Package 'bsynth'

Title: Bayesian Synthetic Control
Description: Implements the Bayesian Synthetic Control method for causal inference in comparative case studies. This package provides tools for estimating treatment effects in settings with a single treated unit and multiple control units, allowing for uncertainty quantification and flexible modeling of time-varying effects. The methodology is based on the paper by Vives and Martinez (2022) <doi:10.48550/arXiv.2206.01779>.
Authors: Ignacio Martinez [aut, cre] , Jaume [aut]
Maintainer: Ignacio Martinez <[email protected]>
License: Apache License 2.0
Version: 1.0
Built: 2024-09-24 06:54:07 UTC
Source: CRAN

Help Index

The 'bsynth' package.

Description

Provides causal inference with a Bayesian synthetic control method.

Author(s)

Maintainer: Ignacio Martinez [email protected] (ORCID)

Authors:

References

Stan Development Team (2020). RStan: the R interface to Stan. R package version 2.21.2. https://mc-stan.org

See Also

Useful links:

Get Parameter Estimates in Long Format

Description

Helper function to get the long dataset of draws given a stan fit object.

Usage

.get_par_long(fit, par)

Arguments

fit

Stan object with the fitted model.
par

Variable to do the long table for.expand_more

Value

A tibble containing the parameter estimates in long format.

Returns Data Frame Ready for Plotting with Confidence Intervals

Description

This function processes data frames containing synthetic and observed outcomes, calculates confidence intervals for the synthetic outcomes, and returns a combined data frame suitable for plotting the results.

Usage

.get_plot_df(y_synth_draws, pre_data, post_data, time, outcome, ci = 0.75)

Arguments

y_synth_draws

A data frame containing draws from the Stan fit object.
pre_data

A data frame with data before the intervention.
post_data

A data frame with data after the intervention.
time

The name of the time period variable (as a string).
outcome

The name of the outcome variable (as a string).
ci

The width of the credible confidence interval (default: 0.75).

Value

A data frame containing:

  • time: The time period.

  • outcome: The observed outcome.

  • y_synth: The mean synthetic outcome.

  • LB: The lower bound of the confidence interval for the synthetic outcome.

  • UB: The upper bound of the confidence interval for the synthetic outcome.

  • tau: The difference between the observed and synthetic outcomes.

  • tau_LB: The lower bound of the confidence interval for tau.

  • tau_UB: The upper bound of the confidence interval for tau.

Prepare Data Frame for Plotting with Multiple Treated Units

Description

This function processes data for multiple treated units, calculating synthetic outcomes, confidence intervals, and treatment effects. It combines this information into a data frame suitable for plotting the results.

Usage

.get_plot_df2(y_synth_draws, data, treated_ids, id, time, outcome, ci = 0.75)

Arguments

y_synth_draws

A data frame containing synthetic outcome draws for each treated unit and time period.
data

A data frame with the original data, including outcomes for treated units.
treated_ids

A vector of identifiers for the treated units.
id

The name of the variable in data that identifies units (as a string).
time

The name of the time period variable (as a string).
outcome

The name of the outcome variable (as a string).
ci

The width of the credible confidence interval (default: 0.75).

Value

A data frame containing:

  • time: The time period.

  • id: The unit identifier (including "Average" for the average treatment effect).

  • outcome: The observed outcome (for treated units).

  • y_synth: The mean synthetic outcome (for treated units and the average).

  • LB: The lower bound of the confidence interval for the synthetic outcome.

  • UB: The upper bound of the confidence interval for the synthetic outcome.

  • tau: The treatment effect (difference between observed and synthetic outcomes).

  • tau_LB: The lower bound of the confidence interval for the treatment effect.

  • tau_UB: The upper bound of the confidence interval for the treatment effect.

Get Synthetic Draws in Tidy Format for Single Treated Unit

Description

This internal helper function extracts synthetic draws from a Stan fit object, combines them with observed outcome data, and returns a tidy data frame suitable for further analysis or plotting. This function is specifically designed for scenarios with a single treated unit.

Usage

.get_synth_draws(fit, pre_data, post_data, time, outcome)

Arguments

fit

A Stan fit object containing the model results.
pre_data

A data frame with outcome data before the intervention.
post_data

A data frame with outcome data after the intervention.
time

The name of the time period variable (as a string).
outcome

The name of the outcome variable (as a string).

Value

A data frame containing:

  • draw: The index of the synthetic draw.

  • time: The time period.

