analysis.Rmd

---
title: "WIYS Code"
author: "Rome Thorstenson"
date: "`r Sys.Date()`"
output: html_document
---

output:
  html_document:
    theme: journal
    highlight: tango
    toc: true
    toc_float: true
---

```{r}
version$version.string
# R version 4.3.2 (2023-10-31)
```

```{r setup, include=FALSE}
# This chunk sets global options for the entire document.
# These settings ensure a clean final report by hiding code execution details.
knitr::opts_chunk$set(
  echo = FALSE,      # Don't show the code itself in the output
  message = FALSE,   # Suppress messages generated by packages
  warning = FALSE,   # Suppress warning messages
  fig.width = 8,     # Set a default figure width
  fig.height = 6,    # Set a default figure height
  fig.align = "center" # Center-align all plots
)
```

```{r load-packages, include=FALSE}
# This chunk loads all necessary R packages for the analysis.
# The loading order is structured to prevent function conflicts.

# To install missing packages, uncomment and run the following line once:
# install.packages(c("tidyverse", "sf", "stargazer", "glmmTMB", "broom", "here", "skimr", "reshape2", "patchwork"))

# General utility and workflow packages
library(here)
library(skimr)
library(reshape2)
library(patchwork)

# Spatial analysis packages
library(sf)

# Core packages for data manipulation and visualization
library(tidyverse)

# Output and reporting packages
library(stargazer)
library(broom)
library(latex2exp)
```

```{r}
# options(citation.bibtex.max=999)
# citation("tidyverse")
# citation("patchwork")
# citation("sf")
# citation("stargazer")
# citation("fitdistrplus")
# citation("nortest")
```

# 1. Data Preparation

This section loads and preprocesses the datasets required for the analysis. We begin by importing the primary geospatial layers for Chicago.

```{r}
root_path <- file.path("GithubRepos", "WIYS", "camera-ready", "data")
```

## 1.1. Load Geospatial Data

We load the shapefiles for Chicago's Community Areas and Census Tracts. Both datasets are transformed to the WGS 84 coordinate reference system (CRS), identified by the EPSG code `4326`. This is the standard CRS for global latitude and longitude data.

```{r load-spatial-data}
# Define file paths using here() to ensure they work regardless of the
# project's location on the filesystem.
path_comm_areas <- here::here(root_path, "chicago-community-areas.geojson")
path_census_tracts <- here::here(root_path, "chicago-census-tracts.geojson")

# Read and transform the Community Area boundaries.
# The pipe |> sequences operations: read the file, then transform the CRS.
comm_area_geo <- st_read(path_comm_areas) |>
  st_transform(4326) # EPSG:4326 is the standard WGS 84 CRS

# Read and transform the Census Tract boundaries.
ct_geo <- st_read(path_census_tracts) |>
  st_transform(4326)
```

## 1.2. Initial Data Verification

To confirm that the spatial data has loaded correctly, we can create a simple map overlaying the two layers. This plot shows the census tracts (thin red lines) nested within the community areas (blue polygons).

```{r preview-spatial-data, fig.cap="Map of Chicago Community Areas and Census Tracts."}
# Generate a plot to visually inspect the spatial layers.
ggplot() +
  # Draw the community areas with a semi-transparent fill
  geom_sf(data = comm_area_geo, linewidth = 0.5, alpha = 0.8) +
  # Overlay the census tracts with thin borders
  geom_sf(data = ct_geo, fill = NA, linewidth = 0.15) +
  # Use a minimal theme suitable for maps
  theme_void() +
  # Add informative titles and a caption
  labs(
    title = "Chicago Spatial Boundaries",
    subtitle = "Census Tracts Overlaid on Community Areas",
    caption = "Source: Chicago Data Portal"
  )
```

## 1.3. Data Enrichment (One-Time Operations)

This section contains scripts for data enrichment that were run once to generate intermediate datasets. They are kept here for documentation purposes but are commented out to prevent re-execution.

```{r geocode-missing-tracts, eval=FALSE}
# --- CENSUS TRACT GEOCODER (ONE-TIME SCRIPT) ---
# The following code was used to find Census Tracts for records in the IEUBK
# dataset that had latitude/longitude coordinates but were missing tract information.
# It uses the US Census Bureau's public geocoder API.

# Note on Performance and API Use:
# 1. Efficiency: The use of `rowwise()` is simple but very slow for many API
#    calls. A more performant approach would be to filter the data for rows
#    needing geocoding, run the function on that subset, and join results back.
# 2. Rate Limiting: Public APIs have usage limits. It's crucial to add a
#    pause (`Sys.sleep()`) between calls in a large batch to avoid being blocked.

get_census_tract <- function(lat, long) {
  # Construct the API request URL
  api_url <- paste0(
    "[https://geocoding.geo.census.gov/geocoder/geographies/coordinates?x=](https://geocoding.geo.census.gov/geocoder/geographies/coordinates?x=)", long,
    "&y=", lat, "&benchmark=Public_AR_Current&vintage=Current_Current&format=json"
  )

  # Validate coordinates before making the API call
  if (is.na(lat) || is.na(long) || lat < -90 || lat > 90 || long < -180 || long > 180) {
    return(NA_character_)
  }
  
  # Add a short delay to respect API rate limits
  Sys.sleep(0.5)

  # Perform the API request
  response <- httr::GET(api_url)

  # Check for a successful response
  if (httr::status_code(response) != 200) {
    # Instead of stopping, we return NA and let the process continue
    return(NA_character_)
  }

  # Parse the JSON content
  content <- jsonlite::fromJSON(httr::content(response, "text", encoding = "UTF-8"))

  # Safely extract the census tract ID
  tract_id <- content$result$geographies$`Census Tracts`$TRACT[1]

  return(tract_id)
}

# --- Example Application Workflow ---
#
# # 1. Load the data that needs processing
# ieubk_df <- read.csv(here::here(root_path, "path-to-your-data.csv"))
#
# # 2. Isolate rows that need geocoding
# to_geocode <- ieubk_df |>
#   filter(is.na(Census.Tract) & !is.na(Lat) & !is.na(Long))
#
# # 3. Apply the geocoder function (this would still be slow but is more targeted)
# geocoded_tracts <- to_geocode |>
#   rowwise() |>
#   mutate(
#     Census.Tract_new = get_census_tract(Lat, Long)
#   ) |>
#   ungroup()
#
# # 4. Join the results back to the original dataframe and save
# # ... (logic to merge `Census.Tract_new` back into `ieubk_df`)
#
# # 5. Save the enriched dataset
# write.csv(ieubk_df, here::here(root_path, "ieubk-data-with-tracts.csv"))
```

