pathmc

name	pathmc
description	Bayesian path analysis (observed-variable SEM) in PyMC. Compiles a lavaan-inspired formula DSL into a generative PyMC model, then layers introspection, identification diagnostics, the `do()` operator, and causal estimands (ATE/CATE/ATT/ATU/prob) on top. Use when the user asks to specify, fit, or query a Bayesian structural causal model; estimate average treatment effects via g-computation; check identification with adjustment sets or the front-door criterion; or simulate panel/longitudinal counterfactuals.
license	MIT
compatibility	Requires Python >=3.12, PyMC >=6.0.
metadata	{"author":"drbenvincent","version":"0.1","homepage":"https://github.com/pymc-labs/pathmc","tags":["causal-inference","bayesian","sem","path-analysis","pymc"]}

pathmc

pathmc lets you specify a system of structural equations as a string, compile it to a generative PyMC model, fit with MCMC, and reason about causal effects using the do-operator.

Installation

pip install pathmc
# Optional faster samplers (nutpie, numpyro, jax):
pip install "pathmc[samplers]"

Quick start

import pathmc

spec = """
M ~ a*X
Y ~ b*M + c*X
indirect := a*b
"""

m = pathmc.model(spec, data=df)   # returns a PathModel (NOT a fitted result)
m.fit(draws=1000, chains=2)       # MCMC happens here

m.effects_summary()                # labeled coefficients + defined params
m.ate("Y", "X", values=(0, 1))     # average treatment effect via do()
m.adjustment_sets("X", "Y")        # valid backdoor adjustment sets

The DSL is lavaan-inspired:

• Y ~ X — regression
• Y ~~ X — residual covariance
• indirect := a*b — defined parameter
• a*X — labeled coefficient
• Transforms: adstock(x, decay=...), logistic_saturation(x, lam=...)

Decision table

Need	Use
Build a model from a spec + data	m = pathmc.model(spec, data=df)
Explore the DAG without data	m = pathmc.model(spec) (data-free mode)
Inspect causal DAG	m.graph()
Inspect structural equations + priors	m.equations()
Inspect priors only	m.priors()
Refine priors	m.set_priors({"beta_Y": Prior(...)})
Prior predictive check	m.sample_prior_predictive()
Run MCMC	m.fit(draws=1000, chains=2)
Summarize posteriors	m.summary() or m.effects_summary()
Standardized (stdyx) coefficients	m.standardized()
Path-specific effect (e.g. X -> M -> Y)	m.effect("X -> M -> Y")
Posterior predictions	m.predict(...)
Average treatment effect	m.ate(outcome, treatment, values=(0, 1))
Conditional ATE (effect modification)	m.cate(outcome, treatment, condition={"Z": z0})
ATE on the treated / untreated	m.att(...) / m.atu(...)
Backdoor-adjusted outcome regression	adj = m.adjustment_model("X -> Y") then adj.fit()
Inspect adjustment set / formula before fit	adj.adjustment_set, adj.formula (before adj.fit())
Interventional / associational predictions	m.predictions(outcome, set={...})
Interventional contrasts (structural model)	m.comparisons(outcome, variable, contrast=(0, 1))
Marginal slopes under intervention	m.slopes(outcome, variable)
Same interpret API on adjustment model	adj.comparisons(...), adj.slopes(...), etc.
Probability under intervention	m.prob("Y > 0", set={"X": 1})
Manual intervention	m.do(set={"X": 1})
Counterfactual / time-forward (panel)	m.do(set={...}, kind="time-forward")
Adjustment sets for identification	m.adjustment_sets(treatment, outcome)
Yes/no identification check	m.is_identifiable(treatment, outcome)
Front-door identification	m.frontdoor_identifiable(treatment, outcome)
Warn about colliders in an adjustment set	m.collider_warnings(adjust, treatment, outcome)
Enumerate implied conditional independences	m.implied_independences()
Test DAG implications against data	m.test_implications()
Falsify the whole DAG (permutation test)	m.falsify()
Sensitivity analysis (unmeasured confounding)	m.sensitivity(outcome, treatment)
Placebo refutation of an estimated effect	m.refute_placebo(outcome, treatment)
Simulate from a fully-specified model	pathmc.simulate(spec, data, params=...)

