Não-normalidade multivariada e multicolinearidade em análise de trilha na cultura de milho

Abstract

The path analysis allows evaluation of the direct and indirect effects of the explicative variables on variable of interest, through the breakdown of the correlation coefficients. In order to make the results obtained through the path analysis reliable, some assumptions must be met. Thus, the objectives of this study were to verify the normality and the multicollinearity interference in the corn path analysis and compare alternative methods for estimating the path coefficients. Data from 44 trials of corn cultivars was used, carried out in the state of Rio Grande do Sul, between the crop years 2002/03 and 2004/05. In each cultivar, of each trial, were measured (number of days until the male flowering, plant height, ear insertion height, relative position of the ear, number of plants, number of ears and prolificacy) and the main variable (grain yield). For each trial, descriptive statistics were calculated and univariate and multivariate normality diagnoses were conducted using the Shapiro-Wilk test and the Shapiro-Wilk multivariate generalized by Royston test, respectively. Thereupon, in the trials data that did not present a normal distribution, a transformation of the data by the Box-Cox family of transformations was carried out. The correlation coefficients between the seven explicative variables (correlation matrix X'X) and the correlation coefficients of each explicative variable with the grain yield (correlation matrix X'Y) were calculated for the original and transformed data. Then, the multicollinearity was diagnosed in the correlation matrix X'X, using four methods: variance inflation factor, tolerance, the condition number and the matrix determinant. Finally, the path analysis was performed, using the normal equations system X X �� = X Y, in three forms: traditional path analysis, path analysis under multicollinearity and traditional path analysis, with elimination of variables. The data transformation, to obtain multivariate normality, contributes to the degree of multicollinearity decrease and in the stabilization of the direct effects in path analysis with high degree of multicollinearity. The high degrees of multicollinearity adverse effects in the estimation of the direct effects in path analysis are larger than the multivariate non-normality. The traditional path analysis, with elimination of variables, is more appropriate than the path analysis under multicollinearity.