Multivariate assumptions and effect of model parameters in path analysis in oat crop

Abstract

Context Path analysis (PA) is a widely used multivariate statistical technique. When performing PA, the effects of the parameters of the mathematical model relating to the experimental design are disregarded, working only with the average effects of the treatments. Aims We aimed to analyse the implications of statistical assumptions, and of removing mathematical model parameters, on the PA results in oat. Methods A field study was conducted in southern Brazil in five crop years. The experimental design employed was a two-factor 22 × 5 randomised complete block design, characterised by 22 cultivars and five fungicide applications, with three repetitions. Six explanatory variables were measured, panicle length, panicle dry mass, panicle spikelet number, panicle grain number, panicle grain dry mass, and harvest index, and the primary variable yield. Initially, normality and multicollinearity diagnoses were carried out and correlation coefficients were calculated. The PA was performed in three ways: traditional, with measures to address multicollinearity (ridge), and traditional with eliminating variables. Key results and conclusions The occurrence of multicollinearity resulted in obtaining path coefficients without biological application. Removing the model’s parameters modifies the path coefficients, with average changes of 10.5% and 13.3% in the direction, and 24.7% and 23.0% in the magnitude, of the direct and indirect effects, respectively. Implications This new approach makes it possible to remove the influences of treatments and experimental design from observations and, consequently, from path coefficients and their interpretations. Therefore, the researcher will reduce possible bias in the coefficient estimates, highlighting the real relationship between the variables, and making the results and interpretations more reliable.