Sample size for evaluation the of multicollinearity degree in productive traits of rye
Keywords:Secale cereale L, Sampling design, Correlation, Multivariate analysis
The objectives of this work were to determine the sample size (number of plants) necessary to estimate the indicators of the of multicollinearity degree - condition number (CN), determinant of the correlation matrix (DET), and variance inflation factor (VIF) - in productive traits of rye and to verify the variability of the sample size between the indicators. Five and three uniformity trials were conducted with the cultivars BRS Progresso and Temprano, respectively, and seven productive traits were evaluated in 780 plants. Twenty-one cases were obtained from seven traits, combined five to five. In each case, 197 sample sizes were planned (20, 25, 30, ..., 1,000 plants) and in each size 2,000 resampling were performed, with replacement. For each resample the CN, DET and FIV were determined and the average among 2,000 estimates of each indicator of the multicollinearity degree was calculated. Then, for each case and indicator, the sample size was determined through three models: models of maximum modified curvature, segmented linear with plateau response, and segmented quadratic with plateau response. There was superiority the quadratic model segmented with plateau in adjusting the degree of multicollinearity according to the sample size for all indicators. There is a need greater sample size to detect multicollinearity when diagnosed by DET and for sizes larger than 101, 258 and 102 plants when diagnosing for the number of conditions, determinant and inflation factor performed, respectively.
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