PLS-SEM MODEL REFINEMENT 1 Introduction

The theoretical research model (Figure 6.2) was tested and refined to improve the model fit. By conducting statistical analysis of the data received from the questionnaire, as well as incorporating the theory from literature, the final exploratory research model was proposed. Hinkin’s (1995) stage one describes the deductive development when researchers utilise a previously-defined theory to create enough items to allow for deletion. The theoretical proposed research model (Figure 6.2) was refined utilising this principle where the variables are extracted and grouped it into factors. This method is used to simplify the expression of a particular model in terms of just a few major items. The next sections demonstrate the process followed to establish the final proposed exploratory model and demonstrate construct validity. In this refined exploratory model, the main constructs remain as per the theoretical proposed model as indicated in Figure 6.8. The paths in the refined exploratory model are linked to the propositions at the end of Chapter 4 and discussed in detail in Chapter 8.

6.5.2 Improving model fit

It is expected for the fit of a proposed model to be initially poor given the complexity of structural equation modelling. Allowing modification indices to drive the process is risky; however, some modifications can be made locally that can substantially improve results. It is good practice to assess the fit of each construct and its items individually to determine whether there are any items that are particularly weak. Items with a low R² (less than 0.20) should be removed from the analysis as this is an indication of high levels of error. Subsequently, each construct should be modelled in conjunction with every other construct in the model to determine whether discriminant validity has been achieved. The value between two constructs is comparable by their covariance. A covariance of 1.0 indicates that the two constructs are measuring the same entity and further inspections of item cross-loadings need to be made. The discriminant validity test determines whether constructs are significantly different (Hooper, Coughlan & Mullen, 2008:56).

6.5.3 The model evaluation and improvement process

This process is summarised in the following steps below (Lowry & Gaskin, 2014:132-140).

(i) Step 1: Model specification

Before conducting a PLS analysis, configure the model in a way that will produce the results required by stating the theoretical model either as a set of structural equations or as a path diagram.

(ii) Step 2: Establish construct validity of reflective constructs

Utilising the observed data, establishing validity and testing the entire path model occurs in one pass. This is done by establishing convergent and discriminant validity for the reflective constructs by (1) examining the t-values of the outer model loadings. These results indicate strong convergent validity if it is greater than 0.05 for the constructs; and (2) determining the discriminant validity of the indicators. To confirm the discriminant validity of the indicators further, calculate the average variance extracted (AVE).

(iii) Step 3: Establish the reliability of the reflective constructs

Reliability refers to the degree to which a scale yields consistent and stable measures over time and applies only to reflective indicators. PLS-SEM computes a composite reliability score as part of its integrated model analysis, similar to Cronbach’s alpha in that they are both measures of internal consistency. Each reflective construct in the model must demonstrate a level of reliability above the recommended threshold of 0.70.

(iv) Step 4: Establish construct validity of formative indicators

The procedures for determining the validity of reflective measures do not apply to formative indicators since formative indicators may move in different directions and can theoretically co-vary with other constructs. Ensure the indicator weights for formative constructs are roughly equal and all have significant t-values. Assess formative validity, which involves testing the multi-collinearity

among the indicators. The final reported validity statistics should be those gathered once all changes to the structure of the measurement model are complete.

(v) Step 5: Test for common methods bias

Since the endogenous variables were collected at the same time and using the same instrument as the exogenous variables, this study tested for common methods bias to establish that such bias did not distort the data collected. The full collinearity test is effective for the identification of common method bias by simultaneously assessing both vertical and lateral collinearity. Through this procedure, variance inflation factors (VIFs) are generated for all latent variables in a model. The occurrence of a VIF greater than 3.3 is an indication of pathological collinearity, and also as an indication that a model may be contaminated by common method bias.

(vi) Step 6: Test for moderation effects (if applicable)

Moderating effects are evoked by variables whose variation influences the strength or the direction of a relationship between an exogenous and an endogenous variable. As this is an exploratory research study to determine influences regarding WTP, moderation effects were not used.

(vii) Step 7: Test for mediation (if applicable)

A mediator is a construct in a causal chain between two other constructs. During this study, no mediator was included in the model.

(viii) Step 8: Assess the predictive power of the model

This indicates how well the model explains variance in the dependent variables, as demonstrated by the path coefficients and R²s in the model. To be ‘substantial’, standardised paths need to be close to 0.20 or ideally higher than 0.30 to indicate that the model has meaningful predictive power.

(ix) Step 9: Provide and interpret final statistics

As the final step of the analysis of the model, provide the measurement model statistics.

In developing models to test propositions using PLS-SEM, researchers use theory, judgment, experience and research objectives to identify and develop propositions about relationships between multiple independent and dependent variables (Hair et al., 2014:108).

As part of Stage 2 of Hinkin’s approach (1995), the development of the questionnaire included the evaluation of the initial variables. Hair et al. (2014:107) quoted Lohmöller and Wold (1980:1):

PLS is primarily intended for research contexts that are simultaneously data-rich and theory-skeletal. The model building is then an evolutionary process, a dialog between the investigator and the computer. In the process, the model extracts fresh knowledge from the data, thereby putting flesh on the theoretical bones. At each step PLS retests content with consistency of the unknowns.

By conducting statistical analysis of the data received from the questionnaire as well as incorporating the theory from literature, the final exploratory research model was proposed. In this refined exploratory model, the main constructs remain as per the theoretical model: culture (in green), technology (in grey), behaviour (in red / brown) and value aspects (in purple) of the exploratory model as indicated in the Figure 6.8. Additionally, theory from literature suggests that the final exploratory model needs to consider the general support for green electricity as well as the relationship between support for green electricity and the perception of the electricity supplier. These components were included in the refined exploratory model.The theoretical exploratory model was uploaded and evaluated by the USB’s statistical support using the STATISTICATM software programme with the assistance of the Stellenbosch University’s Centre for Statistical Consultation.

Figure 6.8: Refined explorative model used for evaluation

When using PLS-SEM, the model refinement does not have a defined completion. Therefore, the researcher decides when the model is sufficiently refined (Hair et al., 2014:107). In order to verify the construct validity of items used in the exploratory model, an evaluation process on each construct was completed as described in the next sections.