A PROPOSAL FOR THE ANALYSIS OF MAIN COMPONENTS IN THE PRESENCE OF NON-RANDOM VARIABLES
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Abstract
For exploratory analysis of the principal components (CPs), the assumption of multivariate normality of the variables is not required, nor necessarily that they are random. This means that variables that do not behave randomly can also be included in this analysis. Thus, in order to carry out the analysis of the PCs with random variables or not, a correction of the matrix based on the coefficients of variation was proposed (Campana et al., 2010) by applying the method of Lenth (1989), whose new array was named . To verify its feasibility, ten data sets of random variables Y1, Y2, Y3 and Y4 were simulated, with 10,000 values each and that followed multivariate normal distribution. After the simulation, 0%, 1%, 2%, 3% and 4% of the random values of Y4 were replaced by the same and respective percentages of outliers, in order to break its randomness. Subsequently, response surface analyzes were performed for eight different absolute mean percentage errors obtained in relation to eight parameters related to the performance of the CP analysis, as a function of the replacement percentages by Y4 outliers (0, 1, 2, 3 and 4 ) and the matrices used in the analysis of the PCs. According to the results, it was concluded that, in the presence of only normal random variables, it is the best matrix. On the other hand, when there are outliers, it is the most recommended.
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