CHAPTER 6: DATA ANALYSIS AND FINDINGS OF RESEARCH
6.10 Basic concepts of Structural Equation Model
According to Hoyle (1995), the Structural Equation Model is an instrument or a procedure used to approximate a number of interconnected dependence or reliance relationships concurrently. Furthermore, the utilisation of SEM in most cases to demonstrate the investigation of the causal processes between variables to a number or a string of certain structural equations, such as regressions (McDonald and Ho, 2002; Raykov, 2005).
The Model (SEM) that is developed can be concurrently analysed statistically and tested in respect of variances (Hoyle, 1995) to establish the degree of consistency in relation to the data of the study. There is an acceptance of the Model, if there is evidence of a good fit (Hoyle, 1995).
6.10.1 Observed and latent variables
The measuring instrument comprises of both the observed and latent variables. However, there are differences between these variables. The difference is that the observation of observed variables is direct and they are the pointers of the specific construct represented.
On the other hand, the observation of latent variables is not explicit but form part of the Model (Hoyle, 1995).
172 6.10.2 Endogenous and exogenous latent variables
Endogenous latent variables are the same as dependent variables. In structural equation model exogenous variable influences endogenous variable. This influence can be both direct and indirect. A number of studies have independent variables, however, in this study, there are exogenous latent variables and the exogenous variables are the same as independent variables (Bentler and Chou, 1987).
These variables are the drivers of the study to achieve its intended objectives. It must be highlighted that it would be difficult to prove anything in the absence of endogenous (dependent) and exogenous (independent) variables.
6.10.3 Goodness-of-fit
The purpose of the SEM is the degree to which hypothesised data fully described the data sample of the study or that the model fitted the data satisfactorily. In line with the full description of data the goodness-of fit may be accepted or rejected.
Therefore, the model fitting includes examining or determining the goodness-of-fit in respect of the data sample and the hypothesised Model (Bentler and Chou, 1987). Goodness-of-fit is useful to determine whether data is able to assist with the achievement of the research objectives. Where data has a good fit, the results of the study will have integrity.
6.10.4 Chi-square and goodness of fit
The purpose of chi-square (CMIN) is to determining or testing whether the Null hypothesis, in respect of the over-identified model and the just-identified model, fits the data. It is, however, important that in the just-identified model there is a straight path or route between variables, without any variable in between (Hoyle, 1995). The chi-square (CMIN) of the above (p<0.05) is considered a good model fit. In addition, to the purpose the chi-square ensures that data is reliable in order to achieve expected results.
6.10.5 Degrees of freedom
Degrees of freedom (Df) are used to determine the degree of parameters in a model. The Df of more than zero (0) is considered a good fit. In this study the Df was used to indicate whether the model could be accepted or whether adjustments are required, if it was found that the Df was more than zero (0). The Df allows the researcher to understand the data
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points in the SEM model and to be able to plot relationships in line with the objectives of the study (Hoyle, 1995; Bollen, 1990; Boomsma, 2000).
6.10.6 The goodness-of-fit index and adjusted goodness-of-fit index
The purpose of goodness-of-fit index (GFI) is to determine whether the model is relevant or requires further reviewing. Furthermore, the adjusted goodness-of-fit index (AGFI) is used in instances where it is found that the model does not fit the data, therefore, AGFI is a revised GFI (Frost, 2013; Jöreskog and Sörbom, 1993; Hoyle, 1995).
The AGFI will be close to zero (0) to be considered a good fit. Hence, the goodness-of-fit index will be =1.0 and therefore considered to be a proper fit. The results in this study in respect of AGFI indicate that the model is a good fit.
6.10.7 Normed fit index
Normed fit index (NFI) is popular and common because of its constant use. It measures all the parameters of the model, especially those that are added (Bentler and Chou, 1987). A perfect fit of this index is one (1) (Bentler and Chou., 1987).
Normed fit index serves as a measure in that each time there is an addition of parameter or variable in the model, the Normed fit index go up and in some other instances down.
However, in this study, the parameters were constant and there was no effect on the Normed fit index.
6.10.8 Relative fit index
The relative fit index (RFI) is used to compare both the proposed and Null model in respect of their performance, like the function of the CFI. The RFI numbers of above (1.000) are an acceptable value of the CFI (Hu and Bentler, 1999). Bollen (1990) posits that RFI is developed or produced from both the NFI and CFI.
The RFI coeffience value is normally between 0-1, wherein the values closer to one (1)are considered a perfect fit, as confirmed by Hu and Bentler (1999). The RFI in this study was 0.845, therefore below one (1). Consequently, the model is a perfect fit considering that its values are closer to one (1).
174 6.10.9 Comparative fit index
Comparative fit index (CFI) compares both the proposed and Null model in respect of their performance. It is an improved NFI (Bentler and Chou, 1987; Hu and Bentler, 1999). Hu and Bentler (1999) proposed a cut-off close to 0.95 values as acceptable. The greater the values of CFI between 0-1, the better the model and considered a good fit. In this study, CFI was closer to one (1), and therefore considered a perfect fit.
6.10.10 Tucker Lewis index
According to Tucker and Lewis (1973), the Tucker Lewis index (TLI) is viewed as the same as the NFI, and is used to contrast the values of chi-square as confirmed by Mulaik, James, Van Alstine, Bennet, Lind and Stilwell (1989). Mulaik et al. (1989) highlighted that for a fit to a good fit; it must have values that are closer to one (1). The model that has a high value indicates a fit that is better than a model with a value that is lower.
6.10.11 Root mean square error of approximation
The purpose of root mean square error of approximation (RMSEA) is to show whether the model has good fit or not. Furthermore, RMSEA utilisation is in respect of supporting or not supporting hypothesised models, especially those with a larger sample size (Hu and Bentler, 1999). The proposed RMSEA value of<0.06 is deemed to have a good fit. Therefore, RMSEA in this study was for the purpose to aid the researcher in accepting or rejecting the hypotheses.
6.10.12 Root mean square residual
The purpose of the root mean square residual index (RMR) is to determine whether the model has a good fit. The root mean square residual index is the square root of the mean of residuals that are not standardised. Hu and Bentler (1999) proposed that a value of greater than 0.02 for a good fit. This study produced a figure of 0.2, which indicated a good model fit.