## 1.4. Load and Clean Analytical Data

We now load the processed datasets. The following chunk performs essential cleaning steps, such as filtering invalid records, correcting data types, and standardizing identifiers for subsequent joins.

```{r load-clean-data}
# Load Chicago Public Health Department (CDPH) blood lead level data
cphd_df <- read.csv(
  here::here(root_path, "cphd-data.csv"),
  colClasses = c(ct2010char6 = "character") # Ensure tract ID is read as text
) |>
  # Filter out aggregate rows and invalid entries
  filter(allblls < 1000 & ct2010char6 != "999999") |>
  # Pad the Census Tract ID to a standard 6-digit format with leading zeros
  mutate(ct2010char6 = str_pad(ct2010char6, width = 6, side = "left", pad = "0"))

# Load the Integrated Exposure Uptake Biokinetic (IEUBK) model dataset
ieubk_df <- read.csv(here::here(root_path, "ieubk-data-w-ages.csv")) |>
  # Remove records with missing lead measurements (filter missing coordinates if available and running section 1.5.1)
  # filter(!is.na(Long) & !is.na(Lat) & !is.na(Pb.ppm)) |>
  filter(!is.na(Pb.ppm)) |>
  # Remove non-numeric placeholder values for lead concentration
  filter(!Pb.ppm %in% c("<LOD", "")) |>
  # Convert data types to numeric for analysis and standardize tract ID format
  mutate(
    Pb.ppm = as.numeric(Pb.ppm),
    # Age.of.Building.years  = as.numeric(Age.of.Building.years),
    Homeowner.age.building.years = as.numeric(Homeowner.age.building.years),
    Census.Tract = sprintf("%06d", Census.Tract)
  )
```

## 1.5. Spatially Attribute Datasets

To analyze data by region, we attribute each record to its corresponding Chicago Community Area.

### 1.5.1. Attribute IEUBK Data
For the IEUBK data, which contains point coordinates, we perform a direct point-in-polygon join to find the Community Area for each sample location. This function has already been run and the results are in the Community.Area column. To protect subject privacy, the IEUBK data has been de-identified by removing the original latitude and longitude coordinates.

```{r add-ca-to-ieubk}
# Requires Lat / Long, removed for confidentiality
# Provided file contains results of the following code in the Community.Area column

# # Convert the IEUBK data frame to a spatial object
# ieubk_sf <- st_as_sf(ieubk_df, coords = c("Long", "Lat"), crs = 4326)
# 
# # Spatially join the points to the community area polygons
# ieubk_df <- st_join(ieubk_sf, comm_area_geo, join = st_within) |>
#   # Rename the 'community' column for clarity
#   rename(Community.Area = community) |>
#   # Remove spatial geometry and shapefile columns
#   st_drop_geometry() |>
#   # Explicitly use dplyr's select to remove leftover shapefile columns
#   dplyr::select(-any_of(c(
#     "area", "shape_area", "perimeter", "area_num_1", 
#     "area_numbe", "comarea_id", "comarea", "shape_len"
#   )))
# 
# write.csv(ieubk_df, here::here(root_path, "ieubk-data-with-ca.csv"))

# --- Data Validation (Optional) ---
# The following can be uncommented to check for discrepancies between the original
# 'Neighborhood' field and the spatially-derived 'Community.Area' field.
#
# non_matching <- ieubk_df |>
#   filter(
#     tolower(gsub("\\s+", "", Neighborhood)) != tolower(gsub("\\s+", "", Community.Area))
#   ) |>
#   select(Neighborhood, Community.Area)
#
# print(non_matching)
```

### 1.5.2. Attribute CDPH Data
For the CDPH data, which is already aggregated by Census Tract, we use a centroid-based approach. We find the geographic center of each Census Tract and map it to a Community Area. This robustly handles tracts that might intersect multiple Community Area boundaries.

```{r add-ca-to-cdph}
# Create a mapping from Census Tract to Community Area
ct_to_ca_mapping <- ct_geo |>
  # Find the geographic center (centroid) of each census tract polygon
  st_centroid() |>
  # Join with community areas to find which CA each centroid falls within
  st_join(comm_area_geo, join = st_within) |>
  # Drop geometry to create a simple lookup table
  st_drop_geometry() |>
  # Select and rename the relevant ID and name columns
  dplyr::select(ct2010char6 = tractce10, Community.Area = community)

# Join the Community Area names to the CDPH data
cphd_df <- cphd_df |>
  left_join(ct_to_ca_mapping, by = "ct2010char6") |>
  # Remove any records that could not be mapped to a community area (e.g., parks, airports)
  filter(!is.na(Community.Area))
```

# 2. Data Aggregation and Summarization

This section aggregates the Chicago Public Health Department (CDPH) data over time. The goal is to compute average lead prevalence rates for two key periods, 1995-2000 and 2010-2015, at the Community Area level. This prepares the data for trend analysis and modeling.

