Explore and Compare Further

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🌟 Explore and Compare Further

Choice-level analysis opens the door to many new research questions that traditional profile-level analysis often overlooks. Below, we demonstrate how to estimate deeper quantities and compare subgroups effectively.

Depending on your objectives, you may want to reorganize the data in a projoint_data object. The helper function below is internal to the package, but you can call it explicitly in your script.”

projoint_data <- function(labels, data) {
  structure(
    list(labels = labels, data = data),
    class = "projoint_data"
  )
}

📦 Setup

We use the already wrangled and cleaned data out1_arranged.

data("out1_arranged")
out1_arranged$labels

## # A tibble: 24 × 4
##    attribute                     level                   attribute_id level_id  
##    <chr>                         <chr>                   <chr>        <chr>     
##  1 Housing Cost (Pre-tax Income) 15%                     att1         att1:leve…
##  2 Housing Cost (Pre-tax Income) 30%                     att1         att1:leve…
##  3 Housing Cost (Pre-tax Income) 40%                     att1         att1:leve…
##  4 Presidential Vote (2020)      50% Dem, 50% Rep        att2         att2:leve…
##  5 Presidential Vote (2020)      30% Dem, 70% Rep        att2         att2:leve…
##  6 Presidential Vote (2020)      70% Dem, 30% Rep        att2         att2:leve…
##  7 Racial Composition            50% White, 50% Nonwhite att3         att3:leve…
##  8 Racial Composition            75% White, 25% Nonwhite att3         att3:leve…
##  9 Racial Composition            90% White, 10% Nonwhite att3         att3:leve…
## 10 Racial Composition            96% White, 4% Nonwhite  att3         att3:leve…
## # ℹ 14 more rows

⚖️ Explore: Compare Trade-offs Directly

Example: Low Housing Costs vs. Low Crime Rates

Goal. Compare choices between two joint profiles:

Low housing cost but high violent‑crime rate, versus
High housing cost but low violent‑crime rate.

# 1) Data: keep only the two joint profiles of interest
data("out1_arranged")
d1 <- out1_arranged$data
d2 <- d1 |> 
  mutate(y1 = case_when(
    # Low housing cost, high crime
    att1 == "att1:level1" & att6 == "att6:level2" ~ 1,
    TRUE ~ 0
  ),
  y0 = case_when(
    # High housing cost, low crime
    att1 == "att1:level3" & att6 == "att6:level1" ~ 1,
    TRUE ~ 0
  )) |> 
  filter(y1 == 1 | y0 == 1)

# 2) Labels: rename only the two att1 levels to reflect the joint trade-offs
labels1 <- out1_arranged$labels
labels2 <- labels1 |> 
  mutate(level = case_when(level_id == "att1:level1" ~ "Housing Cost (Low)\nCrime Rate(High)", 
                           level_id == "att1:level3" ~ "Housing Cost (High)\nCrime Rate(Low)", 
                           TRUE ~ level_id))

(Optional) Sanity checks

d1 |> count(att1, att6)

## # A tibble: 6 × 3
##   att1        att6            n
##   <chr>       <chr>       <int>
## 1 att1:level1 att6:level1  1045
## 2 att1:level1 att6:level2  1069
## 3 att1:level2 att6:level1  1121
## 4 att1:level2 att6:level2  1034
## 5 att1:level3 att6:level1  1059
## 6 att1:level3 att6:level2  1072

d2 |> count(att1, att6) # only the two joint profiles remain

## # A tibble: 2 × 3
##   att1        att6            n
##   <chr>       <chr>       <int>
## 1 att1:level1 att6:level2  1069
## 2 att1:level3 att6:level1  1059

labels1 |> filter(attribute_id == "att1")

## # A tibble: 3 × 4
##   attribute                     level attribute_id level_id   
##   <chr>                         <chr> <chr>        <chr>      
## 1 Housing Cost (Pre-tax Income) 15%   att1         att1:level1
## 2 Housing Cost (Pre-tax Income) 30%   att1         att1:level2
## 3 Housing Cost (Pre-tax Income) 40%   att1         att1:level3

labels2 |> filter(attribute_id == "att1" & level_id %in% c("att1:level1", "att1:level3"))

## # A tibble: 2 × 4
##   attribute                     level                      attribute_id level_id
##   <chr>                         <chr>                      <chr>        <chr>   
## 1 Housing Cost (Pre-tax Income) "Housing Cost (Low)\nCrim… att1         att1:le…
## 2 Housing Cost (Pre-tax Income) "Housing Cost (High)\nCri… att1         att1:le…

Recreate a projoint_data object, set the QOI, and plot.

# 3) Build a new projoint_data object
pj_data_wrangled <- projoint_data("labels" = labels2, 
                                  "data" = d2)

# 4) Quantity of interest: Low vs High housing cost under the specified crime conditions (choice-level MM)
qoi <- set_qoi(
  .att_choose = "att1", 
  .lev_choose = "level1", # Low housing cost (with high crime in this subset)
  .att_notchoose = "att1", 
  .lev_notchoose = "level3" # High housing cost (with low crime in this subset)
)

# 5) Estimate and plot (horizontal layout)
out <- projoint(pj_data_wrangled, qoi)
plot(out)

🧩 Explore: Compare Multiple Levels Simultaneously

Example: Urban vs. Suburban Preferences

Goal. Collapse att7 into two buckets—City (levels 1–2) vs. Suburban (levels 5–6)—then re‑estimate and plot.

