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Thomas Pinder
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Build nbs (#10)
* Build nbs * Build nbs * Build nbs * Build nbs --------- Co-authored-by: Thomas Pinder <[email protected]>
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‎docs/examples/azcausal.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "153aaca2",
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"metadata": {},
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"source": [
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"# AZCausal Integration\n",
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"\n",
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"Amazon's [AZCausal](https://github.com/amazon-science/azcausal) library provides the\n",
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"functionality to fit synthetic control and difference-in-difference models to your\n",
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"data. Integrating the synthetic data generating process of `causal_validation` with\n",
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"AZCausal is trivial, as we show in this notebook. To start, we'll simulate a toy\n",
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"dataset."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b134b49f",
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"metadata": {},
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"outputs": [],
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"source": [
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"from azcausal.estimators.panel.sdid import SDID\n",
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"import scipy.stats as st\n",
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"\n",
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"from causal_validation import (\n",
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" Config,\n",
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" simulate,\n",
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")\n",
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"from causal_validation.effects import StaticEffect\n",
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"from causal_validation.plotters import plot\n",
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"from causal_validation.transforms import (\n",
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" Periodic,\n",
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" Trend,\n",
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")\n",
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"from causal_validation.transforms.parameter import UnitVaryingParameter"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "86ba26f3",
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"metadata": {},
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"outputs": [],
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"source": [
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"cfg = Config(\n",
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" n_control_units=10,\n",
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" n_pre_intervention_timepoints=60,\n",
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" n_post_intervention_timepoints=30,\n",
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" seed=123,\n",
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")\n",
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"\n",
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"linear_trend = Trend(degree=1, coefficient=0.05)\n",
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"data = linear_trend(simulate(cfg))\n",
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"plot(data)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ae979b7b",
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"metadata": {
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"title": "We'll now simulate a 5% lift in the treatment group's observations. This"
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},
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"source": [
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"will inflate the treated group's observations in the post-intervention window."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "45f9e99f",
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"metadata": {},
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"outputs": [],
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"source": [
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"TRUE_EFFECT = 0.05\n",
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"effect = StaticEffect(effect=TRUE_EFFECT)\n",
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"inflated_data = effect(data)\n",
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"plot(inflated_data)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0ff7c192",
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"metadata": {},
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"source": [
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"## Fitting a model\n",
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"\n",
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"We now have some very toy data on which we may apply a model. For this demonstration\n",
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"we shall use the Synthetic Difference-in-Differences model implemented in AZCausal;\n",
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"however, the approach shown here will work for any model implemented in AZCausal. To\n",
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"achieve this, we must first coerce the data into a format that is digestible for\n",
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"AZCausal. Through the `.to_azcausal()` method implemented here, this is\n",
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"straightforward to achieve. Once we have a AZCausal compatible dataset, the modelling\n",
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"is very simple by virtue of the clean design of AZCausal."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "db0f85d8",
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"metadata": {},
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"outputs": [],
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"source": [
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"panel = inflated_data.to_azcausal()\n",
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"model = SDID()\n",
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"result = model.fit(panel)\n",
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"print(f\"Delta: {TRUE_EFFECT - result.effect.percentage().value / 100}\")\n",
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"print(result.summary(title=\"Synthetic Data Experiment\"))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5c71b479",
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"metadata": {
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"title": "We see that SDID has done an excellent job of estimating the treatment"
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},
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"source": [
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"effect. However, given the simplicity of the data, this is not surprising. With the\n",
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"functionality within this package though we can easily construct more complex datasets\n",
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"in effort to fully stress-test any new model and identify its limitations.\n",
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"\n",
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"To achieve this, we'll simulate 10 control units, 60 pre-intervention time points, and\n",
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"30 post-intervention time points according to the following process: $$ \\begin{align}\n",
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"\\mu_{n, t} & \\sim\\mathcal{N}(20, 0.5^2)\\\\\n",
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"\\alpha_{n} & \\sim \\mathcal{N}(0, 1^2)\\\\\n",
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"\\beta_{n} & \\sim \\mathcal{N}(0.05, 0.01^2)\\\\\n",
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"\\nu_n & \\sim \\mathcal{N}(1, 1^2)\\\\\n",
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"\\gamma_n & \\sim \\operatorname{Student-t}_{10}(1, 1^2)\\\\\n",
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"\\mathbf{Y}_{n, t} & = \\mu_{n, t} + \\alpha_{n} + \\beta_{n}t + \\nu_n\\sin\\left(3\\times\n",
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"2\\pi t + \\gamma\\right) + \\delta_{t, n} \\end{align} $$ where the true treatment effect\n",
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"$\\delta_{t, n}$ is 5% when $n=1$ and $t\\geq 60$ and 0 otherwise. Meanwhile,\n",
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"$\\mathbf{Y}$ is the matrix of observations, long in the number of time points and wide\n",
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"in the number of units."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "59d6a88b",
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"metadata": {},
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"outputs": [],
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"source": [
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"cfg = Config(\n",
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" n_control_units=10,\n",
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" n_pre_intervention_timepoints=60,\n",
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" n_post_intervention_timepoints=30,\n",
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" global_mean=20,\n",
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" global_scale=1,\n",
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" seed=123,\n",
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")\n",
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"\n",
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"intercept = UnitVaryingParameter(sampling_dist=st.norm(loc=0.0, scale=1))\n",
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"coefficient = UnitVaryingParameter(sampling_dist=st.norm(loc=0.05, scale=0.01))\n",
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"linear_trend = Trend(degree=1, coefficient=coefficient, intercept=intercept)\n",
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"\n",
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"amplitude = UnitVaryingParameter(sampling_dist=st.norm(loc=1.0, scale=2))\n",
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"shift = UnitVaryingParameter(sampling_dist=st.t(df=10))\n",
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"periodic = Periodic(amplitude=amplitude, shift=shift, frequency=3)\n",
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"\n",
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"data = effect(periodic(linear_trend(simulate(cfg))))\n",
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"plot(data)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5268b01a",
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"metadata": {
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"title": "As before, we may now go about estimating the treatment. However, this"
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},
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"source": [
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"time we see that the delta between the estaimted and true effect is much larger than\n",
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"before."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "71d101a2",
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"metadata": {},
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"outputs": [],
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"source": [
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"panel = data.to_azcausal()\n",
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"model = SDID()\n",
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"result = model.fit(panel)\n",
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"print(f\"Delta: {100*(TRUE_EFFECT - result.effect.percentage().value / 100): .2f}%\")\n",
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"print(result.summary(title=\"Synthetic Data Experiment\"))"
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]
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}
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],
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"metadata": {
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"jupytext": {
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"cell_metadata_filter": "title,-all",
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"main_language": "python",
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"notebook_metadata_filter": "-all"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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