Basis set of independence claims for a distributional SEM

The basis set is the collection of non-adjacent variable pairs (X, Y) where Y is endogenous and X is causally no later than Y. Each claim asserts that X has no effect on any modelled distributional component of Y, conditional on Y's existing parents. This any-component reading is drmSEM's definition of a missing arrow (see docs/design/03-dsep.md).

Usage

basis_set(object, ...)

# S3 method for class 'drm_sem'
basis_set(object, ...)

Arguments

object: A drm_sem object.
...: Unused.

Value

A data frame with columns claim, x, y, given (comma-separated conditioning set = Y's parents).

Details

A covariance edge declared with covary() (a residual rho12 or higher-level corpair arc) is an allowance that the two responses stay associated, so the y1 _||_ y2 claim is dropped from the basis set (Shipley's bidirected-edge rule; OQ-14). A declared feedback motif (drm_cycle(), 0.5) likewise drops independence claims among its nodes — DAG d-separation does not hold across a cycle, and the goodness-of-fit test is scoped to the acyclic part until sigma-separation lands.

The any-component reading of an independence claim is a drmSEM choice on top of the local-likelihood d-separation framework of Shipley; the d-separation graphical criterion itself is due to Pearl, and the bidirected-edge handling of declared residual correlations follows Shipley's path-analysis treatment.

References

Shipley B (2000). “A New Inferential Test for Path Models Based on Directed Acyclic Graphs.” Structural Equation Modeling, 7(2), 206–218. doi:10.1207/S15328007SEM0702_4 .

Shipley B (2009). “Confirmatory Path Analysis in a Generalized Multilevel Context.” Ecology, 90(2), 363–368. doi:10.1890/08-1034.1 .

Shipley B (2016). Cause and Correlation in Biology: A User's Guide to Path Analysis, Structural Equations and Causal Inference with R, 2nd edition. Cambridge University Press, Cambridge.

Pearl J (2009). Causality: Models, Reasoning, and Inference, 2nd edition. Cambridge University Press, Cambridge.

Lefcheck JS (2016). “piecewiseSEM: Piecewise Structural Equation Modelling in R for Ecology, Evolution, and Systematics.” Methods in Ecology and Evolution, 7(5), 573–579. doi:10.1111/2041-210X.12512 .

Examples

if (FALSE) { # \dontrun{
sem <- drm_sem(
  size = drm_node(drmTMB::bf(size ~ temp + habitat, sigma ~ temp),
                  family = stats::gaussian()),
  abundance = drm_node(drmTMB::bf(abundance ~ size + temp, zi ~ habitat),
                       family = drmTMB::nbinom2()),
  data = dat)
basis_set(sem)
} # }