| name | dsep-basis |
| description | Build basis sets and run any-component d-separation / Fisher's C correctly — adjacency = direct parent on ANY component, causal ordering, conditioning on parents, LRT df bookkeeping, honest framing as drmSEM's definition. |
d-separation & basis sets (any-component)
drmSEM's d-separation is the ANY-COMPONENT definition (DECISIONS.md #2,
docs/design/03-dsep.md): a missing arrow X → Y asserts X has NO effect on ANY
modelled distributional component of Y. This is drmSEM's definition of a
missing arrow — frame it that way, not as a generic graphical-SEM claim.
Adjacency = direct parent on ANY component
- X is adjacent to Y if X is a direct parent of Y on
mu, sigma, nu, zi,
hu, sd(group), or rho12 — any one suffices (drm_is_parent, scanning the
full typed edge table from drm_build_edges).
- A predictor that appears only in Y's
sigma formula still makes X adjacent to
Y. Do not restrict adjacency to mu.
Basis set construction (basis_set.drm_sem)
For each endogenous Y and each variable X (endogenous or exogenous):
- Skip X == Y.
- Skip if X is causally LATER than Y (
drm_order_index: topological position;
exogenous variables sort at index 0, before all nodes).
- Skip if X is already a parent of Y (adjacent → not a missing arrow).
- Skip if Y is a parent of X (orientation guard).
- Otherwise emit claim
X _||_ Y | {parents(Y)}. The conditioning set is Y's
existing parents (drm_parents), so the LRT controls for them.
Testing a claim (dsep.drm_sem)
- Refit Y's node adding X to EVERY modelled component sub-formula
(
drm_refit_augmented, with se = TRUE). This realizes the any-component
alternative hypothesis.
- LRT:
LR = 2*(logLik_aug - logLik_base), df = df_aug - df_base.
- df bookkeeping: df is the number of extra coefficients across ALL augmented
components (one per component sub-formula in the simplest case, more with
factors/interactions). Read both df values from
drm_fit_logLik — never
hard-code df = 1.
- Guard degenerate cases: status
no_data_column, refit_failed, degenerate
(df <= 0 or NA LR) are recorded and EXCLUDED from Fisher's C.
Fisher's C (fisher_c, drm_fisher_c_from_p)
C = -2 * sum(log p) over the ok claims with p > 0; df = 2k where k is
the number of contributing claims; p = pchisq(C, df, lower.tail = FALSE).- A SMALL Fisher p-value means the DAG omits a needed path (reject the model's
independence claims). Report C, df = 2k, k, and p together.
Do / Don't
- DO: state results as "X carries information about some component of Y beyond
Y's parents" when a claim's p is small — not "X affects the mean of Y".
- DO: require nodes fitted with
se = TRUE (declarative drm_sem() does this)
so refits converge and vcov/LRT work; warn via check_sem() if not.
- DON'T: build claims only from
mu edges, or condition on non-parents.
- DON'T: feed failed/degenerate claims into Fisher's C.
- DON'T: add or change a d-sep rule without a recovery test (a DGP where the
true missing arrow is known) — see
validation-harness.