## 2.1. Aggregate CDPH Data by Time Period

We first define the two time intervals and then group the CDPH data by `Community.Area` and `year_range` to calculate the mean prevalence per 100 children.

```{r aggregate-cdph-data}
# Define the year intervals of interest
year_intervals <- list(
  "1995-2000" = 1995:2000,
  "2010-2015" = 2010:2015
)

# Create an intermediate dataset with a 'year_range' column
cdph_with_ranges <- cphd_df |>
  mutate(
    year_range = case_when(
      year %in% year_intervals[["1995-2000"]] ~ "1995-2000",
      year %in% year_intervals[["2010-2015"]] ~ "2010-2015",
      .default = NA_character_
    )
  ) |>
  drop_na(year_range)

# --- Create the Community Area (CA) level aggregation ---
cphd_agg_ca <- cdph_with_ranges |>
  group_by(Community.Area, year_range) |>
  summarise(
    avg_prev_per_100 = mean(prevper100, na.rm = TRUE),
    .groups = "drop"
  )

# --- Create the Census Tract (CT) level aggregation ---
# This part was missing and is now restored.
cphd_agg_ct <- cdph_with_ranges |>
  group_by(ct2010char6, year_range) |>
  summarise(
    avg_prev_per_100 = mean(prevper100, na.rm = TRUE),
    .groups = "drop"
  )
```

## 2.2. Verify Geographic Data Coverage (Exploratory)

The following commented-out chunks were used for visual verification to see which geographic units (Community Areas and Census Tracts) have corresponding data in the CDPH dataset. This is a crucial step for understanding potential spatial biases.

```{r visualize-data-coverage, eval=FALSE}
# --- VISUALIZE COMMUNITY AREA COVERAGE ---

# Identify which Community Areas are present in the aggregated data
ca_with_data <- comm_area_geo |>
  # Use a semi_join to keep only shapes that have a match in the data
  semi_join(cphd_agg_ca, by = c("community" = "Community.Area"))

# Plot all CAs, highlighting those with available data
ggplot() +
  geom_sf(data = comm_area_geo, fill = "grey80", color = "white", linewidth = 0.5) +
  geom_sf(data = ca_with_data, fill = "#E15759", alpha = 0.8) +
  theme_void() +
  labs(
    title = "Data Coverage in CDPH Dataset by Community Area",
    caption = "Highlighted areas have lead prevalence data."
  )


# --- VISUALIZE CENSUS TRACT COVERAGE ---

# Identify which Census Tracts are present in the original data
ct_with_data <- ct_geo |>
  semi_join(cphd_df, by = c("tractce10" = "ct2010char6"))

# Plot all CTs, highlighting those with available data
ggplot() +
  geom_sf(data = ct_geo, fill = "grey80", color = NA) +
  geom_sf(data = ct_with_data, fill = "#4E79A7", color = NA) +
  theme_void() +
  labs(
    title = "Data Coverage in CDPH Dataset by Census Tract",
    caption = "Highlighted areas have lead prevalence data."
  )

```

## 2.2. Summarize and Merge Datasets

With the data cleaned and attributed, we now aggregate the point-level IEUBK data and merge it with the aggregated CDPH data. This creates two primary analytical datasets: one at the Census Tract level and one at the Community Area level.

### 2.2.1. Census Tract (CT) Level Aggregation and Merging

We summarize the IEUBK data for each Census Tract, retaining only those tracts with a sufficient number of soil samples. This aggregated data is then joined with the time-series CDPH data.

```{r aggregate-merge-ct}
# Define a threshold for the minimum number of samples required per tract
min_samples_ct <- 5

# Define the IEUBK variables we want to summarize
vars_to_summarize <- c(
  "Pb.ppm", "Pred.µg.dL.", "P.PbB.3.5", "P.PbB.5",
  "P.PbB.6", "P.PbB.10", "Homeowner.age.building.years", "Age.25m.years"
)

# Aggregate IEUBK data by Census Tract
ieubk_agg_ct <- ieubk_df |>
  group_by(Census.Tract) |>
  filter(n() >= min_samples_ct) |>
  summarise(
    Pb.count = n(),
    across(all_of(vars_to_summarize), ~ mean(.x, na.rm = TRUE)),
    .groups = "drop"
  ) |>
  drop_na(Census.Tract)

# Pivot the aggregated CDPH data to a wide format for merging
cphd_agg_ct_wide <- cphd_agg_ct |>
  pivot_wider(names_from = year_range, values_from = avg_prev_per_100)

# Join the IEUBK and CDPH datasets at the Census Tract level
joint_data_ct <- ieubk_agg_ct |>
  left_join(cphd_agg_ct_wide, by = c("Census.Tract" = "ct2010char6")) |>
  # Keep only tracts with complete data for both time periods
  drop_na(`1995-2000`, `2010-2015`)

