Simulated Data to Empirical Evaluation Based on The Monte Carlo Method

Based on prior methodological research in the field of factor analysis, the techniques of Tucker et al. (1969) with appropriate adaptations was used to generate four Monte Carlo population correlation matrices based on communality magnitudes (high, moderate, low, and mixed) with 100 indicator variables in each matrix. The population matrices were generated with the following characteristics: (a) continuous variables (measurement scale), (b) normal distribution, (c) 5-factor solutions (common factor), and (d) orthogonal solution (factor structure). Four correlation matrices for each level of VTF ratio, 4:1, 7:1 and 10:1, were randomly sampled from each set of population correlation matrices. Using five systematically increased STV ratios (2:1, 4:1, 8:1, 16:1, and 32:1), data sets with 1000 replications for each level of VTF ratio were generated.