationship quality criteria

PCA was run on the thirteen supply chain relationship quality assessment criteria (variables) and the result presented in Table 5.10. The initial PCA result with varimax rotation show that three components had eigenvalues greater than one, cumulatively explaining 60% of the total variance. However, a further visual inspection of the scree plot (Figure 5.4) revealed that only one component should be retained for further investigation as indicated by the inflection point after the first component. Given that the thirteen relationship quality variables were developed to measure a latent relationship quality construct, a one-component solution also meets the interpretability criterion of achieving simple structure (Laerd Statistics, 2015; Thurstone, 1947). Hence, the PCA was re-run with forced factor extraction to retain only one component.

The PCA results with forced factor extraction also showed three components having eigenvalues greater than one as the initial PCA. However, communality values indicated that not all relationship quality criteria fit well into one component or construct with six variables having communality values below the recommended minimum of 0.4 (Costello and Osborne,

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2005). Therefore, PCA with eigenvalue-one criterion was re-run for the third time excluding the three variables with the lowest communality values – form of contract (0.001), procurement method (0.001), procurement selection criteria (0.178); and the fourth time excluding the next two variables with the lowest communality values – prospect for future work (0.252), and objectives alignment & benefits (0.327); and finally excluding the variable with the highest communality value below 0.4 – balance of risk and reward (0.362).

The third, fourth and final PCA results produced a one-component solution to satisfy the interpretability criterion of achieving simple structure. However, only the final PCA result explained at least 60% (63%) of the total variance as recommended by several researchers (Laerd Statistics, 2015; Pallant, 2012). The final PCA results also show that all the retained relationship quality variables loaded above 0.6 on component matrix; thus, they can be retained for hypothesis testing and model validation.

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Table 5.10: Principal components analysis results for supply chain relationship quality variables Supply Chain

Relationship quality variables

Initial PCA PCA 2 PCA 3 PCA 4 Final PCA

Rotated Components Comp. Comp. Comp. Comp.

1 2 3 Commu. 1 Commu. 1 Commu. 1 Commu. 1 Communalities

Trust .813 .683 .810 .656 .818 .670 .827 .684 .835 .697

Joint problem-solving .800 .647 .775 .601 .787 .620 .798 .636 .796 .634

Information exchange .765 .611 .772 .595 .781 .610 .786 .618 .809 .654

Working relationship .756 .616 .766 .597 .772 .596 .773 .597 .776 .602

Learning and Innovation Sharing .752 .685 .819 .670 .817 .668 .816 .666 .829 .686

Risk sharing and allocation .734 .541 .701 .492 .706 .498 .720 .518 .699 .489

Cost data transparency .715 .640 .793 .629 .786 .617 .797 .636 .805 .648

Balance of risk and reward .617 .461 .602 .362 .605 .366 .612 .374

Procurement selection criteria .780 .709 .422 .178

Objectives alignment and benefits .580 .512 .572 .327 .556 .309

Procurement method .735 .646 - .001

Prospect for future work .606 .548 .502 .252 .497 .247

Form of contract .569 .545 - .001

Total eigenvalues of variance 5.351 1.354 1.139 5.351 5.201 4.730 4.410

% of variance 41.164 10.419 8.763 41.164 52.014 59.120 63.003

Cumulative % 41.164 51.183 60.346 41.164 52.014 59.120 63.003

Extraction method: principal component; Rotation method: varimax with Kaiser normalization Commu.: communalities; Comp.: components

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Figure 5.4: Scree plot from initial PCA (13 variables) and final PCA (7 variables) for relationship quality

5.5.2.3 PCA: SMC Development

PCA was used to determine the dimensionality of the indicators of SMC development, in order to establish specific measures or indicators of growth performance and development that can be used to objectively evaluate the effect of Targeted Procurement strategies on SMC development. PCA was run on nine SMC development variables comprising of five variables for economic indicators and four social indicators. Initial PCA results show that three components had eigenvalues greater than one, cumulatively explaining 70% of the total variance (see Table 5.11). However, a further visual inspection of the scree plot (Figure 5.4) revealed that only two components should be retained for further investigation as indicated by the inflection point after the second component. Hence, the PCA was re-run with forced factor extraction to retain only two components. The second PCA result also produced three components having eigenvalues greater than one. However, company profits (.008), JV partnerships (0.187) and advancement on cidb RoC (0.389) did not meet the communality criteria (> 0.4). Therefore, the PCA with eigenvalue-one criterion and varimax rotation was re- run for a third time excluding company profits and JV partnerships. The third PCA result produced a two-component rotated solution (eigenvalues greater than one), explaining 73% of the total variance. The two-component solution satisfies the interpretability criterion of achieving simple structure which is consistent with the SMC development indicators the questionnaire was designed to measure with strong loadings (> 0.6) of social indicators on Component 1 and economic indicators on Component 2; hence, they can be retained for model validation.

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Table 5.11: Principal components analysis results for SMC development indicators SMC development indicators

Initial PCA PCA 2 Final PCA

Rotated Components Rotated Components Rotated Components

1 2 3 Commu. 1 2 Commu. 1 2 Communalities

Social

Skills development .915 .914 .945 .899 .956 .919

Application of innovation & technology .932 .871 .928 .862 .934 .874

Skills transfer .931 .873 .926 .859 .936 .877

Advancement on cidb RoC .613 .442 .623 .389 .624 .390

JV partnerships .413 .228 .420 .187

Economic

Turnover .858 .747 .859 .743 .861 .748

Assets .818 .682 .819 .672 .818 .669

Employees .789 .627 .788 .622 .789 .623

Profits .948 .900 - .008

Total eigenvalues of variance 3.250 1.991 1.043 3.250 1.991 3.110 1.990

% of variance 36.110 22.126 11.584 36.110 22.126 44.425 28.429

Cumulative % 36.110 58.236 69.820 36.110 58.236 44.425 72.854

Extraction method: principal component; Rotation method: varimax with Kaiser normalization Comp.: components

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Figure 5.5: Scree plot from initial PCA (9 variables) and final PCA (7 variables) for SMC development

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