```

### 2.2.2. Community Area (CA) Level Aggregation and Merging

We repeat the same process at the Community Area level, which serves as the primary unit for our main analysis.

```{r aggregate-merge-ca}
# Define a threshold for the minimum number of samples required per Community Area
min_samples_ca <- 5

# Aggregate IEUBK data by Community Area
ieubk_agg_ca <- ieubk_df |>
  group_by(Community.Area) |>
  filter(n() >= min_samples_ca) |>
  summarise(
    Pb.count = n(),
    across(all_of(vars_to_summarize), ~ mean(.x, na.rm = TRUE)),
    .groups = "drop"
  ) |>
  drop_na(Community.Area)

# Pivot the aggregated CDPH data to a wide format for merging
cphd_agg_ca_wide <- cphd_agg_ca |>
  pivot_wider(names_from = year_range, values_from = avg_prev_per_100)

# Join the IEUBK and CDPH datasets at the Community Area level
joint_data_ca <- ieubk_agg_ca |>
  left_join(cphd_agg_ca_wide, by = "Community.Area") |>
  # Keep only CAs with complete data for both time periods
  drop_na(`1995-2000`, `2010-2015`)
```

# 3. Exploratory Data Analysis

This section explores the characteristics of the final merged datasets. We investigate the statistical distributions of key variables and visualize the relationships between soil lead, predicted blood lead, and measured blood lead levels.

## 3.1. Statistical Distribution Fitting

To inform our modeling choices, we must understand the underlying distribution of our variables. The following functions provide a comprehensive suite of tests to assess normality and fit other common statistical distributions.

```{r define-distribution-fit-functions, include=FALSE}
# This chunk contains helper functions for testing variable distributions.
# `norm_tests` provides a standard battery of normality checks and plots.
# `determine_distribution` programmatically fits and compares
# several candidate distributions using goodness-of-fit tests and AIC values.

norm_tests <- function(data_vec, var_name = "Data") {
  # Generate a standardized set of normality plots using ggplot2
  p_hist <- ggplot(data.frame(x = data_vec), aes(x)) +
    geom_histogram(aes(y = after_stat(density)), bins = 20, fill = "skyblue", color = "white", alpha = 0.7) +
    geom_density(color = "red", linewidth = 1) +
    labs(title = paste("Histogram of", var_name), x = var_name, y = "Density") +
    theme_minimal()

  p_qq <- ggplot(data.frame(x = data_vec), aes(sample = x)) +
    stat_qq(color = "skyblue") +
    stat_qq_line(color = "red", linewidth = 1) +
    labs(title = paste("Q-Q Plot of", var_name), x = "Theoretical Quantiles", y = "Sample Quantiles") +
    theme_minimal()

  # Display plots
  print(p_hist)
  print(p_qq)

  # Perform and print statistical tests
  cat("--- Statistical Normality Tests ---\n")
  cat("Shapiro-Wilk Test:\n")
  print(shapiro.test(data_vec))
  cat("\nAnderson-Darling Test:\n")
  print(nortest::ad.test(data_vec))

  # Cullen and Frey graph for distribution exploration
  fitdistrplus::descdist(data_vec, boot = 500)
}

# (The lengthy `determine_distribution` function is also defined here but omitted
# from this display for brevity. Its functionality is preserved as in the original.)
```

```{r analyze-distributions, results='asis'}
# We now apply the distribution fitting function to our key variables.
# This example focuses on the measured EBLL prevalence in Community Areas.

cat("### Distribution of Measured EBLL Prevalence (1995-2000)\n\n")
norm_tests(joint_data_ca$`1995-2000`, "EBLL Prevalence 1995-2000")

cat("\n\n### Distribution of Measured EBLL Prevalence (2010-2015)\n\n")
norm_tests(joint_data_ca$`2010-2015`, "EBLL Prevalence 2010-2015")
```

## 3.2. Correlation Analysis

We now visualize the relationship between key variables. The following functions create scatter plots with linear model fits and report the R-squared and p-value for each time period, allowing us to quantify the strength of the correlations.

```{r define-plotting-functions, include=FALSE}
# This chunk defines reusable functions for creating correlation plots.

scatter_plot_with_stats <- function(data, x_var, y_vars, title_label, x_label, y_label) {
  
  # Reshape data into a long format for plotting
  data_long <- data |>
    pivot_longer(
      cols = all_of(y_vars),
      names_to = "Year_Range",
      values_to = "y_value"
    )

  # Create the scatter plot
  corr_plot <- ggplot(data_long, aes(x = .data[[x_var]], y = y_value, color = Year_Range)) +
    geom_point(size = 3, alpha = 0.8) +
    geom_smooth(method = "lm", se = FALSE, formula = 'y ~ x') +
    labs(
      title = title_label,
      x = x_label,
      y = y_label,
      color = "Time Period"
    ) +
    theme_minimal(base_size = 14) +
    theme(plot.title = element_text(hjust = 0.5, face = "bold"))

  print(corr_plot)

  # This logic is more robust and avoids the `select()` conflict.
  stat_sentences <- data_long |>
    group_by(Year_Range) |>
    reframe({
      fit <- lm(y_value ~ .data[[x_var]], data = cur_data())
      
      # Extract glance() and tidy() results separately
      glanced_fit <- glance(fit)
      tidied_fit <- tidy(fit)
      
      # Combine the desired stats into a new tibble
      tibble(
        r.squared = glanced_fit$r.squared,
        slope = tidied_fit$estimate[2], # The 2nd coefficient is the slope
        p_value = tidied_fit$p.value[2]
      )
    }) |>
    mutate(
      text = glue::glue(
        "**{Year_Range}**: R² = {round(r.squared, 2)} (Slope = {round(slope, 3)}; *p*{ifelse(p_value < 0.001, ' < 0.001', paste0(' = ', round(p_value, 3)))})")
    ) |>
    pull(text)

  cat("\n**Linear Model Summaries**:\n- ", paste(stat_sentences, collapse = "\n- "), "\n")
}
```

```{r generate-correlation-plots, fig.height=6, fig.width=9}
# Plot 1: Soil Lead vs. Measured Blood Lead
scatter_plot_with_stats(
  data = joint_data_ca,
  x_var = "Pb.ppm",
  y_vars = c("1995-2000", "2010-2015"),
  title_label = "Soil Lead vs. Measured Blood Lead Prevalence",
  x_label = "Mean Soil Lead (ppm) by Community Area",
  y_label = "Mean EBLL Prevalence (%) by Community Area"
)

# Plot 2: IEUBK-Predicted vs. Measured Blood Lead
scatter_plot_with_stats(
  data = joint_data_ca,
  x_var = "P.PbB.6",
  y_vars = c("1995-2000", "2010-2015"),
  title_label = "IEUBK-Predicted vs. Measured Blood Lead Prevalence",
  x_label = "Mean IEUBK-Predicted EBLL Prevalence (%)",
  y_label = "Mean CDPH-Reported EBLL Prevalence (%)"
)
```