  • y_synth: The synthetic outcome for the given draw and time period.

  • outcome: The observed outcome for the given time period.

Get Synthetic Draws in Tidy Format for Single Treated Unit (Predictor Match Model)

Description

This internal helper function extracts synthetic draws from a Stan fit object generated by a predictor match model. It combines these draws with observed outcome data and returns a tidy data frame suitable for analysis or plotting. It specifically works with variable definitions from the predictor match model.

Usage

.get_synth_draws_predictor_match(fit, pre_data, post_data, time, outcome)

Arguments

fit

A Stan fit object containing the model results.
pre_data

A data frame with outcome data before the intervention.
post_data

A data frame with outcome data after the intervention.
time

The name of the time period variable (as a string).
outcome

The name of the outcome variable (as a string).

Value

A data frame containing:

  • draw: The index of the synthetic draw.

  • time: The time period.

  • y_synth: The synthetic outcome for the given draw and time period.

  • outcome: The observed outcome for the given time period.

Get Synthetic Draws in Tidy Format for Multiple Treated Units (3D Array)

Description

This internal helper function extracts synthetic draws from a Stan fit object where the draws are stored in a 3D array. It handles multiple treated units and combines the draws with observed outcome data, returning a tidy data frame suitable for analysis or plotting.

Usage

.get_synth_draws3d(fit, data, id, treated_ids, time, outcome, intervention)

Arguments

fit

A Stan fit object containing the model results.
data

A data frame with the input data, including outcome, time, and unit identifier.
id

The name of the variable in data that identifies units (as a string).
treated_ids

A vector of identifiers for the treated units.
time

The name of the time period variable (as a string).
outcome

The name of the outcome variable (as a string).
intervention

The name of the variable in data that indicates the intervention time (as a string).

Value

A data frame containing:

  • draw: The index of the synthetic draw.

  • id: The identifier of the treated unit.

  • time: The time period.

  • y_hat: The synthetic outcome for the given draw, unit, and time period.

Convert Data to Wide Format

Description

This internal helper function transforms data from a long format, where each row represents an observation for a specific unit and time, to a wide format, where each row represents a time period and each column represents a unit's outcome. It specifically focuses on separating treated and untreated units.

Usage

.makeWide(data, id, time, outcome, treatment)

Arguments

data

A data frame containing the input data.
id

The name of the variable in data that identifies units (as a string).
time

The name of the time period variable (as a string).
outcome

The name of the outcome variable (as a string).
treatment

The name of the variable in data that indicates treatment status (as a string).

Value

A data frame in wide format, where each row corresponds to a time period, and columns include the time variable, the treatment indicator, and the outcome values for each treated unit and all untreated units.

Plot Treatment Effect Estimate

Description

This internal helper function creates a plot to visualize the estimated treatment effect over time. It allows for faceting by a specified variable and optional subsetting of units to include in the plot.

Usage

.plot_tau(data, x, y, ymin, ymax, xintercept, facet, id, subset = NULL)

Arguments

data

A data frame containing the data to be plotted.
x

The name of the x-axis variable (typically the time period) (as a string).
y

The name of the y-axis variable (typically the treatment effect) (as a string).
ymin

The name of the variable containing the lower bound of the confidence interval (as a string).
ymax

The name of the variable containing the upper bound of the confidence interval (as a string).
xintercept

The time point of the intervention to be marked with a vertical dashed line.
facet

(Optional) The name of the variable to facet the plot by (as a string).
id

The name of the variable identifying the units (as a string).
subset

(Optional) A vector specifying a subset of units to include in the plot. If NULL, all units are included.

Value

A ggplot object displaying the treatment effect plot.

Create a Bayesian Synthetic Control Object Using Panel Data

Description

A Bayesian Factor Model has raw data and draws from the posterior distribution. This is represented by an R6 Class.

Code and theory based on Pinkney 2021.

public methods:

  • initialize() initializes the variables and model parameters

  • fit() fits the stan model and returns a fit object

  • updateWidth updates the width of the credible interval

  • placeboPlot generates a counterfactual placebo plot

  • effectPlot returns a plot of the treatment effect over time

  • summarizeLiftreturns descriptive statistics of the lift estimate

  • biasDraws returns a plot of the relative bias in a LFM

  • liftDraws returns a plot of the posterior lift distribution

  • liftBias returns a plot of the relative bias given a lift offset

Value

vizdraws object with the relative bias with offset.

