Augmented Synthetic Control Method
==================================

The *Augmented Synthetic Control Method* is due to Ben-Michael, Feller & Rothstein
:cite:`augsynth2021` and adapts the :doc:`Synthetic Control Method <synth>` in an
effort to adjust for poor pre-treatment fit.

The authors do this by adjusting the Synthetic Control Method estimate by adding
a term that is an imbalance in a particular function of the pre-treatment outcomes.
In the *Ridge Augmented Synthetic Control Method* this function is
linear in the pre-treatment outcomes and fit by ridge regression of the control
post-treatment outcomes against pre-treatment outcomes.

In particular, the method constructs a vector of weights :math:`w = (w_1, w_2, \dots, w_k)`
such that

.. math::
   w = w_\mathrm{scm} + w_\mathrm{aug},

where :math:`w_\mathrm{scm}` are the weights obtained from the standard
:doc:`Synthetic Control Method <synth>` and :math:`w_\mathrm{aug}` are
augmentations that are included when the treated unit lies outside the
convex hull defined by the control units. The weights may be negative and
larger than 1, the degree of extrapolation is controlled by a ridge
parameter :math:`\lambda`.

In general, this method will obtain weights at least as good as the synthetic
control method in terms of pre-treatment fit.

The :class:`AugSynth` class
***************************

The :class:`AugSynth <pysyncon.AugSynth>` class implements the Ridge Augmented
Synthetic Control Method. The expected way to use the class is to first create a
:class:`Dataprep <pysyncon.Dataprep>` object that defines the study data and
then use it as input to a :class:`AugSynth <pysyncon.Synth>` object. See the
`examples folder <https://github.com/sdfordham/pysyncon/tree/main/examples>`_
of the repository for examples illustrating usage.

The implementation is based on the same method in the R
`augsynth package <https://github.com/ebenmichael/augsynth>`_
and aims to produce results that can be reconciled with that package.

.. autoclass:: pysyncon.AugSynth
   :members:
   :inherited-members: