library(tidyverse)
library(Amelia)
library(broom)
# Use the africa dataset from Amelia
data(africa)
set.seed(1234)
imp_amelia <- amelia(x = africa, m = 5, cs = "country", ts = "year", logs = "gdp_pc", p2s = 0)
# Gather all the imputed datasets into one data frame and run a model on each
models_imputed_df <- bind_rows(unclass(imp_amelia$imputations), .id = "m") %>%
group_by(m) %>%
nest() %>%
mutate(model = data %>% map(~ lm(gdp_pc ~ trade + civlib, data = .)))
models_imputed_df
#> # A tibble: 5 x 3
#> m data model
#> <chr> <list> <list>
#> 1 imp1 <tibble [120 × 7]> <S3: lm>
#> 2 imp2 <tibble [120 × 7]> <S3: lm>
#> 3 imp3 <tibble [120 × 7]> <S3: lm>
#> 4 imp4 <tibble [120 × 7]> <S3: lm>
#> 5 imp5 <tibble [120 × 7]> <S3: lm>
# We want to see how GDP per capita varies with changes in civil liberties, so
# we create a new data frame with values for each of the covariates in the
# model. We include the full range of civil liberties (from 0 to 1) and the mean
# of trade.
new_data <- data_frame(civlib = seq(0, 1, 0.1),
trade = mean(africa$trade, na.rm = TRUE))
new_data
#> # A tibble: 11 x 2
#> civlib trade
#> <dbl> <dbl>
#> 1 0. 62.6
#> 2 0.100 62.6
#> 3 0.200 62.6
#> 4 0.300 62.6
#> 5 0.400 62.6
#> 6 0.500 62.6
#> 7 0.600 62.6
#> 8 0.700 62.6
#> 9 0.800 62.6
#> 10 0.900 62.6
#> 11 1.00 62.6
meld_predictions <- function(x) {
# x is a data frame with m rows and two columns:
#
# m .fitted .se.fit
# 1 1.05 0.34
# 2 1.09 0.28
# x ... ...
# Meld the fitted values using Rubin's rules
x_melded <- mi.meld(matrix(x$.fitted), matrix(x$.se.fit))
data_frame(.fitted = as.numeric(x_melded$q.mi),
.se.fit = as.numeric(x_melded$se.mi))
}
# We augment/predict using new_data in each of the imputed models, then we group
# by each of the values of civil liberties (so each value, like 0.1 and 0.2 has
# 5 values, 1 from each of the imputed models), and then we meld those 5
# predicted values into a single value with meld_predictions()
predict_melded <- data_frame(models = models_imputed_df$model) %>%
mutate(m = 1:n(),
fitted = models %>% map(~ augment(., newdata = new_data))) %>%
unnest(fitted) %>%
group_by(civlib) %>% # Group by each of the variables that you vary
nest(.fitted, .se.fit) %>%
mutate(fitted_melded = data %>% map(~ meld_predictions(.))) %>%
unnest(fitted_melded) %>%
mutate(ymin = .fitted + (qnorm(0.025) * .se.fit),
ymax = .fitted + (qnorm(0.975) * .se.fit))
# Plot!
ggplot(predict_melded, aes(x = civlib, y = .fitted)) +
geom_line(color = "blue") +
geom_ribbon(aes(ymin = ymin, ymax = ymax), alpha = 0.2, fill = "blue")
# How does this compare with a single, non-imputed model?
model_simple <- lm(gdp_pc ~ trade + civlib, data = africa)
simple_predict <- augment(model_simple, newdata = new_data) %>%
mutate(ymin = .fitted + (qnorm(0.025) * .se.fit),
ymax = .fitted + (qnorm(0.975) * .se.fit))
ggplot(predict_melded, aes(x = civlib, y = .fitted)) +
geom_line(color = "blue") +
geom_ribbon(aes(ymin = ymin, ymax = ymax), alpha = 0.2, fill = "blue") +
geom_line(data = simple_predict, color = "red") +
geom_ribbon(data = simple_predict, aes(ymin = ymin, ymax = ymax), alpha = 0.2, fill = "red")
