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The study sought to develop measures for the study constructs. Therefore, the study used Structural Equation Modeling (SEM) to test the internal consistency (reliability) of the items in the measure to determine the retention of each item as a measure of the observed factor (variable) or any exclusion of the item from the measure should be done. Consequently, the study developed individual measurement model for each construct measure to confirmatory factor analysis (CAF) and the overall measurement model to check the dimensionality of the construct and the validity of the measures.
SEM is a quantitative data analytical method which specifies, estimates, and tests hypothetical relationships between observed endogenous factors (variables) and latent, unobserved exogenous factors (Byrne,2001). SEM is not a title for a single statistical procedure but a family of relevant procedures including analysis of covariance structure which combines factor analysis and regression analysis as well (Diamantopoulos and Siguaw,2000). The approach started with model specification which linked the items hypothesized to affect the individual study constructs and the directionalities of their effects (Kline, 2005). Model specification is a visual representation of hypothesized relationships between various factors (Diamantopoulos and Siguaw, 2000). In the estimation process, SEM produced regression weights, variances, covariances and correlations which converged on a set of parameters estimates on iteration (Holmes- Smith et al., 2004).
Through the process of estimation, fit statistics was evaluated to check whether the proposed model was a fit to the data or not, or whether any modification was required to increase the fit. The model fit statistics is divided into absolute fit indices, incremental fit or comparative fit indices and indices of model parsimony (Holmes-Smith et al., 2004). In each of these types, there are different fit indices and rule of thumb about the required minimum level of score/value for good fit propagated by different authors (Arbuckle, 199; Byrne, 2001). However, this study, in consideration of sample sensitivity and model complexity effect, used χ2/df (chi-square mean -CMIN/ degree of freedom-Df), incremental fit index (IFI), tucker lewis index (TLI), component fit index (CFI) and root mean square error of approximation (RMSEA) fit statistics to assess the degree of overall fitness of the measurement model and the structural model (Truxillo, 2003). Additional reason for the choice of these model fit measures was because they have been commonly used and reported in the literature (Truxillo, 2003). The scale for measuring model fitness in this study according to Byrne (2001); Holmes-Smith et al., (2004); Truxillo, (2003); and Kline (2005) is presented in Table 3.6.
Table 3. 6 Scale for SEM Fit Indices Level of Model
Fit
Overall Model Fit
Model Fit Model Comparison
Fit Measures CMIN/DF RMSEA IFI TLI CFI
Recommended for Further Analysis if
>2 >0.08 0.90 <0.90 <0.90
Acceptable Scale for Good as well as Adequate Fit
≤2 <0.06
(Reasonable fit up to 0.08)
≥0.90 ≥0.90 ≥0.90
Source: Adopted from Byrne (2001), Holmes-Smith et al. (2004), and Kline (2005) Holmes-Smith et al. (2004) observed that in a large sample size, χ2 testmayshow that the data are significantly different from those expected on a given theory even though the difference may be negligible or unimportant on other criteria. Based on this, Holmes-
Smith et al., (2004) preferred the use of ―normed‖ χ2 where χ2 is divided by the degree of freedom. The normed χ2
is given by χ2∕ df. Accordingly, a value of normed χ2 greater
than 1 and smaller than 2 indicates a very good model fit (Byrne, 2001; Hair et al. 2006). However, given the limitation of χ2
statistics for assessing structural model fit (Bentler, 1990), CIF, TLI and IFI were preferred for baseline comparison and were used to evaluate and report the model fit in this study. IFI, TLI and CFI were used to evaluate the relative improvement in fit to the model based on the baseline model. IFI, TLI and CFI values range from zero to one. Values close to one (e.g. 0.90 to 0.95) suggests adequate fit and more than 0.95 suggests a very well fit model (Truxillo, 2003). Thus this study considered values between 0.90 and 1.00 as adequate to evaluate the incremental fitness of the model (Holmes-Smith et al., 2004; Kline, 2005). RMSEA values less than 0.05 indicates good fit and values between 0.06 and 0.08 are considered reasonable fit (Byrne, 2001). These model fit indices were used in assessing the initial measurement models for the construct measures and the final structural model for the variable measures reported in the section four of this study.
Confirmatory factor analysis (CFA) incorporates the testing of unidimensionality and evaluation of data set by confirming the underlying structure on the basis of theoretical ground (Kline, 2005). It further proposes adjustment, simplification, and/or any required improvement in the measurement model for hypothesis testing and probing the level of fit (Truxillo, 2003). Even though model identification is the requirement of CFA, modification and standardized loadings (standardized regression weights) in the SPSS- Amos output were the options to verify the dimensionality of the measurement or verify the model fit. Modification indices (MIs) comprised of variances, covariance, and regression weights. These indices were examined during evaluation of model fit to get the direction of adjustment, for example, whether freeing or incorporating parameters either between or among unobserved factors is required in attaining better model fit (Holmes- Smith et al., 2004; Kline, 2005). Holmes-Smith et al., (2004) suggested deletion and adding a new path indicator as best ways to get better fitting model. A change or deletion
of item in iterative processes results in changes in parameters and model fit statistics (Holmes-Smith et al., 2004).