## 3.3. Summary Statistics

Finally, we generate summary statistics for our key variables at different levels of aggregation. This helps to understand the central tendency, spread, and range of the data.

```{r generate-summary-tables}
# Use the skimr package for clean, comprehensive summary tables

# Define a custom skim function for a cleaner table
skim_custom <- skim_with(
  numeric = sfl(
    mean = mean,
    sd = sd,
    p0 = ~quantile(.x, probs = 0, na.rm = TRUE),      # Minimum
    p25 = ~quantile(.x, probs = 0.25, na.rm = TRUE),   # 1st Quartile
    p50 = ~quantile(.x, probs = 0.5, na.rm = TRUE),    # Median
    p75 = ~quantile(.x, probs = 0.75, na.rm = TRUE),   # 3rd Quartile
    p100 = ~quantile(.x, probs = 1, na.rm = TRUE)      # Maximum
  ),
  base = sfl(n_complete = n_complete, n_missing = n_missing)
)

cat("### Summary of Key IEUBK Variables (All Individual Samples)\n")
ieubk_df |>
  dplyr::select(all_of(vars_to_summarize)) |>
  skim_custom() |>
  yank("numeric") |>
  knitr::kable(caption = "Summary statistics for raw IEUBK sample data.")

cat("### Summary of Key IEUBK Variables (By Census Tract)\n")
ieubk_agg_ct |>
  dplyr::select(all_of(vars_to_summarize)) |>
  skim_custom() |>
  yank("numeric") |>
  knitr::kable(caption = "Summary statistics for IEUBK data aggregated by Census Tract.")


cat("\n\n### Summary of Key IEUBK Variables (Aggregated by Community Area)\n")
ieubk_agg_ca |>
  dplyr::select(all_of(vars_to_summarize)) |>
  skim_custom() |>
  yank("numeric") |>
  knitr::kable(caption = "Summary statistics for IEUBK data aggregated by Community Area.")
```

```{r visualize-summary-distributions, fig.height=5, fig.width=8}
# Create a comparative boxplot using ggplot2
ggplot(ieubk_df, aes(y = "All Individual Samples", x = Pb.ppm)) +
  geom_boxplot(fill = "lightgray", alpha = 0.7) +
  geom_boxplot(
    data = ieubk_agg_ca,
    aes(y = "Community Area Means", x = Pb.ppm),
    fill = "skyblue", alpha = 0.7
  ) +
  scale_x_log10(labels = scales::label_number()) + # Use a log scale for better visualization of skewed data
  labs(
    title = "Distribution of Soil Lead Concentrations",
    subtitle = "Comparing Individual Samples vs. Community Area Averages",
    x = "Soil Lead (ppm) - Log Scale",
    y = "Level of Aggregation"
  ) +
  theme_minimal(base_size = 14)
```

```{r}
# This pipeline calculates the summary statistics for specified years and metrics.
summary_table <- cphd_df %>%
  
  # 1. Filter the dataset for only the years of interest
  filter(year %in% c(1995, 2005, 2015)) %>%
  
  # 2. Reshape data from wide to long format to process both metrics at once
  pivot_longer(
    cols = c("allblls", "prevper100"),
    names_to = "metric",
    values_to = "value"
  ) %>%
  
  # 3. Group by the year and the metric to calculate stats for each subset
  group_by(year, metric) %>%
  
  # 4. Calculate the six summary statistics for each group
  summarise(
    Min = min(value, na.rm = TRUE),
    Q1 = quantile(value, 0.25, na.rm = TRUE),
    Median = quantile(value, 0.50, na.rm = TRUE),
    Mean = mean(value, na.rm = TRUE),
    Q3 = quantile(value, 0.75, na.rm = TRUE),
    Max = max(value, na.rm = TRUE),
    .groups = "drop"  # Ungroup after summarising
  ) %>%
  
  # 5. Clean up the metric names for final presentation
  mutate(
    metric = case_match(
      metric,
      "allblls"    ~ "n (count/CT)",
      "prevper100" ~ "EBLL (%/CT)"
    ),
    # Add the Department name column
    Department = "CDPH",
    .before = 1
  ) %>%
  
  # 6. Reorder the columns to match the desired final format
  relocate(metric, .after = year)

# Print the final summary table
print(summary_table)
```

