Block-Recursive Path Models for Rooting-Medium and Plant-Growth Variables Measured in Greenhouse Experiments

Searching for statistically significant and biologically relevant relationships in complex datasets is generally a difficult task, in many fields including agronomy. Path analysis is an accessible, graphical, and inferential method for multivariate data exploration, which allows for more than unidirectional causal relationships between the measured variables. Here, data from experimental rooting media, and from corn plants grown in a greenhouse experiment, are used to introduce the theory and methodology of path analysis. Block-recursive path diagrams are hypothesized for each set of variables measured from the rooting media and the plants. A path model is hypothesized for the union of the two sets of variables. Several reciprocal relationships between rooting medium and plant variables are pointed out, which challenge the usual assumption of unidirectional causality. Besides other relationships between experimental variables, modeling the union set of variables led to the conclusion that the measurement of any of the variables from this experimental system gives information about all of the other experimental variables. The diagrams that are presented include covariances between disturbance terms, which suggest the presence of shared unmeasured causes of variation. In some other cases, such covariance indicates shared variation due to the measurement of variables with the same machine.