Tamanho de amostra para avaliar a multicolinearidade em caracteres de cultivares de centeio

Abstract

The aim of this work was to determine the sample size (number of plants) necessary to estimate the indicators of the degree of multicollinearity - condition number (NC), determinant of correlation matrix (DET) and variance inflation factor (FIV) - in matrices of correlation coefficients between rye characters, and verify the variability of sample size between indicators. The experiments were conducted in Santa Maria, Rio Grande do Sul, in five sowing seasons for the cultivar BRS Progresso and three sowing for the cultivar Temprano, totaling eight uniformity trials. In each uniformity trials, 100 plants were randomly collected and eight morphological and seven productive characters were evaluated. Cases of study were formed by the combination of characters, being 22 with the morphological characters and 21 with the productive ones. For each case, 197 sample sizes were planned and, within these, averages of 2,000 resamples were obtained, with replacement, of the degree of multicollinearity considering the three indicators (NC, DET and FIV). Based on the 197 averages, were fitted modified maximum curvature method (MMCM), segmented linear model with plateau response (MLRP), and segmented quadratic model with plateau response (MQRP). The parameters of the models were obtained and, based on these, the sample size was determined, multicollinearity degree corresponding the sample size and the adjusted coefficient of determination (R²) for each model. The MMCM provided the lowest R² values and the MLRP and MQRP models presented the best fit and are suitable for determining the sample size to evaluate the degree of multicollinearity in morphological and productive rye characters. The MQRP was the model that presented the highest R² values and, therefore, based on this model, the inferences were conducted to determine the sample size. Variability in sample size was verified to diagnose the degree of multicollinearity in morphological and productive rye characters. For both characters, larger sample sizes are required for the DET indicator, as for this indicator, greater variability was observed in the estimation in the master sample. In morphological characters, it is necessary to evaluate sample size not less than 116 plants for NC, 180 for DET and 85 for FIV. As for productive characters, the sample size for the NC and FIV indicators does not differ by the t-test for paired samples with a probability of 5% error, with a sample not less than 99 plants, and 169 plants for the DET indicator. In general, there is variability in the sample size between the indicators and between the morphological and productive characters, and there is a need for larger sample sizes in morphological characters to detect the degree of multicollinearity by the use of NC and DET and smaller size when FIV is used.