# 1) Data: collapse levels for att7
d1 <- out1_arranged$data
d2 <- d1 |>
  mutate(
    att7 = case_when(
      att7 %in% c("att7:level1", "att7:level2") ~ "att7:level7",  # City
      att7 %in% c("att7:level5", "att7:level6") ~ "att7:level8",  # Suburban
      TRUE ~ att7
    )
  )

# 2) Labels: create matching level IDs and readable names
labels1 <- out1_arranged$labels
labels2 <- labels1 |>
  mutate(
    level_id = case_when(
      level_id %in% c("att7:level1", "att7:level2") ~ "att7:level7",
      level_id %in% c("att7:level5", "att7:level6") ~ "att7:level8",
      TRUE ~ level_id
    ),
    level = case_when(
      level_id == "att7:level7" ~ "City",
      level_id == "att7:level8" ~ "Suburban",
      TRUE ~ level
    )
  ) |>
  distinct()

(Optional) Sanity checks

d1 |> count(att7)

## # A tibble: 6 × 2
##   att7            n
##   <chr>       <int>
## 1 att7:level1  1032
## 2 att7:level2  1047
## 3 att7:level3  1117
## 4 att7:level4  1092
## 5 att7:level5  1045
## 6 att7:level6  1067

d2 |> count(att7)

## # A tibble: 4 × 2
##   att7            n
##   <chr>       <int>
## 1 att7:level3  1117
## 2 att7:level4  1092
## 3 att7:level7  2079
## 4 att7:level8  2112

labels1 |> filter(attribute_id == "att7")

## # A tibble: 6 × 4
##   attribute     level                       attribute_id level_id   
##   <chr>         <chr>                       <chr>        <chr>      
## 1 Type of Place City, more residential area att7         att7:level1
## 2 Type of Place City, downtown area         att7         att7:level2
## 3 Type of Place Rural area                  att7         att7:level3
## 4 Type of Place Small town                  att7         att7:level4
## 5 Type of Place Suburban, only houses       att7         att7:level5
## 6 Type of Place Suburban, downtown area     att7         att7:level6

labels2 |> filter(attribute_id == "att7")

## # A tibble: 4 × 4
##   attribute     level      attribute_id level_id   
##   <chr>         <chr>      <chr>        <chr>      
## 1 Type of Place City       att7         att7:level7
## 2 Type of Place Rural area att7         att7:level3
## 3 Type of Place Small town att7         att7:level4
## 4 Type of Place Suburban   att7         att7:level8

Recreate a projoint_data object, set the QOI, and plot.

# 3) Build a new projoint_data object
pj_data_wrangled <- projoint_data("labels" = labels2, 
                                  "data" = d2)

# 4) Quantity of interest: City vs. Suburban (choice-level MM)
qoi <- set_qoi(
  .structure     = "choice_level",
  .att_choose    = "att7",
  .lev_choose    = "level7",  # City
  .att_notchoose = "att7",
  .lev_notchoose = "level8"   # Suburban
)

# 5) Estimate and plot (horizontal layout)
out <- projoint(pj_data_wrangled, qoi)
plot(out)

📊 Compare: Subgroup Differences

Choice-Level Subgroup Comparison: Party Differences

data("exampleData1")

outcomes <- c(paste0("choice", 1:8), "choice1_repeated_flipped")

df_D <- exampleData1 |> filter(party_1 == "Democrat") |> reshape_projoint(outcomes)
df_R <- exampleData1 |> filter(party_1 == "Republican") |> reshape_projoint(outcomes)
df_0 <- exampleData1 |> filter(party_1 %in% c("Something else", "Independent")) |> reshape_projoint(outcomes)

qoi <- set_qoi(
  .structure = "choice_level",
  .estimand = "mm",
  .att_choose = "att2",
  .lev_choose = "level3",
  .att_notchoose = "att2",
  .lev_notchoose = "level1"
)

out_D <- projoint(df_D, qoi)
out_R <- projoint(df_R, qoi)
out_0 <- projoint(df_0, qoi)

out_merged <- bind_rows(
  out_D$estimates |> mutate(party = "Democrat"),
  out_R$estimates |> mutate(party = "Republican"),
  out_0$estimates |> mutate(party = "Independent")
) |> filter(estimand == "mm_corrected")

# Plot

ggplot(out_merged, aes(y = party, x = estimate)) +
  geom_vline(xintercept = 0.5, linetype = "dashed", color = "gray") +
  geom_pointrange(aes(xmin = conf.low, xmax = conf.high)) +
  geom_text(aes(label = format(round(estimate, 2), nsmall = 2)), vjust = -1) +
  labs(y = NULL, x = "Choice-level Marginal Mean",
       title = "Preference for Democratic-majority areas") +
  theme_classic()

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