Multivariate Data Analysis

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These variables need to be specified prior to setting up a structural model. The process through which these latent variables are decided is known as Confirmatory Factor Analysis (CFA). Thus, the measurement model for a CFA also comes in the form of a multivariate regression equation. However, CFA precedes SME since the exogenous variables included in an SME are determined through CFA. CFA and SME together form a measurement model and help in evaluating the underlying relationship between variables, with least measurement errors.
An SEM generally consists of a number of multivariate equations which often leads to errors in recording the inputs. Hence the preferred form of input representation in an SEM should be through a covariance matrix with defined row and column names, so as to avoid confusion and errors in providing inputs. Post-estimation, there remains the task of assessing the fitness of the predicted model. Model fit implies the degree to which the estimated model can resemble the observed population model. Hence, the more that the observed covariance matrix corresponds to the estimated one, the better is the model fitness. Generally, model fit could be of two types – goodness of fit and badness of fit. in the former case, the estimated model is considered to be a good representation as the value of the statistic rises in contrast to what the defining factor should be in case of the badness of fit. Examples of the goodness of fit are GFI, CFI, and TLI and those of badness of fit are RMSEA and SRMR. However, there is no benchmark to evaluate the validity of the model based on the value of goodness of fit of the same. The only way-out would be to assess the goodness of fit by figuring out the same via multiple indices.