sportscausal function

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

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

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

• y.exp: Response of experiment group, from pre-treatment to post-treatment
• y.con: Response of control group, from pre-treatment to post-treatment
• pre.period: Time period before the treatment
• post.period: Time period during the treatment
• is.plot: If is.plot = TRUE, by default, a pdf containing summary figures will be returned to the current working directory as getwd()
• model.select: Model used to predict the time series without treatment. If model.select = "AIC", by default, the ARIMA model using AIC selection would be applied. If model.select = "CV", the ARIMA model using cross validation would be applied. If model.select = "lstm", the Long Short-Term Memory model would be applied
• max.p: The max number of autoregressive terms in ARIMA model, by default max.p = 3
• max.d: The max number of nonseasonal differences needed for stationarity in ARIMA model, by default max.d = 3
• max.q: The max number of lagged forecast errors in the prediction equation in ARIMA model, by default max.p = 3
• feature: The covariate matrix associated with the response. By default, feature = NULL but can be non-null when model.select = "lstm"

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.

Returns

• est.treatment: Information of treatment effect estimation, containing point estimation, confidence interval and p-value

• est.spillover: Information of spillover effect estimation, containing point estimation, confidence interval and p-value

References

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

Author(s)

Zihao Zheng and Feiyu Yue

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"