Active bindings

timeTiles

ggplot2 object that shows when the intervention happened.

plotData

tibble with the observed outcome and the counterfactual data.

interventionTime

returns the intervention time period.

synthetic

ggplot2 object that shows the observed and counterfactual outcomes over time.

Methods

Public methods

Method new()

Create a new bayesianFactor object.

Usage
bayesianFactor$new(
  data,
  time,
  id,
  treated,
  outcome,
  ci_width = 0.75,
  covariates
)
Arguments
data

Long data.frame object with fields outcome, time, id, and treatment indicator.

time

Name of the variable in the data frame that

id

Name of the variable in the data frame that identifies the units (e.g. country, region etc).

treated

Name of the variable in the data frame that contains the treatment assignment of the intervention.

outcome

Name of the outcome variable.

ci_width

Credible interval's width. This number is in the (0,1) interval.

covariates

Dataframe with a column for id and the other columns Defaults to NULL if no covariates should be included in the model.

Details

params described in the data structure section of the documentation of the R6 class at the top of the file.

Returns

A new bayesianFactor object.

Method fit()

Fit Stan model.

Usage
bayesianFactor$fit(L = 8, ...)
Arguments
L

Number of factors.

...

other arguments passed to rstan::sampling().

Method updateWidth()

Update the width of the credible interval.

Usage
bayesianFactor$updateWidth(ci_width = 0.75)
Arguments
ci_width

New width for the credible interval. This number should be in the (0,1) interval.

Method summarizeLift()

summarizeLift returns descriptive statistics of the lift estimate.

Usage
bayesianFactor$summarizeLift()

Method effectPlot()

effectPlot returns ggplot2 object that shows the effect of the intervention over time.

Usage
bayesianFactor$effectPlot()

Method liftDraws()

Plots lift.

Usage
bayesianFactor$liftDraws(from, to, ...)
Arguments
from

First period to consider when calculating lift. If infinite, set to the time of the intervention.

to

Last period to consider when calculating lift. If infinite, set to the last period.

...

other arguments passed to vizdraws::vizdraws().

Returns

vizdraws object with the posterior distribution of the lift.

Method liftBias()

Plot bias magnitude in terms of lift for period (firstT, lastT)

Usage
bayesianFactor$liftBias(firstT, lastT, offset, ...)
Arguments
firstT

Start of the time period to compute relative bias over. Must be after the intervention.

lastT

End of the time period to compute relative bias over. Must be after the intervention. over. They must be after the intervention.

offset

Target lift %.

...

other arguments passed to vizdraws::vizdraws().

Method biasDraws()

Plots relative upper bias / tau for a time period (firstT, lastT).

Usage
bayesianFactor$biasDraws(small_bias = 0.3, firstT, lastT)
Arguments
small_bias

Threshold value for considering the bias "small".

firstT, lastT

Time periods to compute relative bias over, they must after the intervention.

Returns

vizdraw object with the posterior distribution of relative bias. Bias is scaled by the time periods.

Method clone()

The objects of this class are cloneable with this method.

Usage
bayesianFactor$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Create a Bayesian Synthetic Control Object Using Panel Data

Description

A Bayesian Synthetic Control has raw data and draws from the posterior distribution. This is represented by an R6 Class.

public methods:

  • initialize() initializes the variables and model parameters

  • fit() fits the stan model and returns a fit object

  • updateWidth updates the width of the credible interval

  • placeboPlot generates a counterfactual placebo plot

  • effectPlot returns a plot of the treatment effect over time

  • summarizeLiftreturns descriptive statistics of the lift estimate

  • biasDraws returns a plot of the relative bias in a LFM

  • liftDraws returns a plot of the posterior lift distribution

  • liftBias returns a plot of the relative bias given a lift offset Data structure:

Value

vizdraws object with the relative bias with offset.

Active bindings

timeTiles

ggplot2 object that shows when the intervention happened.

plotData

returns tibble with the observed outcome and the counterfactual data.

interventionTime

returns intervention time period (e.g., year) in which the treatment occurred.

synthetic

returns ggplot2 object that shows the observed and counterfactual outcomes over time.

checks

returns MCMC checks.

lift

draws from the posterior distribution of the lift.

Methods

Public methods

Method new()

Create a new bayesianSynth object.

