Acquires the set of independence claims--or the 'basis set'--for use in evaluating the goodness-of-fit for piecewise structural equation models.

basisSet(modelList, direction = NULL)

## Arguments

modelList A list of structural equations. a vector of claims defining the specific directionality of any independence claim(s)

## Value

A list of independence claims.

## Details

This function returns a list of independence claims. Each claim is a vector of the predictor of interest, followed by the response, and, if present, any conditioning variables.

Relationships among exogenous variables are omitted from the basis set because the directionality is unclear--e.g., does temperature cause latitude or does latitude cause temperature?--and the assumptions of the variables are not specified in the list of structural equations, so evaluating the relationship becomes challenging without further input from the user. This creates a circular scenario whereby the user specifies relationships among exogenous variables, raising the issue of whether they should be included as directed paths if they can be assigned directional relationships.

Paths can be omitted from the basis set by specifying them as correlated errors using %~~% or by assigning a directionality using the argument direction, e.g. direction = c("X <- Y"). This can be done if post hoc examination of the d-sep tests reveals nonsensical independence claims (e.g., arthropod abundance predicting photosynthetically-active radiation) that the user may wish to exclude from evaluation.

## References

Shipley, Bill. "A new inferential test for path models based on directed acyclic graphs." Structural Equation Modeling 7.2 (2000): 206-218.

dSep