plot_mspe_ratio {tidysynth}

plot_mspe_ratio

Description

Plot the MSPE ratios for each case (observed and placebos). The ratio is used for inference in the synthetic control setup. The following plot ranks the RMSE ratio's in descending order.

Usage

plot_mspe_ratio(data, time_window = NULL)

Arguments

data

nested data of type tbl_df.

time_window

time window that the pre- and post-period values should be used to compute the MSPE ratio.

Details

Inferential statitics are generated by comparing the observed difference between the actual treated unit and its synthetic control to each placebo unit and its synthetic control. The rarity of the actual to the placebo is used to infer the likelihood of observing the effect.

Inference in this framework leverages the mean squared predictive error (MSPE) of the fit in the pre-period to the fit in the post-period as a ratio.

\frac{RMSE_{Post}}{RMSE_{Pre}}

The ratio captures the differences between the pre-intervention fit and the post-intervention divergence of the trend (i.e. the causal quantity). A good fit in the pre-period denotes that the observed and synthetic case tracked well together. Divergence in the post-period captures the difference brought about by the intervention in the two trends. Thus, when the ratio is high, we observe more of a difference between the two trends. If, however, the pre-period fit is poor, or there is not substantial divergence in the post-period, then this ratio amount will be smaller. A more detailed outline of inference within the synthetic control framework can be found in Adabie et al. 2010.

Value

ggplot object plotting the MSPE ratios by case.

Examples

# Smoking example data
data(smoking)

smoking_out <-
smoking %>%

# initial the synthetic control object
synthetic_control(outcome = cigsale,
                  unit = state,
                  time = year,
                  i_unit = "California",
                  i_time = 1988,
                  generate_placebos=TRUE) %>%

# Generate the aggregate predictors used to generate the weights
  generate_predictor(time_window=1980:1988,
                     lnincome = mean(lnincome, na.rm = TRUE),
                     retprice = mean(retprice, na.rm = TRUE),
                     age15to24 = mean(age15to24, na.rm = TRUE)) %>%

  generate_predictor(time_window=1984:1988,
                     beer = mean(beer, na.rm = TRUE)) %>%

  generate_predictor(time_window=1975,
                     cigsale_1975 = cigsale) %>%

  generate_predictor(time_window=1980,
                     cigsale_1980 = cigsale) %>%

  generate_predictor(time_window=1988,
                     cigsale_1988 = cigsale) %>%


  # Generate the fitted weights for the synthetic control
  generate_weights(optimization_window =1970:1988,
                   Margin.ipop=.02,Sigf.ipop=7,Bound.ipop=6) %>%

  # Generate the synthetic control
  generate_control()

# Plot the observed and synthetic trend
smoking_out %>% plot_mspe_ratio(time_window = 1970:2000)