Essay On Structural Equation Modelling

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The use of structural equation modelling (SEM) has steadily increased in behavioural science where two submodels are identified including a measurement model and a structural model. In this study the research paradigm indicates and concurrently strives to combine measurement and structural model for complete parameter tests. SEM is a quantitative data analytical technique which specifies, estimates and tests theoretical relationships between observed endogenous variables and latent, unobserved exogenous variables. (Byrne, 2001) The SEM is a statistical methodology that takes a confirmatory that is, hypothesis testing approach to the analysis of a structural theory. This theory represents causal processes that generate observations on multiple variables. (Yuan & Bentler, 1998) The SEM procedure starts with model specification that links the variables assumed to affect other variables and directionalities of their effects. (Kline, 2011) Specification is a way of structural relations being modelled pictorially to enable clearer conceptualisation of the theory under study. In the estimation process, SEM produces regression weights, variances, covariances and correlations in its iterative procedures converged on a set of parameter estimates. (Holmes-Smith, Coote, & Cunningham, 2004) On specification the model is then tested for plausibility based on the sample data that comprise all observed variables in the model. The main task in model testing is to determine the goodness-of-fit between the hypothesized model and the sample data.

Fit Indices
There is abundance of fit indices and wide variety of disparity in agreement on which indices to report and also the cut-offs for various indices, (Hooper, Coughlan, & Mullen, 2008) because dif...

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...are the options to verify the dimensionality of the measurement or to verify the model fit. The modification of the model is aided by modification indices (MIs) sometimes in conjunction with parameter estimates statistics. (Lei & Wu, 2007) These indices were examined during evaluation of model fit to get the direction of modification, for example whether freeing or incorporating parameters either between or among unobserved variables is required in obtaining better model fit. Anderson and Gerbing (1988) suggested that under unacceptable but converged and proper solutions, relating or deleting the indicator from the model are the preferred basic ways to respecify the model. Hence, item deletion or adding new path indicator are the best ways to get a more parsimonious model. The measurements models for each construct measure are discussed in the following sections.

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