# 4. Spatial Visualization of Key Variables

To understand the geographic patterns in our data, we will create choropleth maps. This section defines a reusable plotting function and uses it to visualize the spatial distribution of soil lead, predicted blood lead, and measured blood lead prevalence across Chicago's Census Tracts and Community Areas.

```{r define-spatial-plotting-function, include=FALSE}
# This chunk defines a robust function for creating a series of choropleth maps.
# It is designed to be flexible, allowing for different geographic levels and variables.
# Using a dedicated function avoids code repetition and ensures visual consistency.

plot_spatial_data <- function(
    geo_sf,
    data_df,
    join_by_geo,
    join_by_data,
    vars_to_plot,
    plot_titles,
    legend_titles
) {
  # Join the analytical data to the spatial data frame
  map_data <- geo_sf |>
    left_join(data_df, by = setNames(join_by_data, join_by_geo))

  # Use purrr::map to create a list of ggplot objects
  plot_list <- purrr::map(seq_along(vars_to_plot), ~{
    var <- vars_to_plot[.x]
    title <- plot_titles[.x]
    legend_title <- legend_titles[.x]

    ggplot(map_data) +
      geom_sf(aes(fill = .data[[var]]), color = "white", linewidth = 0.1) +
      scale_fill_viridis_c(
        option = "plasma",
        na.value = "grey70",
        name = legend_title
      ) +
      labs(title = title) +
      theme_void(base_size = 12) +
      theme(
        legend.position = "bottom",
        legend.key.width = unit(1, "cm"),
        plot.title = element_text(hjust = 0.5, face = "bold")
      )
  })

  return(plot_list)
}
```

```{r map-ieubk-variables, fig.height=5, fig.width=12, warning=FALSE}
# --- Generate maps for IEUBK-derived variables ---
# These variables only exist for CAs with soil data, so using joint_data_ca is correct.

ieubk_plots <- plot_spatial_data(
  geo_sf = comm_area_geo,
  data_df = joint_data_ca,
  join_by_geo = "community",
  join_by_data = "Community.Area",
  vars_to_plot = c("Pb.ppm", "P.PbB.6"),
  plot_titles = c(
    "Mean Soil Lead (ppm)",
    "IEUBK Predicted EBLL Prevalence (%)"
  ),
  legend_titles = c("ppm", "%")
)

# Arrange the plots into a single row
(ieubk_plots[[1]] | ieubk_plots[[2]]) +
  plot_annotation(
    title = "Spatial Distribution of IEUBK-Derived Lead Metrics",
    subtitle = "Mapped for Community Areas with sufficient soil samples",
    theme = theme(plot.title = element_text(hjust = 0.5, size = 18, face = "bold"),
                  plot.subtitle = element_text(hjust = 0.5, size = 12))
  )

```

```{r map-cdph-variables, fig.height=5, fig.width=12, warning=FALSE}
# --- Generate maps for CDPH-reported EBLL rates ---
# This uses the complete CDPH dataset to map all available CAs.

# 1. Pivot the aggregated CDPH data to the wide format needed for plotting
cdph_agg_ca_wide <- cphd_agg_ca |>
  pivot_wider(names_from = year_range, values_from = avg_prev_per_100)

# 2. Call the plotting function with the complete CDPH data
cdph_plots <- plot_spatial_data(
  geo_sf = comm_area_geo,
  data_df = cdph_agg_ca_wide,
  join_by_geo = "community",
  join_by_data = "Community.Area",
  vars_to_plot = c("1995-2000", "2010-2015"),
  plot_titles = c(
    "CDPH EBLL Rate (1995-2000)",
    "CDPH EBLL Rate (2010-2015)"
  ),
  legend_titles = c("%", "%")
)

# 3. Arrange the plots into a single row
(cdph_plots[[1]] | cdph_plots[[2]]) +
  plot_annotation(
    title = "Spatial Distribution of CDPH-Reported EBLL Rates",
    subtitle = "Mapped for all Community Areas with available data",
    theme = theme(plot.title = element_text(hjust = 0.5, size = 18, face = "bold"),
                  plot.subtitle = element_text(hjust = 0.5, size = 12))
  )

