A parsimonious discriminant analysis model through a comparison of stepwise LDA and factor analysis-based LDA

Abstract

The aim of this study was to identify the best approach in fitting parsimonious Discriminant Analysis (DA) model(s) with several independent variables, using two comparison models; SDA and CFA-LDA. The objectives of the study were to: compress too many independent variables using Exploratory Factor Analysis (EFA); verify results of Exploratory Factor Analysis (EFA) using Confirmatonary Factor Analysis (CFA); use factor scores from CFA-LDA to fit LDA; use all candidate variables to fit SDA; and use several comparison criteria to compare two models: CFA-LDA and SDA. One thousand three hundred and thirteen (1313) learners were selected to participate in the study, with 23 independent variables. Data was obtained from DataFirst and learners drawn from various schools across the nine provinces of South Africa. Results of Exploratory Factor Analysis (EFA) revealed 16 variables that can be grouped into three factors. CFA models support EFA in selecting the best model fit indices of Standardized Root Mean Squared Residual (SRMR), Root Mean Square Error of Approximation (RMSEA), Goodness of Fit Index (GFI), Adjusted Goodness of Fit Index (AGFI) and Comparative Fit Index (CFI) with the appropriate cut off criterion within the ranges of adequate fit, found in all the models, with the exception of NFI. The results obtained using Chi-square test of association (<0.000) and Mann Whitney’s U test (<0.05) showed significance statistical difference. SDA had high accuracy of classification. The hit ratio was 55.7% while Apparent Error Rate (APER) was 41.3%. Using all 23 independent variables revealed SDA as the efficient and best model selected. This confirms results from the literature and it is concluded that SDA is the best and efficient model to fit a parsimonious model. Thus, the study is relevant and it is recommended that SDA be used in other fields of study.