Andrew Gelman, Jennifer Hill, Aki Vehtari 2021-04-20
Tidyverse version by Bill Behrman.
Simple analysis of incentives data. See Chapter 19 in Regression and Other Stories.
# Packages
library(tidyverse)
library(rstanarm)
# Parameters
# Incentives data
file_incentives <- here::here("Incentives/data/incentives.csv")
# Common code
file_common <- here::here("_common.R")
#===============================================================================
# Run common code
source(file_common)Data from a meta-analysis of studies of incentives in sample surveys.
incentives <- read_csv(file_incentives)
incentives#> # A tibble: 62 x 5
#> rr_diff value prepay gift burden
#> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 3 1.24 1 0 0
#> 2 6 2.47 1 1 0
#> 3 9 14.7 0 0 1
#> 4 4 24.6 0 0 1
#> 5 6 43.1 0 0 1
#> 6 13 17.3 0 0 1
#> 7 10 21.6 0 0 1
#> 8 15 43.2 0 0 1
#> 9 16 10.3 0 0 1
#> 10 -1 5.65 0 0 1
#> # … with 52 more rows
Fit linear regression.
set.seed(447)
fit <-
stan_glm(
rr_diff ~ value + prepay + gift + burden,
data = incentives,
refresh = 0
)
print(fit, digits = 2)#> stan_glm
#> family: gaussian [identity]
#> formula: rr_diff ~ value + prepay + gift + burden
#> observations: 62
#> predictors: 5
#> ------
#> Median MAD_SD
#> (Intercept) 1.61 1.63
#> value 0.12 0.04
#> prepay 4.02 2.06
#> gift -5.37 2.23
#> burden 2.94 1.58
#>
#> Auxiliary parameter(s):
#> Median MAD_SD
#> sigma 6.02 0.56
#>
#> ------
#> * For help interpreting the printed output see ?print.stanreg
#> * For info on the priors used see ?prior_summary.stanreg
The above coefficients should not be directly interpreted as causal effects. Although incentive conditions were assigned randomly within each experiment, the differences in the conditions were not assigned at random between experiments. Thus, when comparing incentives implemented in different surveys, what we have is an observational study.