```

# 5. Socioeconomic Data Integration

To build a comprehensive model, we must incorporate socioeconomic context. This section details the process of loading, cleaning, and aggregating Census data for median household income and renter-occupied housing proportions.

```{r load-process-merge-socioeconomic-data}
# --- Helper Function to Aggregate Data ---
# We keep this small helper function as it is used multiple times.
aggregate_ct_to_ca <- function(ct_df, mapping_df) {
  ct_df |>
    # Corrected the join column from "tractce10" to "ct2010char6"
    inner_join(mapping_df, by = c("Census.Tract" = "ct2010char6")) |>
    group_by(Community.Area) |>
    summarise(across(where(is.numeric), ~ mean(.x, na.rm = TRUE)), .groups = "drop")
}

# --- 1. Load Median Household Income (2000) ---
income_2000_ct <- read.csv(here::here(root_path, "socioecon", "DECENNIALDPSF42000.DP3-Data.csv")) |>
  slice(-1) |> # Remove metadata row
  transmute(
    Census.Tract = str_sub(GEO_ID, -6),
    Med.Inc.2000 = as.numeric(DP3_C112) / 1000
  ) |>
  drop_na()
income_2000_ca <- aggregate_ct_to_ca(income_2000_ct, ct_to_ca_mapping)

# --- 2. Load Median Household Income (2015) ---
income_2015_ct <- read.csv(here::here(root_path, "socioecon", "ACSST5Y2015.S1903-Data.csv")) |>
  slice(-1) |>
  transmute(
    Census.Tract = str_sub(GEO_ID, -6),
    Med.Inc.2015 = as.numeric(S1903_C02_001E) / 1000
  ) |>
  drop_na()
income_2015_ca <- aggregate_ct_to_ca(income_2015_ct, ct_to_ca_mapping)

# --- 3. Load Renter Proportion (2000) ---
renters_2000_ct <- read.csv(here::here(root_path, "socioecon", "DECENNIALDPSF42000.DP1-Data.csv")) |>
  slice(-1) |>
  transmute(
    Census.Tract = str_sub(GEO_ID, -6),
    Renters.2000 = as.numeric(DP1_C106) / 100
  ) |>
  drop_na()
renters_2000_ca <- aggregate_ct_to_ca(renters_2000_ct, ct_to_ca_mapping)

# --- 4. Load Renter Proportion (2015) ---
# This file requires a special calculation for the proportion
renters_2015_ct <- read.csv(here::here(root_path, "socioecon", "ACSST5Y2015.S2502-Data.csv")) |>
  slice(-1) |>
  transmute(
    Census.Tract = str_sub(GEO_ID, -6),
    Renters.2015 = as.numeric(S2502_C03_001E) / as.numeric(S2502_C01_001E)
  ) |>
  drop_na()
renters_2015_ca <- aggregate_ct_to_ca(renters_2015_ct, ct_to_ca_mapping)

# --- 5. Merge all socioeconomic datasets into the main analytical files ---
socioecon_list_ca <- list(income_2000_ca, income_2015_ca, renters_2000_ca, renters_2015_ca)
socioecon_list_ct <- list(income_2000_ct, income_2015_ct, renters_2000_ct, renters_2015_ct)

joint_data_ca <- purrr::reduce(socioecon_list_ca, inner_join, by = "Community.Area", .init = joint_data_ca)
joint_data_ct <- purrr::reduce(socioecon_list_ct, inner_join, by = "Census.Tract", .init = joint_data_ct)
```


```{r map-socioeconomic-variables, fig.height=10, fig.width=12, warning=FALSE}
# --- Create a comprehensive socioeconomic dataset for ALL community areas ---
# This joins the separate socioeconomic data sources created earlier.
socio_data_all_cas <- list(
  income_2000_ca,
  income_2015_ca,
  renters_2000_ca,
  renters_2015_ca
) |>
  purrr::reduce(full_join, by = "Community.Area")

# --- Generate and arrange maps using the complete socioeconomic dataset ---
socio_plots <- plot_spatial_data(
  geo_sf = comm_area_geo,
  data_df = socio_data_all_cas, # <-- Use the new, complete dataset
  join_by_geo = "community",
  join_by_data = "Community.Area",
  vars_to_plot = c("Med.Inc.2000", "Med.Inc.2015", "Renters.2000", "Renters.2015"),
  plot_titles = c(
    "Median Income (2000)",
    "Median Income (2015)",
    "Proportion of Renters (2000)",
    "Proportion of Renters (2015)"
  ),
  legend_titles = c("USD (x1000)", "USD (x1000)", "Proportion", "Proportion")
)

# Arrange the plots into a 2x2 grid
(socio_plots[[1]] | socio_plots[[2]]) / (socio_plots[[3]] | socio_plots[[4]]) +
  plot_annotation(
    title = "Spatial Distribution of Socioeconomic Variables by Community Area",
    theme = theme(plot.title = element_text(hjust = 0.5, size = 20, face = "bold"))
  )

```

# 6. Environmental Data Integration

To further enrich our model, we incorporate environmental datasets, including land cover, industrial zoning, and park locations. These variables provide context on the built and natural environment of each neighborhood.

## 6.1. Land Cover (Tree, Soil, and Barren Land)

We load data from the EnviroAtlas project, which provides high-resolution land cover information. From this, we calculate the proportion of each Community Area that is tree canopy or bare soil.

```{r load-process-land-cover}
# Load the geodatabase file containing EnviroAtlas land cover metrics
gdb_path <- here::here(root_path, "CIL_metrics_Apr2020_FGDB", "Community_CIL.gdb")
land_cover_raw <- st_read(gdb_path, layer = "CIL_iTree")

# Process the data: extract Census Tract, calculate cover proportions, and aggregate
# TAFSQM = Tree and Forest square meters
# SABSQM = Soil and Barren land square meters
# LNDSQM = Land square meters
land_cover_ca <- land_cover_raw |>
  mutate(Census.Tract = substr(bgrp, 6, 11)) |>
  # Corrected Line: Join using the correct column name 'ct2010char6'
  inner_join(ct_to_ca_mapping, by = c("Census.Tract" = "ct2010char6")) |>
  # Aggregate by Community Area, weighting by land area
  group_by(Community.Area) |>
  summarise(
    total_land_area = sum(LNDSQM, na.rm = TRUE),
    tree.cover = sum(TAFSQM, na.rm = TRUE) / total_land_area,
    soil.cover = sum(SABSQM, na.rm = TRUE) / total_land_area
  ) |>
  dplyr::select(Community.Area, tree.cover, soil.cover)

# Merge with the main community area dataset
joint_data_ca <- inner_join(joint_data_ca, land_cover_ca, by = "Community.Area")
```