Usage
bayesianSynth$new(
  data,
  time,
  id,
  treated,
  outcome,
  ci_width = 0.75,
  gp = FALSE,
  covariates = NULL,
  predictor_match = FALSE,
  predictor_match_covariates0 = NULL,
  predictor_match_covariates1 = NULL,
  vs = NULL
)
Arguments
data

Long data.frame object with fields outcome, time, id, and treatment indicator.

time

Name of the variable in the data frame that identifies the time period (e.g. year, month, week etc).

id

Name of the variable in the data frame that identifies the units (e.g. country, region etc).

treated

Name of the variable in the data frame that contains the treatment assignment of the intervention.

outcome

Name of the outcome variable.

ci_width

Credible interval's width. This number is in the (0,1) interval.

gp

Logical that indicates whether or not to include a Gaussian Process as part of the model.

covariates

Data.frame with time dependent covariates for for each unit and time field. Defaults to NULL if no covariates should be included in the model.

predictor_match

Logical that indicates whether or not to run the matching version of the Bayesian Synthetic Control. This option can not be used with gp, covariates or multiple treated units.

predictor_match_covariates0

data.frame with time independent covariates on each row and column indicating the control unit names (dim k x J+1).

predictor_match_covariates1

Vector with time independent covariates for the treated unit (dim k x 1).

vs

Vector of weights for the importance of the predictors used in creating the synthetic control. Defaults to equal weight for all predictors.

Returns

A new bayesianSynth object.

Method fit()

Fit Stan model.

Usage
bayesianSynth$fit(...)
Arguments
...

other arguments passed to rstan::sampling().

Method updateWidth()

Update the width of the credible interval.

Usage
bayesianSynth$updateWidth(ci_width = 0.75)
Arguments
ci_width

New width for the credible interval. This number should be in the (0,1) interval.

Method summarizeLift()

returns descriptive statistics of the lift estimate.

Usage
bayesianSynth$summarizeLift()

Method effectPlot()

effect ggplot2 object that shows the effect of the intervention over time.

Usage
bayesianSynth$effectPlot(facet = TRUE, subset = NULL)
Arguments
facet

Boolean that is TRUE if we want to divide the plot for each unit.

subset

Set of units to use in the effect plot.

Method placeboPlot()

Plot placebo intervention.

Usage
bayesianSynth$placeboPlot(periods, ...)
Arguments
periods

Positive number of periods for the placebo intervention.

...

other arguments passed to rstan::sampling().

Returns

ggplot2 object for placebo treatment effect.

Method biasDraws()

Plots relative upper bias / tau for a time period (firstT, lastT).

Usage
bayesianSynth$biasDraws(small_bias = 0.3, firstT, lastT)
Arguments
small_bias

Threshold value for considering the bias "small".

firstT

Start of the time period to compute relative bias over. Must be after the intervention.

lastT

End of the time period to compute relative bias over. Must be after the intervention.

Returns

vizdraw object with the posterior distribution of relative bias. Bias is scaled by the time periods.

Method liftDraws()

Plots lift.

Usage
bayesianSynth$liftDraws(from, to, ...)
Arguments
from

First period to consider when calculating lift. If infinite, set to the time of the intervention.

to

Last period to consider when calculating lift. If infinite, set to the last period.

...

other arguments passed to vizdraws::vizdraws().

Returns

vizdraws object with the posterior distribution of the lift.

Method liftBias()

Plot Bias magnitude in terms of lift for period (firstT, lastT) pre_MADs / y0 relative to lift thresholds.

Usage
bayesianSynth$liftBias(firstT, lastT, offset, ...)
Arguments
firstT

start of the time period to compute relative bias over. They must be after the intervention.

lastT

end of the Time period to compute relative bias over. They must be after the intervention.

offset

Target lift %.

...

other arguments passed to vizdraws::vizdraws().

Method weightDraws()

Plot implicit weight distribution across draws.

Usage
bayesianSynth$weightDraws()
Returns

ggplot object with weight distribution per unit.

Method weightCorr()

Plots correlations between weights across draws.

Usage
bayesianSynth$weightCorr()
Returns

ggplot heatmap object with correlations.

Method clone()

The objects of this class are cloneable with this method.

Usage
bayesianSynth$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Time Tiles Plot of Intervention Impact

Description

This function creates a time tiles plot visualizing when and which units are affected by an intervention. Each tile represents a unit at a specific time point, with the color indicating the treatment status.

Usage

time_tiles(data, time, id, status)

Arguments

data

A data frame containing the input data.
time

The name of the time period variable (as a string).
id

The name of the unit identifier variable (as a string).
status

The name of the variable that identifies the treatment status (as a string).

Value

A ggplot object displaying the time tiles plot.