Multicollinearity in path analysis of maize (Zea mays L.)

Abstract

The objective was to evaluate the effect of multicollinearity on three types of path analysis (traditional, under multicollinearity and traditional with elimination of variables) in maize (Zea mays L.). We used data from 14 maize cultivar competition trials. Seven explanatory variables (number of days to 50% tasselling, plant height, ear height, relative ear position, number of plants, number of ears and prolificity) and a response variable (grain yield) were measured for each cultivar of each trial. For each trial, descriptive statistics, correlation coefficients between the seven explanatory variables (correlation matrix X'X) and correlation coefficients between each explanatory variable and grain yield (correlation matrix X'Y) were calculated. The multicollinearity in the X'X correlation matrix was determined by using three methods, including tolerance, condition number and matrix determinant. Path analysis was conducted by using a system of normal equations, X'Xβˆ = X'Y, in three distinct ways (traditional, under multicollinearity and traditional with elimination of variables). The tolerance, condition number and matrix determinant, indicated high degree of multicollinearity between the seven explanatory variables. The addition of the k = 0.10 constant and the elimination of variables were both effective for reducing the degree of multicollinearity. Traditional path analysis, with a high degree of multicollinearity in the correlation matrix generates path coefficient estimates without biological significance that should not be considered. Using traditional path analysis with the elimination of highly correlated variables is more adequate than path analysis under multicollinearity for estimating the true direct and indirect effects of path analysis in maize crop.