VALIDATION OF CONCEPTUAL MODEL
6.3 MODEL ANALYSIS AND FITTING USING PLS-SEM
6.3.1 Model validation: assessment of measurement (outer) model
PLS-SEM analysis was conducted using SmartPLS (version 2.0 M3) software because of a special feature that deals with unobserved heterogeneity through the finite mixture routine (FIMIX) technique (Ringle et al., 2010; Sarstedt et al., 2011; Sarstedt and Ringle 2010). In order to obtain the measurement model results, all possible structural relationships among the constructs were drawn with reflective indicators for endogenous latent variables (SMC development and relationship quality) and formative indicators for the exogenous latent variable (Targeted Procurement strategies). Reflective models indicate that the indicators shown are effects of the latent construct or variable (Garson, 2016).
The measurement model was then assessed using PLS algorithm in SmartPLS which sets the inner weighting (Chin, 2010) and number of iterations which was set to SmartPLS default 300 iterations.
The psychometric traits of the indicators of the latent constructs were then examined for item (factor) loadings, discriminant validity and reliability on the latent constructs (Elbanna et al., 2013;
Nandakumar, 2008). Standardised regression coefficient and total variance (R2 value) explained by the explanatory latent variables were also estimated.
Although convergence is not often a problem in PLS-SEM, Garson (2016) posited that if the measurement model result fails to converge, then coefficients in the output are unreliable.
Therefore, the model was examined for convergence prior to reporting the PLS algorithm results.
The convergence check showed that the solution converged in six iterations which is below the maximum (default = 300) and is acceptable.
As mentioned in the previous section, the endogenous latent variables of relationship quality and SMC development are reflective. In a reflective model, arrows go from the latent construct to the indicator variables, signifying that a unidimensional underlying construct determines the values of the measured and representative indicator variables (Garson, 2016). Appropriate measures employed in testing for internal consistency, convergent validity and divergent validity in reflective models include composite reliability, average variance extracted (AVE) and Cronbach’s
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alpha (Garson, 2016). Convergent validity represents the extent of agreement between two or more indicators of the same latent construct, and was assessed by examining the AVE which reflects the average communality for each latent construct in a reflective model. In an adequate model, convergent validity is established if the AVE is: higher than 0.5 (Chin, 1998b; Henseler et al., 2009; Höck and Ringle, 2006), as well as greater than the cross-loadings which means factors should explain at least half the variance of their respective indicators (Garson, 2016). Composite reliability varies from 0 to 1, with 1 being perfect estimated reliability (Garson, 2016). Garson (2016) posited that the acceptable cut-off for composite reliability is the same as for any measure of reliability, including Cronbach's alpha. Composite reliability should be equal to or greater than 0.6 for exploratory purposes (Chin, 1998b; Höck and Ringle, 2006), and equal to or greater than 0.7 for confirmatory purposes (Henseler et al., 2009).
The result obtained indicate that the latent constructs were robust in terms of their convergent validity and internal consistency as shown by the AVE and composite reliability values which were above the 0.5 and 0.7 thresholds respectively (see Table 6.1). Moreover, AVE vales of latent constructs was greater than the cross-loadings (see Appendix D1). AVE and composite reliability values were not computed for Targeted Procurement strategies (TPS) since it is a formative composite latent construct in the model. Furthermore, discriminant validity was established by the Fornell-Larcker criterion that examines the square root of AVE (diagonal cells in the Table 6.1), which should be higher than the correlations that appear below it (Fornell and Lacker, 1981).
Results from Table 6.1 indicates that the square root of AVE in all cases are greater than the off- diagonal elements in their corresponding column, thus satisfying the Fornell-Larcker criterion for discriminant validity.
Table 6.1: Latent variables inter-construct correlation and reliability measures Latent
Constructs
AVE Composite Reliability
R2 Cronbach’s Alpha
RQ SD_ECO SD_
SOC
TPS*
RQ .7094 .9445 .0854 .9321 .8423
SD_ECO .6997 .8745 .1407 .7836 .0679 .8365
SD_SOC .7844 .9332 .3131 .8953 .5253 .1190 .8857
TPS* - - - - .2922 .3729 .3379 -
AVE: average variance extraction; *. formative model
Indicator reliability or outer (measurement) model path loadings was also assessed to provide another set of criteria for evaluating the reliability of indicators in the (reflective) model. Indicator reliability may be interpreted as the square of the measurement loading: thus, if 0.7 is the acceptable measurement loading, 0.72 = 0.5 which is the reliability threshold (Hair et al.,
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2014:103). Chu et al. (2004) and Hulland (1999) posited that latent variable items with small and insignificant item loadings (< 0.5) are to be removed since their contribution to the model is insignificant. However, this does not apply to formative models because indicators represent different dimensions of the latent composite factor (Garson, 2016). Item loadings of all reflective indicators to their latent constructs is presented in Table 6.2 and show that they are above 0.5, ranging from 0.56 to 0.98 which is acceptable, hence all the variables in the model were retained.
A further examination of the item cross-loadings showed that simple structure was achieved with cross-cross-loadings below the recommended 0.4 threshold (Garson, 2016), except for relationship quality variables which had substantial cross-loadings with social indicators of SMC development (see Appendix D2). However, no reflective indicator variable had a higher correlation with another latent variable other than its own latent variable. These results mean that the PLS-SEM measurement (outer) model had acceptable reliability and validity in explaining and predicting the links among the model constructs which is highly significant to the achievement of the study objective of developing a causal model for the Targeted Procurement strategies – SMC development relationship.
Table 6.2: Item loadings for measurement (outer) model TPS* RQ SD_SOC SD_ ECO
TS_ARO .3871 TS_MSU .2135 TS_PRE .6797 TS_TEQ .6416 TS_TPM .5240 TS_UNB .0153
RQ_CDT .8670
RQ_IEX .8647
RQ_JPS .8119
RQ_LIS .8756
RQ_RSA .7415
RQ_TRU .8903
RQ_WRE .8355
SD_ACR .5601
SD_ITE .9812
SD_SDE .9834
SD_STR .9456
ED_AST .7937
ED_EMP .8069
ED_TUR .9045
*. formative latent construct
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