The Full Model 128

This next stage of the research was the analysis of the full hypothesized engagement model as presented in section 5.2. This was approached in two ways: hierarchical regression and SEM. Hierarchical regression tests the predictor relationships of variables entered into a regression equation in a sequential order (Tabachnick & Fidell 2007). The reason for using this type of approach is to test relationships while controlling for variation caused from other variables (Pedhazur 1997). In this study, hierarchical regression was used to determine the predictability and extent of contribution for unique variation of the engagement capabilities on the engagement outcomes while controlling for variation from the organisational characteristics and contextual variables. On the other hand SEM does two things, it examines the causal processes with a series of regression equations (Byrne 2001) and factor analyses (Hair et al. 2006). It is the simulations analysis of all paths at once to determine the goodness of fit with the data

(Byrne 2001; Kline 2005). It can be argued that to test the model as described in Chapter 4 and pictorially drawn in Figure 5-2 that either statistical analysis are appropriate to determine the significance relationships. To provide greater robustness this thesis relies on hierarchical regression to test the impact of all the individual engagement capabilities (emotional and cognitive) on the individual engagement outcomes and SEM is used to test the full model and the impacts of the individual paths within the model.

5.6.6.1.

Hierarchical Regression

Hierarchical regression is a technique that allows the researcher to determine the sequence of the independent variables entering the regression equation. The independent variable is assessed according to what it adds to the equation at its entry point (Tabachnick & Fidell 2007). The sequence of entry is determined either logically or theoretically. The benefit of this approach is the degree of researcher control. This technique was used in this study to determine whether the individual engagement capabilities predicated individual engagement outcomes whilst controlling for variation from the contextual variables and the organisational characteristics. Item bundles of the common underlying constructs were used, for example cognitive engagement capabilities were calculated as the mean of the absorption, attention, dedication, job involvement and intrinsic motivation. The intention was to control for variation on both the contextual variables and the organisational characteristics, and to test whether the individual engagement capabilities have a significant positive impact on the individual engagement outcomes.

Due to the hierarchical (sequential) elements of this regression, the first level introduced the contextual variables (personal and structural organisational variables). Then as specified in the conceptual framework, the organisational characteristics were both introduced (Job Characteristics and POS) then the individual engagement capabilities (emotional and cognitive engagement capabilities) all measured against the dependant variable: individual engagement outcomes. Hierarchical regression allowed the researcher to determine the predictability of the variables entering the model at each of the levels on the individual engagement outcomes and determine the unique variance accounted for. The full model was built into a hierarchical regression, as follows in Figure 5-6.

Figure 5-6 Hierarchical Regression Model

Individual Engagement Outcomes Individual Engagement Capabilities Organisational Characteristics Contextual Variables

Hierarchical regression is evident where each of the dimensions (boxes within the diagram) represents the timing of the entrance into the regression equation. Once analysed the hierarchical regression may identify the importance of each of the dimensions on the individual engagement outcomes. As well as provide support for the developed hypothesis. The results were verified with the validation sample.

5.6.6.2.

The Measurement Model

SEM as detailed so far, is the simultaneous analysis of all paths at once to determine the goodness of fit with the data (Byrne 2001; Kline 2005). There are two explicit methods used in the analysis of the data, CFA (measurement model) and SEM (the structural model). CFA is a common way to determine the viability of the measures, and is often the selected method in the testing of the measurement model when the measures are pre-established (see sections; 5.6.3 & 5.6.5.2). CFA is appropriate when there is some idea of the underpinning latent structures (Byrne 2001), based on the knowledge of the theory and applications the explicit variable relations are indicated within a model. The CFA extraction method that has been used is the maximised reliability with composite reliability and congeneric factors (Munck 1979; Politis 2001, 2002).

Each of the proposed common underlying constructs held at the alpha weighted level as demonstrated in section 5.6.5 therefore the item bundles of the higher order constructs were calculated. As presented previously, item parcels are useful when there is a lot of information and many items to consider (Hair et al. 2006). Given that the measures held up at the higher order alpha level they were treated as composites, each of the bundled measures will be treated as an item representing the common underlying constructs, indicating the properties of higher order constructs. These items will be bundled in the full model.

