Precision of Principal Component Analysis in a Larger Phenotypic Data Sets of Maize

In maize, research with multiple variables has been carried out and the principal component analysis (PCA) has been used in order to reduce the data dimensionality. The objective of this work was to study the impact of observations number and correlation matrix coefficients (r) magnitude in the eigenvalue estimates precision of the PCA, with simulated and real larger phenotypic data sets of maize. Seven data files were simulated, formed by twelve variables and 6340 observations. The first data file was simulated with 66 r of the correlation matrix equal to 0.35. The remaining six files were simulated with 66 r equal to 0.45, 0.55, 0.65, 0.75, 0.85 and 0.95. Real data file with twelve variables of 6340 maize plants with r in the interval |0.01 ≤ r ≤ 0.99| was used. For the eight cases, PCA were performed in 3000 resamples with replacement, for sample sizes of 12 to 1000 observations. Insufficient sampling generates inaccurate and biased principal components (PC1 and PC2) eigenvalues estimates, and samples with a high observations number allow reliable PCA. The precision of the PC1 and PC2 eigenvalues estimates increases with the highest observations number. The precision of the PC1 eigenvalues estimates increases with larger r magnitudes, and the PC2 eigenvalues decreases.