How-to#

On this page you can find a gallery of example notebooks that demonstrate the use of CausalPy.

Panel data methods#

Causal methods for longitudinal data where the same units are observed over multiple time periods.

ANCOVA#

Analysis of covariance is a simple linear model, typically with one continuous predictor (the covariate) and a categorical variable (which may correspond to treatment or control group). In the context of this package, ANCOVA could be useful in pre-post treatment designs, either with or without random assignment. This is similar to the approach of difference in differences, but only applicable with a single pre and post treatment measure.

ANCOVA for pre/post treatment nonequivalent group designs

Panel Fixed Effects#

Panel data tracks the same units over multiple time periods. Fixed effects exploit this structure to control for unobserved confounders that are stable within units or common across time.

Panel Fixed Effects for Causal Inference

Synthetic Control#

The synthetic control method is a statistical method used to evaluate the effect of an intervention in comparative case studies. It involves the construction of a weighted combination of groups used as controls, to which the treatment group is compared.

Synthetic control with scikit-learn models

Synthetic control with pymc models

Synthetic control with pymc models

The effects of Brexit

Synthetic Difference-in-Differences with pymc models

Synthetic Difference-in-Differences with pymc models

Choosing the right counterfactual: ITS vs. synthetic control

Choosing the right counterfactual: ITS vs. synthetic control on the same data

Geographical lift testing#

Geolift (geographical lift testing) is a method for measuring the causal impact of interventions in geographic regions. It combines synthetic control methods with difference-in-differences approaches to estimate treatment effects when interventions are applied to specific geographic areas.

Bayesian geolift with CausalPy

Multi-cell geolift analysis

Difference in Differences#

Analysis where the treatment effect is estimated as a difference between treatment conditions in the differences between pre-treatment to post treatment observations.

Difference in Differences with scikit-learn models

Difference in Differences with pymc models

Difference in Differences with pymc models

Banking dataset with a pymc model

Banking dataset with a pymc model

Staggered Difference-in-Differences

Interrupted Time Series#

A quasi-experimental design that uses time series methods to generate counterfactuals and estimate treatment effects. A series of observations are collected before and after a treatment, and the pre-treatment trend (or any time-series model) is used to predict what would have happened in the absence of treatment.

Interrupted Time Series (ITS) with scikit-learn models

Bayesian Interrupted Time Series

Interrupted Time Series for fixed-period interventions

Excess deaths due to COVID-19

Lift Testing with Interrupted Time Series

Lift Testing with Interrupted Time Series: A Marketing Case Study

Placebo-in-time and falsification: a UK CO₂ case study

Comparative Interrupted Time Series#

Comparative interrupted time series extends standard ITS by incorporating control units as predictors, helping disentangle treatment effects from coincidental changes that affect both treated and control units.

Comparative Interrupted Time Series: a geo-experimentation example

Piecewise Interrupted Time Series#

Piecewise interrupted time series (segmented regression) models the outcome with separate slopes before and after the intervention, allowing the level and trend to change at the treatment point.

Piecewise Interrupted Time Series (Segmented Regression)

Cross-sectional methods#

Quasi-experimental designs that identify causal effects from cross-sectional assignment rules, instruments, or weighting.

Regression Discontinuity#

A quasi-experimental design where treatment assignment is determined by a cutoff point along a running variable (e.g., test score, age, income). The treatment effect is estimated by comparing outcomes just above and below the cutoff, assuming units near the cutoff are similar except for treatment status.

Sharp regression discontinuity with scikit-learn models

Sharp regression discontinuity with pymc models

Sharp regression discontinuity with pymc models

Drinking age with a scikit-learn model

Drinking age - Bayesian analysis

Donut Regression Discontinuity

Regression Kink Design#

A variation of regression discontinuity where treatment affects the slope (rate of change) of the outcome with respect to the running variable, rather than causing a discrete jump. The treatment effect is identified by a change in the slope at the cutoff point.

Regression kink design with pymc models

Regression kink design with pymc models

Instrumental Variables Regression#

A quasi-experimental design to estimate a treatment effect where there is a risk of confounding between the treatment and the outcome due to endogeneity. Instrumental variables help identify causal effects by using variables that affect treatment assignment but not the outcome directly.

Instrumental Variable Modelling (IV) with pymc models

Instrumental Variable Modelling (IV) with pymc models

Instrumental Regression and Justifying Instruments with pymc

Instrumental Regression and Justifying Instruments with pymc

Variable Selection Priors and Instrumental Variable Designs

Inverse Propensity Score Weighting#

A method for estimating causal effects by weighting observations by the inverse of their probability of receiving treatment (propensity score). This helps adjust for confounding by creating a pseudo-population where treatment assignment is independent of observed covariates.

Inverse Propensity Score Weighting with pymc

Inverse Propensity Score Weighting with pymc

The Paradox of Propensity Scores in Bayesian Inference

Workflow#

End-to-end workflows for running analyses, sensitivity checks, and reporting results.

Pipeline#

CausalPy’s pipeline API chains causal inference steps into a single, reproducible workflow.

Pipeline Workflow

Sensitivity Checks#

Sensitivity checks help assess whether a causal estimate is robust or fragile. CausalPy’s pipeline API makes sensitivity analysis a first-class step in reproducible workflows.

Sensitivity Checks in Pipeline Workflows

Reporting#

Every CausalPy experiment can produce a self-contained HTML report summarising the analysis.

HTML Report Generation