Maximised Reliability Method

The maximised reliability method is a method that like the alpha weighted model presented in section 5.6.5.2 which allows for all the data to be used to determine the λ and the θ on the model. However, the difference between the alpha weighted model and maximised reliability method is the use of composite reliability (rc). Composite reliability is built on factor score regression weights of the subjects and is calculated on the initiating structure composite score. This method is consistent with Munck (1979) and Politis (2001, 2002) and the methods are detailed below.

According to Jöreskog and Sorbom (1989) it is possible to provide an estimate score for each of the subjects using the factor score regression weights, this results in the initiating structure composite score (Equation 3).

Equation 3 ξi = Σωi xi

Where ξi = estimated score

ω = is the row vector of factor score regression weights

x = is a column vector of the subjects observed indicator variable

These scores are built into the full structural model. It is then possible to fix the error variances and regression coefficient using the initiating structure composite score. At this stage because the matrix used is a matrix of covariance, as produced in AMOS (Politis 2001; 2002; Munck 1979) then as used in section 5.6.5.2, the following equations are used. However, the difference exists in the use of reliability of the composite (rc) rather than the Cronbach reliability of the

measure.

Equation 4 λ = σ√α

Equation 5 θ = σ²(1-α)

Where: α = Composite reliability coefficient (rc)

σ = Standard deviation of the composite measure σ²= Variance of the composite measure

The next section will detail the steps for the determination of the composite reliability (rc) using the initiating structure composite score and the subsequent λ and θ as calculated in equation four and five. The result will be congeneric factor scores which can be fixed in the full structural model. The steps are presented in Table 5-5.

Finally, the congeneric factors can be applied to the full structural model, for this thesis the congeneric factor composites were calculated for the common underlying engagement dimensions; emotion and cognitive capabilities and the individual engagement outcomes. The full calculations are presented in Appendix A4. The measures of POS and job characteristics were assessed within the full model with alpha weighted loadings because both of these measures were pre-established as valid and reliable measures.

Table 5-5 Steps Required for the Maximised Reliability Method

Step 1 Fit the model

Step 2 Compute a composite using the factor score regression weights by; a. Sum the factor score regression weights

b. Divide each factor score weight by the total to get new values.

c. In SPSS, calculate the composite by running the syntax of item number multiplied by factor score weight that was generated in step 2 b.

Step 3 In SPSS, find the standard deviation, variance, minimum and maximum of the composite. Step 4 Calculate the reliability by;

a. In AMOS find the implied covariance matrix and construct matrix.

b. In AMOS find the error variances and enter on the diagonal of the theta- delta matrix c. Using the recalibrated (those summed to equal 1) factor score weights to put into the

WFS vector.

d. Run the syntax window and record the reliability.

Step 5 Calculate the factor loading and error variances using Equation 4 and Equation 5 above. Step 6 These values will then be used to fix the λ and θ in the full structural model.

Determining Model Significance

The model was assessed for model fit (as described in Table 5-4) and then validated using the validation sample. Once model fit was established the hypotheses (H4-H11) were considered and evaluated using path analysis. Path analysis provides in the standardised model (which is the results that will be presented) a measure of the regression co-efficient (beta – β). This is provided in the AMOS output and it measures the direct effect between two variables.

The indirect effects are estimated as a product of the direct effect, as measured as a regression coefficient (Kline 2005). It is calculated as the β of A Æ B and BÆ C, for instance βAB (βBC) = indirect effect. Using the explanation by Kline (2005) A has a direct impact on B but only part of it (βBC) is transmitted to C. The indirect effect says that the level of C will change by the indirect effect as a standard deviation for every increase in 1 full standard deviation on A prior to the effect on B. Kline (2005) also says that if the indirect effects are significant and the direct paths are not then this demonstrates the mediator effect. The total effects are the sum of the direct and indirect paths. The standardised paths are interpreted as the 1 standard deviation increase in A changes C by the total effect via all direct and indirect paths assuming that there is a direct path between AÆC.

Model fit and the individual path analysis will provide the analysis to support the engagement model within this thesis, and test the viability of the developed hypotheses. Once a significant model is established, then the model is fitted on to the validation sample to develop support and robustness of the findings.