Proposition of a new index for projection pursuit in the multiple factor analysis
Paulo César Ossani, Mariana Figueira Ramos, Marcelo Ângelo Cirillo · Computational and Mathematical Methods · 2020
This study proposes a new index for projection pursuit used to reduce the dimensions of groups of variables using multiple factor analysis. The main advantage with respect to other indexes is that the methodological procedure preserves the variance and covariance structures to perform singular value decomposition, when the index is used to compare groups of variables. Among other contributions, the study presents a modification in the grand tour algorithm with simulated annealing, adapting it to deal with groups of variables. The methodology used to assess the proposed index was based on Monte Carlo simulations, in several scenarios and with configurations of the following factors: degrees of correlation between the variables; and number of groups and degrees of heterogeneity among groups of variables. The proposed index was compared with thirteen indexes known in the literature. It was concluded that the proposed index was efficient in the reduction of data to use multiple factor analysis. This index is recommended for situations in which the groups exhibit low or high heterogeneity and a strong degree of correlation between the variables (ρ=0.9). In general terms, indexes are affected by the increase in the number of groups, depending on the scenarios assessed.