In jrnold/marfx: Yet Another Marginal Effects Package

library("marfx")
library("dplyr")
library("ggplot2")
library("purrr")

Conflicing Interests and Trade

Example from Kastner (2007) replicated in Berry et. al (2012).

$$ \begin{aligned}[t] \text{Trade} &= \beta_0 + \beta_C \text{Conflict} + \beta_B \text{(Trade Barriers)} \ & + \beta_{BC} (\text{(Trade Barriers)} \times \text{Conflict}) \ & + \beta Z + \varepsilon \end{aligned} $$

Xenophobic Voting in Russia

Alexseev (2006) ``Ballot-Box Vigilantism: Ethnic Population Shifts and Xenophobic Voting in Post-Soviet Russia.'' Political Behavior replicated in Berry et. al (2012).

Alexseev (2006) examines how changes in ethnic composition of Russian regions affects the vote share of the Russian nationalist Zhirinovsky Bloc in the 2003 elections of the Russian State Duma.

The model is, $$ \begin{aligned}[t] \text{(Xenophobic Voing)} &= \beta_0 + \beta_{S} \text{(Slavic Share)} \ &+ \beta_{N} \Delta \text{(non-Slavic Share)} \ &+ \beta_{SN} (\text{(Slavic Share)} \times \Delta \text{(non-Slavic Share)} \ &+ \beta Z + \varepsilon \end{aligned} $$ where $Z$ are control variables.

data("alexseev", package = "marfx")
mod1 <- lm(xenovote ~ slavicshare * changenonslav +
     inc9903 + eduhi02 + unemp02 + apt9200 + vsall03 + brdcont, 
   data = alexseev)

Note that even though the alexseev dataset includes a variable slavicshare_changenonslav which is the interaction between Slavic share and $\Delta$ non-Slavic share, this model specifies the interaction in the formula. This makes it much simpler for analysis since the lm object will contain information about the relationship between the variables and the terms in the regression, so in the analysis we will only need to specify changes in slavicshare or changenonslav and the functions can infer that the interaction will need to change. If instead, the varible slavicshare_changenonslav was used, the lm object would not know that the variable was an interaction between slavicshare and changenonslav and we would need to be careful to always change both the variable of interest and the interaction when considering any marginal or partial effects.

Berry et. al (2012, p. 14) present two marginal effect plots. The marginal effect of Slavic share on xenophobic voting, and the marginal effect of $\Delta$ non-Slavic share on xenophobic voting.

.data <- cross_d(list(changenonslav =
                   seq(min(alexseev$changenonslav),
                       max(alexseev$changenonslav),
                       length.out = 30),
                 slavicshare = mean(alexseev$slavicshare),
                 inc9903 = mean(alexseev$inc9903),
                 eduhi02 = mean(alexseev$eduhi02),
                 unemp02 = mean(alexseev$unemp02),
                 apt9200 = mean(alexseev$apt9200),
                 vsall03 = mean(alexseev$vsall03),
                 brdcont = FALSE))

.data <- cbind(.data, mfx(mod1, data = .data, "slavicshare"))

ggplot() +
  geom_ribbon(data = .data, mapping = aes(x = changenonslav, 
                                          ymin = conf.low, 
                                          ymax = conf.high),
              alpha = 0.3) +
  geom_line(data = .data, mapping = aes(x = changenonslav, y = estimate)) +
  geom_rug(data = alexseev, mapping = aes(x = changenonslav)) +
  geom_hline(yintercept = 0, color = "gray") + 
  scale_x_continuous(name = expression(paste(Delta, "non-Slavic Share")), breaks = seq(-2, 12, by = 2)) +
  scale_y_continuous(name = "Marginal Effect of Slavic Share",
                     breaks = seq(-.05, .25, by = .05)) +
  theme_minimal() +
  theme(panel.grid = element_blank())

The marginal effects of $\Delta$ non-Slavic Share on Xenophobic voting:

