SyntheticDifferenceInDifferencesWeightFitter

class causalpy.pymc_models.SyntheticDifferenceInDifferencesWeightFitter

Bayesian weight fitter for Synthetic Difference-in-Differences.

Encodes both the unit-weight module and the time-weight module in a single PyMC model. Unit weights balance control units against treated units in the pre-treatment period; time weights balance pre-treatment periods against post-treatment periods for control units. Both use the softmax-over-Normal-logits parameterization with a pinned reference level.

The treatment effect is not estimated inside this model. It is computed analytically from the weight posteriors via the double-difference formula in the experiment class.

Defines the PyMC model:

\[\begin{split}\omega &= \mathrm{softmax}(0, \tilde{\omega}_2, \ldots, \tilde{\omega}_{N_\text{co}}) \\ \bar{Y}_{\text{tr},t} &\sim \mathrm{Normal}(\omega_0 + \boldsymbol{\omega}^\top \mathbf{Y}_{\text{co},t},\; \sigma_\omega) \\ \lambda &= \mathrm{softmax}(0, \tilde{\lambda}_2, \ldots, \tilde{\lambda}_{T_\text{pre}}) \\ \bar{Y}_{i,\text{post}} &\sim \mathrm{Normal}(\lambda_0 + \boldsymbol{\lambda}^\top \mathbf{Y}_{i,\text{pre}},\; \sigma_\lambda)\end{split}\]

Notes

This model implements the cut-posterior formulation of Bayesian SDiD. Modules 1 and 2 share no parameters and are conditionally independent given the data. Running them in a single MCMC call is a convenience; the important property is that no treatment-effect likelihood feeds back into the weight posteriors.

The prior scales on the logits play the role of the regularization parameter in the frequentist SDiD:

• omega_raw default sigma=1.0 (zeta_omega=1.0): moderate regularization, allowing weights between SC-sparse and DiD-uniform.

• lam_raw default sigma=100.0 (zeta_lambda=0.01): essentially flat, letting time weights concentrate on the most informative pre-treatment periods.

References

[1]

Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021). Synthetic Difference-in-Differences. American Economic Review, 111(12), 4088-4118.