Gotchas

1. pathmc.model(...) returns a PathModel, not a fitted result. You must call .fit() separately. model() only parses, builds the DAG, and compiles the PyMC graph — it does not sample.
2. m.do(...) is a structural intervention, not conditioning. It applies pm.do() graph surgery and forward-simulates from the intervened model, propagating posterior uncertainty through the causal chain (g-computation; Robins, 1986). It is not the same as conditioning on observed values. For typical user-facing queries, prefer the wrappers m.ate(), m.cate(), m.att(), m.atu(), m.prob().
3. ate()/cate()/att()/atu() return an EstimandResult, not a DoResult. It knows the outcome, so r.mean(), r.hdi(), and r.prob("> 0") need no variable argument, float(r) gives the posterior mean, and printing it shows a tidy summary. m.do(...) returns a DoResult describing the whole system, where accessors still take a variable name (r.mean("Y")).
4. The DSL is lavaan-inspired, not a 1:1 reimplementation. ~, ~~, :=, and labeled coefficients all work. Latent-variable measurement models (=~) are out of scope in v0.1 — see the user guide for the full operator list.
5. Prior is re-exported from pymc_extras for convenience. from pathmc import Prior is a shortcut for from pymc_extras.prior import Prior. The canonical reference and list of supported distributions live in pymc_extras.
6. Panel lag terms are declared in the model spec. Use lag(sales) directly in the DSL and pass panel={"unit": "region", "time": "week"} to pathmc.model(...). pathmc builds the lagged design internally.
7. Data-free models have a partial method surface. When data=None, graph(), equations(), priors(), adjustment_sets(), is_identifiable(), collider_warnings(), implied_independences() all work. fit(), do(), ate(), cate(), design(), sample_prior_predictive(), test_implications(), falsify(), sensitivity(), refute_placebo() raise RuntimeError until the model is rebuilt with data (and refute_placebo() also needs a prior .fit()).
8. PathModel is not in pathmc.__all__ — it's the class returned by model(). You don't import it directly; you receive it. Type annotations can use pathmc.PathModel (it is reachable as an attribute) but the public entrypoint is the model() function.
9. adjustment_model() returns an AdjustmentModel facade. Inspect adj.adjustment_set and adj.formula before calling adj.fit(). An empty set {} is valid when no covariates are needed to block backdoors; if no valid set exists, construction raises (effect not identifiable via backdoor). When several minimal sets exist, pass adjustment_set= explicitly; pathmc does not pick among them. Pass data= when the parent structural model is data-free. Panel models are not supported on the adjustment path.
10. predictions() / comparisons() / slopes() share one API on PathModel and AdjustmentModel. On the structural model they use truncated-factorization g-computation; on adjustment_model() they delegate to the reduced outcome equation with estimator="regression_adjustment". Read result.causal: only queries on the designated treatment support a causal reading; slopes or contrasts on adjustment covariates are interventional on the fitted surface, not causal effects of those covariates. See the user guide page Predictions, Comparisons, and Slopes.

Capabilities and boundaries

Agents using pathmc can:

• Write spec strings in the DSL (regressions, residual covariances, defined parameters, labeled coefficients, transforms).
• Configure custom priors via Prior objects from pymc_extras.
• Run fit() with PyMC's NUTS sampler (or nutpie / numpyro via the samplers extra).
• Query ate/cate/att/atu/prob/effect with full posterior uncertainty.
• Fit a DAG-derived backdoor adjustment model via adjustment_model() when a single treatment-outcome query suffices.
• Run predictions() / comparisons() / slopes() on structural PathModel or fitted AdjustmentModel objects for interpret-style queries (check result.causal on adjustment models).
• Check identification (adjustment_sets, is_identifiable, frontdoor_identifiable, collider_warnings).
• Test the DAG's conditional-independence implications against data (test_implications).
• Falsify the whole DAG with a permutation-based test (falsify), which grades the graph against randomly-rewired competitors (a port of dowhy's gcm.falsify_graph).
• Build hierarchical panel models with random intercepts/slopes and use lag() terms.
• Run sensitivity analysis to quantify robustness to unmeasured confounding.
• Refute an estimated effect with a Bayesian placebo treatment (refute_placebo): permute the treatment, re-fit, and pool the per-permutation ATE posteriors through a hierarchical normal-normal null model whose null predictive should straddle zero. Upgrades dowhy's placebo_treatment_refuter with a calibrated z_cal/p_tail for the real effect.

Out of scope (do not attempt):

• Latent variables / SEM measurement models (the =~ operator). Out of scope in v0.1; on the post-v1 roadmap.
• Categorical mediators or treatments with >2 levels in ate()/cate() without manual do() calls. Use m.do(set={...}) with explicit values for non-binary interventions.
• Editing the compiled pm.Model object directly. pathmc owns the graph; mutating it bypasses the introspection layer and breaks do() propagation. To customize, change the spec or pass priors= / families= to model().

Patterns

Inspect before sampling (data-free DAG exploration)

m = pathmc.model("""
    M ~ a*X
    Y ~ b*M + c*X
    indirect := a*b
""")
m.graph()                      # DAG plot
m.equations()                  # structural equations + priors
m.adjustment_sets("X", "Y")    # what to adjust for
m.is_identifiable("X", "Y")    # can we estimate the effect at all?

Standard fit-and-query workflow

m = pathmc.model(spec, data=df)
m.fit(draws=1000, chains=2)
m.effects_summary()                          # labeled coefs
m.ate("Y", "X", values=(0, 1))               # ATE
m.cate("Y", "X", condition={"Z": 1})         # CATE | Z=1
m.test_implications()                        # DAG vs data check

Backdoor adjustment model

m = pathmc.model(spec, data=df)              # structural DAG + data
adj = m.adjustment_model("X -> Y")           # inspect before fit
adj.adjustment_set                           # validated backdoor set
adj.formula                                  # reduced outcome equation
adj.fit(draws=1000, chains=2)
adj.ate(values=(0, 1))                       # outcome-regression standardization
adj.comparisons(comparison="lift")             # same API as PathModel
adj.slopes(wrt="X")                            # defaults to designated treatment

When several minimal adjustment sets exist, pass adjustment_set= explicitly. When the structural model has no data, pass data= to adjustment_model().

Panel model

import pathmc
m = pathmc.model(
    "sales ~ b*price + a*lag(sales) + trend",
    data=df,
    panel={"unit": "region", "time": "week"},
    pooling="partial",
)
m.fit()