Results of Prospective Power Simulations

Loading Packages

We load the required packages and the data:

Show the packages used

library("groundhog")
packages <- c(
  "here",
  "tidyverse", 
  "knitr",
  "patchwork", 
  "mediocrethemes"
  # "vincentbagilet/mediocrethemes"
)

# groundhog.library(packages, "2022-11-28")
lapply(packages, library, character.only = TRUE)

set_mediocre_all(pal = "leo")

General Simulations

Loading Data

# load small sample simulation results
summary_evol_large <- readRDS(here("data", "simulations", "summary_evol_large.RDS")) %>%
  mutate(sample_size = "large")

# load large sample simulation results
summary_evol_small <- readRDS(here("data", "simulations", "summary_evol_small.RDS")) %>%
  mutate(sample_size = "small")

# prepare data for graphs
summary_evol_all <- summary_evol_large %>%
  bind_rows(summary_evol_small) %>%
  mutate(
    id_method = case_when(
      id_method == "IV" ~ "Instrumental Variable",
      id_method == "OLS" ~ "Standard Regression",
      id_method == "reduced_form" ~ "Reduced-Form",
      id_method == "RDD" ~ "Discontinuity Design"
    ),
    n_obs = n_days * n_cities
  ) %>%
  pivot_longer(
    cols = c("power", "type_m", "mean_f_stat"),
    names_to = "metrics",
    values_to = "stat_value"
  ) %>%
  mutate(
    metrics_name = case_when(
      metrics == "power" ~ "Statistical Power (%)",
      metrics == "type_m" ~ "Exaggeration Ratio",
      metrics == "mean_f_stat" ~ "F-Statistic",
    ),
    id_method_name = fct_relevel(
      id_method,
      "Standard Regression",
      "Reduced-Form",
      "Instrumental Variable"
    )
  )

Influence of Sample Size on Power and Exaggeration

Influence of Effect Size on Power and Exaggeration

Influence of Propotion of Exogenous Shocks on Power and Exaggeration

Influence of IV Strength on Power and Exaggeration

Influence of Number of cases on Power and Exaggeration

Metric	Non-Accidental Causes	Respiratory Causes	COPD Elderly
Statistical Power (%)	89.7	15.8	7.5
Exaggeration Ratio	1.0	2.4	5.9
F-Statistic	7980.3	8002.9	8045.9

Cases Studies

Public Transport Strikes Design

Air Pollution Alerts Design

Instrumental Variable Design