.data <- cross_d(list(slavicshare =
                   seq(min(alexseev$slavicshare),
                       max(alexseev$slavicshare),
                       length.out = 30),
                 changenonslav = mean(alexseev$changenonslav),
                 inc9903 = mean(alexseev$inc9903),
                 eduhi02 = mean(alexseev$eduhi02),
                 unemp02 = mean(alexseev$unemp02),
                 apt9200 = mean(alexseev$apt9200),
                 vsall03 = mean(alexseev$vsall03),
                 brdcont = FALSE))

.data <- cbind(.data, mfx(mod1, data = .data, "changenonslav"))

ggplot() +
  geom_ribbon(data = .data, mapping = aes(x = slavicshare,
                                          ymin = estimate - 1.96 * std.error, 
                                          ymax = estimate + 1.96 * std.error),
              alpha = 0.3) +
  geom_line(data = .data, mapping = aes(x = slavicshare, y = estimate)) +
  geom_rug(data = alexseev, mapping = aes(x = slavicshare)) +
  geom_hline(yintercept = 0, color = "gray") + 
  scale_x_continuous(name = "Slavic Share", breaks = seq(30, 100, by = 10)) +
  scale_y_continuous(name = expression(paste("Marginal Effect of", Delta, "non-Slavic Share")),
                     breaks = seq(-1, .5, by = .25)) +
  theme_minimal() +
  theme(panel.grid = element_blank())

By using the std.error, this plot has smoother confidence intervals than the one using conf.low and conf.high, which are generated from the quantiles of the simulations.

TODO: Add clustered standard errors.

To summarize the effect of Slavic Share and $\Delta$ non-Slavic Share on xenophobic vote share we can calculate the average marginal effects of these variables,

variables <- c("slavicshare" = "Slavic Share",
               "changenonslav" = "Change non-Slavic Share")
.data <- list()
for (i in seq_along(variables)) {
  .data[[i]] <-
    amfx(mod1, names(variables)[i], data = alexseev) %>%
    mutate(variable = names(variables)[i],
           description = variables[i])
}
.data <- bind_rows(.data)

ggplot(.data, aes(x = description, y = estimate, ymin = conf.low, ymax = conf.high)) +
  geom_hline(yintercept = 0, colour = "gray") +
  geom_pointrange() +
  coord_flip() +
  scale_x_discrete("") +
  scale_y_continuous("Average Marginal Effects") +
  theme_minimal() +
  theme(panel.grid = element_blank())

TODO What to do if interactions are specified in the data rather than the formula.

Logit

A logit model of voting turnout.

library("Zelig")
data("turnout", package = "Zelig")
mod_turnout <- glm(vote ~ poly(age, 2) + race + educate, data = turnout, family = binomial)
summary(mod_turnout)

Calculate the average marginal effect of age,

amfx(mod_turnout, "age", data = turnout)

the average marginal effect of all variables,

data.frame(variable = c("age", "race", "educate")) %>%
  group_by(variable) %>%
  do({
    amfx(mod_turnout, .$variable, data = turnout)
  })

Calculate the average marginal effects of age at its mean value, holding the other values at their means and race = "white",

summarize(turnout, age = mean(age), educate = mean(educate)) %>%
  mutate(race = "white") %>%
  mfx(mod_turnout, "age", data = .)

Calculate the marginal effects of age at each decade, 20 to 80, holding educate at its mean, and setting race to "white":

data_frame(age = seq(20, 80, by = 10)) %>%
  mutate(race = "white",
         educate = mean(turnout$educate)) %>%
  bind_cols(., mfx(mod_turnout, "age", data = .)) %>%
  ggplot(aes(x = age, y = estimate,
             ymin = estimate - 2 * std.error, ymax = estimate + 2 * std.error)) +
  geom_ribbon(alpha = 0.3) +
  geom_line()

Calculate the average marginal effects of each variable holding the others at representative values within each group

mfx(mod_turnout, "age", data = summarize(group_by(turnout, race),
                                         age = mean(age),
                                         educate = mean(educate)))

Average finite difference effect of moving from 20 to 80,

afdfx(mod_turnout,
      data1 = mutate(turnout, age = 20),
      data2 = mutate(turnout, age = 80))

afdfx(mod_turnout,
      data1 = mutate(turnout, race = "white"),
      data2 = mutate(turnout, race = "other"))

jrnold/marfx documentation built on May 20, 2019, 1:03 a.m.