Methods

SyntheticDifferenceInDifferencesWeightFitter.add_coord(name)	Register a dimension coordinate with the model.
SyntheticDifferenceInDifferencesWeightFitter.add_coords(...)	Vectorized version of Model.add_coord.
SyntheticDifferenceInDifferencesWeightFitter.add_named_variable(var)	Add a random graph variable to the named variables of the model.
SyntheticDifferenceInDifferencesWeightFitter.build_model(X, ...)	Build the PyMC model with both unit-weight and time-weight modules.
SyntheticDifferenceInDifferencesWeightFitter.calculate_cumulative_impact(impact)
SyntheticDifferenceInDifferencesWeightFitter.calculate_impact(...)	Calculate the causal impact as the difference between observed and predicted values.
SyntheticDifferenceInDifferencesWeightFitter.check_start_vals(...)	Check that the logp is defined and finite at the starting point.
SyntheticDifferenceInDifferencesWeightFitter.compile_d2logp([...])	Compiled log probability density hessian function.
SyntheticDifferenceInDifferencesWeightFitter.compile_dlogp([...])	Compiled log probability density gradient function.
SyntheticDifferenceInDifferencesWeightFitter.compile_fn(outs, *)
SyntheticDifferenceInDifferencesWeightFitter.compile_logp([...])	Compiled log probability density function.
SyntheticDifferenceInDifferencesWeightFitter.copy()	Clone the model.
SyntheticDifferenceInDifferencesWeightFitter.create_value_var(...)	Create a TensorVariable that will be used as the random variable's "value" in log-likelihood graphs.
SyntheticDifferenceInDifferencesWeightFitter.d2logp([...])	Hessian of the models log-probability w.r.t.
SyntheticDifferenceInDifferencesWeightFitter.debug([...])	Debug model function at point.
SyntheticDifferenceInDifferencesWeightFitter.dlogp([...])	Gradient of the models log-probability w.r.t.
SyntheticDifferenceInDifferencesWeightFitter.eval_rv_shapes()	Evaluate shapes of untransformed AND transformed free variables.
SyntheticDifferenceInDifferencesWeightFitter.fit(X, y)	Draw samples from posterior, prior predictive, and posterior predictive distributions.
SyntheticDifferenceInDifferencesWeightFitter.get_context([...])
SyntheticDifferenceInDifferencesWeightFitter.initial_point([...])	Compute the initial point of the model.
SyntheticDifferenceInDifferencesWeightFitter.logp([...])	Elemwise log-probability of the model.
SyntheticDifferenceInDifferencesWeightFitter.logp_dlogp_function([...])	Compile a PyTensor function that computes logp and gradient.
SyntheticDifferenceInDifferencesWeightFitter.make_obs_var(...)	Create a TensorVariable for an observed random variable.
SyntheticDifferenceInDifferencesWeightFitter.name_for(name)	Check if name has prefix and adds if needed.
SyntheticDifferenceInDifferencesWeightFitter.name_of(name)	Check if name has prefix and deletes if needed.
SyntheticDifferenceInDifferencesWeightFitter.point_logps([...])	Compute the log probability of point for all random variables in the model.
SyntheticDifferenceInDifferencesWeightFitter.predict(X)	Predict data given input data X
SyntheticDifferenceInDifferencesWeightFitter.print_coefficients(labels)	Print the model coefficients with their labels.
SyntheticDifferenceInDifferencesWeightFitter.priors_from_data(X, y)	Set default priors for unit and time weight modules.
SyntheticDifferenceInDifferencesWeightFitter.profile(outs, *)	Compile and profile a PyTensor function which returns outs and takes values of model vars as a dict as an argument.
SyntheticDifferenceInDifferencesWeightFitter.register_data_var(data)	Register a data variable with the model.
SyntheticDifferenceInDifferencesWeightFitter.register_rv(...)	Register an (un)observed random variable with the model.
SyntheticDifferenceInDifferencesWeightFitter.replace_rvs_by_values(...)	Clone and replace random variables in graphs with their value variables.
SyntheticDifferenceInDifferencesWeightFitter.score(X, y)	Score the Bayesian \(R^2\) given inputs X and outputs y.
SyntheticDifferenceInDifferencesWeightFitter.set_data(...)	Change the values of a data variable in the model.
SyntheticDifferenceInDifferencesWeightFitter.set_dim(...)	Update a mutable dimension.
SyntheticDifferenceInDifferencesWeightFitter.set_initval(...)	Set an initial value (strategy) for a random variable.
SyntheticDifferenceInDifferencesWeightFitter.shape_from_dims(dims)
SyntheticDifferenceInDifferencesWeightFitter.to_graphviz(*)	Produce a graphviz Digraph from a PyMC model.

Attributes

basic_RVs	List of random variables the model is defined in terms of.
continuous_value_vars	All the continuous value variables in the model.
coords	Coordinate values for model dimensions.
datalogp	PyTensor scalar of log-probability of the observed variables and potential terms.
default_priors
dim_lengths	The symbolic lengths of dimensions in the model.
discrete_value_vars	All the discrete value variables in the model.
isroot
observedlogp	PyTensor scalar of log-probability of the observed variables.
parent
potentiallogp	PyTensor scalar of log-probability of the Potential terms.
prefix
root
unobserved_RVs	List of all random variables, including deterministic ones.
unobserved_value_vars	List of all random variables (including untransformed projections), as well as deterministics used as inputs and outputs of the model's log-likelihood graph.
value_vars	List of unobserved random variables used as inputs to the model's log-likelihood (which excludes deterministics).
varlogp	PyTensor scalar of log-probability of the unobserved random variables (excluding deterministic).
varlogp_nojac	PyTensor scalar of log-probability of the unobserved random variables (excluding deterministic) without jacobian term.

__init__(sample_kwargs=None, priors=None)

Parameters:

• sample_kwargs (dict[str, Any] | None) – Dictionary of kwargs that get unpacked and passed to the pymc.sample() function. Defaults to an empty dictionary if None.

• priors (dict[str, Any] | None) – Dictionary of priors for the model. Defaults to None, in which case default priors are used.

Return type:

None

classmethod __new__(*args, **kwargs)