Spillover Time Series Causal Inference

Description

A time series causal inference model for Randomized Controlled Trial (RCT) under spillover effect. 'SPORTSCausal' (Spillover Time Series Causal Inference) separates treatment effect and spillover effect from given responses of experiment group and control group by predicting the response without treatment. It reports both effects by fitting the Bayesian Structural Time Series (BSTS) model based on 'CausalImpact', as described in Brodersen et al. (2015) <doi:10.1214/14-AOAS788>.

Details

The DESCRIPTION file:

Index of help topics:

SPORTSCausal-package    Spillover Time Series Causal Inference
ad_cost                 Advertising cost: a real experimental data
                        under spillover effect
sportscausal            Time series causal inference of Randomized
                        Controlled Trial (RCT) under spillover effect

Author(s)

Zihao Zheng and Feiyu Yue

Maintainer: Feiyu Yue <yuefyopals@gmail.com>

References

Brodersen et al. Inferring causal impact using Bayesian structural time-series models. Annals of Applied Statistics, 2015

See Also

http://google.github.io/CausalImpact/CausalImpact.html

Examples

## For more detail of the package, try ?sportscausal and ?ad_cost

Advertising cost: a real experimental data under spillover effect

Description

This dataset comes from an A/Btest, which is to evaluate how a newly-proposed algorithm will affect the cost of advertising. Assuming that the bidding environment of an advertising market is stable in a short period of time, there will be no net increase or decrease of cost. When a treatment is applied, the mutual interference between the experiment group and the control group can not be ignored. For example, the difference in cost between the experiment group and the control group might not only come from the increase of experiment group, caused by treatment effect, but also from the potential decrease in control group. That is the typical situation for spillover causal inference to be implemented.

Usage

data("ad_cost")

Format

A data frame with 49 observations on the following 3 variables.

y.exp

A numeric vector of responses in experiment group.

y.con

A numeric vector of responses in control group.

time

A numeric vector indicating time period before/after the treatment, time = 1 represents post treatment period.

Details

This data has been linearly transformed for confidential issue.

Examples

### load data

data(ad_cost)

### define variables and visualize

y.exp = ad_cost$y.exp

y.con = ad_cost$y.con

plot(y.exp, col = "red", type = "l", 
     xlab = "time", ylab = "response")

lines(y.con, col = "blue")

### fit the model and return treatment/spillover effect

# notice that day-34 is the first day of treatment

fit = sportscausal(y.exp = y.exp, y.con = y.con,
                   pre.period = c(1:33), post.period = c(34:49), is.plot = FALSE)

fit$est.treatment

fit$est.spillover

Time series causal inference of Randomized Controlled Trial (RCT) under spillover effect

Description

'SPORTSCausal' produces treatment effect and spillover effect estimation from responses of experiment group and control group.

Usage

sportscausal(y.exp, y.con, pre.period, post.period, is.plot = TRUE, 
  model.select = "AIC", max.p = 3, max.d = 3, max.q = 3, feature = NULL)

Arguments

Details

In the presense of spillover effect, the response of control group could be interferenced by the treatment. In order to seprate the treatment effect and spillover effect, sportscausal uses ARIMA model or LSTM model to predict the response behavior without treatment. The point estimator and significance of both effect follow using Bayesian Structrual Time Series (BSTS) model.

Value

Author(s)

Zihao Zheng and Feiyu Yue

References

Brodersen et al. Inferring causal impact using Bayesian structural time-series models. Annals of Applied Statistics, 2015

See Also

See also ?ad_cost

Examples

  ## simulate data
  
  set.seed(1)

  y0 = 100 + arima.sim(model = list(ar = 0.3), n = 125)

  y.con = y0 + rnorm(125)
  y.con[101:125] = y.con[101:125] - 10 ## -10 as spillover effect

  y.exp = y0 + rnorm(125)
  y.exp[101:125] = y.exp[101:125] + 10 ## 10 as treatment effect

  pre.period = c(1:100)
  post.period = c(101:125)

  ## visualize

  plot(y.exp, col = "red", type = "l", ylab = "response",
     ylim = c(80, 120))

  lines(y.con, col = "blue")

  abline(v = 101, col = "grey", lty = 2, lwd = 2)

  legend("topleft", legend = c("exp", "con"), col = c("red", "blue"),
       cex = 1, lty = 1)

  ## try SPORTSCausal with ARIMA + AIC

  fit.aic = sportscausal(y.exp = y.exp, y.con = y.con, 
            pre.period = pre.period, post.period = post.period, is.plot = FALSE)

  fit.aic$est.treatment
  fit.aic$est.spillover

  ## you can also try model.select = "CV" or "lstm"