3 Assumptions of Path Analysis

Sewall Wright (Wright, 1968, p. 299) described path diagrams in the following manner:

``[In path analysis] every included variable, measured or hypothetical, is represented by arrows as either completely determined by certain others (the dependent variables), which may in turn be represented as similarly determined, or as an ultimate variable (our independent variables). Each ultimate factor in the diagram must be connected by lines with arrowheads at both ends with each of the other ultimate factors, to indicate possible correlations through still more remote, unrepresented factors, except in cases in which it can safely be assumed that there is no correlation .... the strict validity of the method depends on the properties of formally complete linear systems of unitary variables.''

Some assumptions of the method, implicit or explicit in Wright's description, are:

• Linearity: All relationships between variables are linear. The assumption of a linear model seems valid as a wide variety of non-linear functions are well approximated by linear ones particularly within a limited range. (Sometimes non-linearity can be removed by appropriate transformation of the data prior to statistical analysis; but some models are inherently non-linear).
• Causal closure: All direct influences of one variable on another must be included in the path diagram. Hence the non-existence of an arrow between two variables means that it is assumed that these two variables are not directly related. The formal completeness of the diagram requires the introduction of residual variables if they are not represented as one of the ultimate variables, unless there is reason to assume complete additivity and determination by the specified factors.
• Unitary Variables: Variables may not be composed of components that behave in different ways with different variables in the system, but they should vary as a whole. For example, if we have three variables, A, B, and C, but A is really a composite of A1 and A2, and A1 is positively correlated with B and C, but A2 is positively correlated with B but negatively correlated with C, we have a potential for disaster!