Números de ensaios, observações e variáveis na correlação canônica em centeio

Abstract

Multivariate techniques are important analysis tools for understanding the object of study. For greater reliability in the interpretations of models, the correct sample size is necessary. Little has been explored about the number of measurements or tests needed in the diagnosis of multicollinearity and the correlation of the first canonical pair and the relationship between the number of observations and variables for estimating the correlation in the first canonical pair. Thus, the objectives of this study were to determine: the number of trials necessary to estimate the degree of multicollinearity by the condition number (NC) and variance inflation factor (FIV) indicators and the estimate of the correlation of the first canonical pair; and the relationship between the number of observations and variables for estimating the canonical correlation. Eight uniformity tests were conducted with two rye cultivars, with the evaluation of morphological and productive characters. To study the number of tests for the diagnosis of the degree of multicollinearity in each group of variables, cases were planned – different combinations of characters – and the diagnosis of multicollinearity was performed using the NC and FIV indicators. The repeatability analysis and the number of trials to estimate multicollinearity were performed by five methods in each case, cultivar and group of variables. In determining the number of trials for estimating the correlation of the first canonical pair, scenarios were considered, consisting of cases with the same number of characters combined in each group of variables. For each scenario and cultivar, repeatability analysis was performed by five methods: analysis of variance, principal components and structural analysis, based on correlation and variance and covariance matrices. Then, the number of trials for different levels of accuracy was determined. To study the relationship between the number of observations and variables (n:p) to estimate the correlation of the first canonical pair, 1,000 samples with multivariate normal distribution were simulated in 100 sample sizes (n:p = 1, 2, 3, . .., 100), three sowing dates and two cultivars. Then, with the averages' estimates in each planned sample size, was determined the n:p relationship through two segmented regression models with plateau. There is need of three and 16 trials for the diagnosis of multicollinearity and of four and eight trials for estimating the first pair correlation canonical in the cultivars BRS Progresso and Temprano, respectively, with a minimum accuracy of 95%. While, in canonical correlation analysis, it is recommended the use at least 27 observations for each variable.