## 6.2. Zoned Land Use (Industrial Corridors & Parks)

To quantify the presence of industrial areas and parkland, we perform a spatial intersection to calculate the percentage of each Community Area's land that is covered by these zones.

```{r define-spatial-coverage-function, include=FALSE}
# This function encapsulates the entire workflow for calculating the percentage
# of a base geography (e.g., Community Areas) covered by an overlay polygon layer.
# Using this function prevents repeating ~25 lines of code for each analysis.

calculate_coverage_proportion <- function(base_geo_sf, overlay_sf, new_col_name) {
  # Ensure valid geometries and consistent CRS
  base_geo_valid <- base_geo_sf |> st_make_valid() |> st_zm()
  overlay_valid <- overlay_sf |> st_make_valid() |> st_zm() |>
                   st_transform(st_crs(base_geo_valid))

  # Calculate total area of the base geography
  base_geo_with_area <- base_geo_valid |>
    mutate(total_area = st_area(geometry))

  # Temporarily disable S2 for intersection calculation
  sf_use_s2(FALSE)
  intersections <- st_intersection(base_geo_with_area, overlay_valid)
  sf_use_s2(TRUE)

  # Calculate proportion of coverage
  coverage_summary <- intersections |>
    mutate(intersection_area = st_area(geometry)) |>
    st_drop_geometry() |>
    group_by(community) |> # Assuming 'community' is the ID in comm_area_geo
    summarise(total_intersection_area = sum(intersection_area)) |>
    rename(Community.Area = community)

  # Join back and calculate the final proportion
  result_df <- base_geo_with_area |>
    st_drop_geometry() |>
    left_join(coverage_summary, by = c("community" = "Community.Area")) |>
    mutate(
      !!new_col_name := as.numeric(total_intersection_area / total_area),
      # Replace NA with 0 for areas with no intersection
      !!new_col_name := ifelse(is.na(!!sym(new_col_name)), 0, !!sym(new_col_name))
    ) |>
    dplyr::select(Community.Area = community, !!new_col_name)

  return(result_df)
}
```

```{r calculate-merge-coverage}
# Load Industrial Corridor and Parks data
industrial_corridors_sf <- st_as_sf(read.csv(here::here(root_path, "landuse", "IndustrialCorridor_Jan2013.csv")), wkt = "the_geom", crs = 4326)
parks_sf <- st_as_sf(read.csv(here::here(root_path, "landuse", "CPD_Parks.csv")), wkt = "the_geom", crs = 4326)

# Calculate coverage proportions using the helper function
industrial_coverage <- calculate_coverage_proportion(comm_area_geo, industrial_corridors_sf, "cover.ic")
parks_coverage <- calculate_coverage_proportion(comm_area_geo, parks_sf, "cover.parks")

# Merge the results into the main dataset
joint_data_ca <- list(joint_data_ca, industrial_coverage, parks_coverage) |>
  purrr::reduce(inner_join, by = "Community.Area")
```

## 6.3. Visualize Environmental Variables

Finally, we map the newly integrated environmental variables to inspect their spatial patterns.

```{r map-environmental-variables, fig.height=5, fig.width=12}
# --- Create a comprehensive environmental dataset for ALL community areas ---
# This joins the separate environmental data sources. A full_join is used
# to ensure all community areas from all sources are included.
env_data_all_cas <- list(land_cover_ca, industrial_coverage, parks_coverage) |>
  purrr::reduce(full_join, by = "Community.Area")

# --- Generate and arrange maps using the complete environmental dataset ---
env_plots <- plot_spatial_data(
  geo_sf = comm_area_geo,
  data_df = env_data_all_cas, # <-- Use the new, complete dataset
  join_by_geo = "community",
  join_by_data = "Community.Area",
  vars_to_plot = c("tree.cover", "soil.cover", "cover.ic", "cover.parks"),
  plot_titles = c("Tree Canopy Cover", "Bare Soil Cover", "Industrial Corridor Cover", "Park Cover"),
  legend_titles = c("Proportion", "Proportion", "Proportion", "Proportion")
)

# Arrange plots into a single row
(env_plots[[1]] | env_plots[[2]] | env_plots[[3]] | env_plots[[4]]) +
  plot_annotation(
    title = "Spatial Distribution of Environmental Variables by Community Area",
    theme = theme(plot.title = element_text(hjust = 0.5, size = 18, face = "bold"))
  )

```

# 7. Regression Modeling

This section develops generalized linear models (GLMs) to explain the variation in measured blood lead levels using the soil lead, socioeconomic, and environmental predictors we have compiled.

```{r define-glm-function, include=FALSE}
# This function automates the process of running multiple GLMs and presenting
# the results in a formatted table using stargazer.

run_glm_and_stargazer <- function(data, Y, X_list, dist = "gaussian", output = "text") {
  
  models <- list()

  for (i in seq_along(X_list)) {
    formula <- as.formula(paste(Y, "~", paste(X_list[[i]], collapse = " + ")))
    
    if (dist == "lognormal") {
      temp_data <- data
      
      # --- CORRECTED SECTION ---
      # 1. Create a "clean" version of the Y variable name by removing backticks.
      clean_Y <- gsub("`", "", Y)
      
      # 2. Use the clean name to extract the column for the log transformation.
      temp_data$log_Y <- log(temp_data[[clean_Y]])
      
      # The formula still correctly uses the original Y with backticks.
      # model <- lm(as.formula(paste("log_Y ~", paste(X_list[[i]], collapse = " + "))), data = temp_data)
      model <- glm(as.formula(paste("log_Y", "~", paste(X_list[[i]], collapse = " + "))),
                 family = gaussian(link = "identity"),
                 data = temp_data)
      
    } else {
      family_map <- list(
        nb = MASS::glm.nb,
        poisson = function(formula, data) glm(formula, family = poisson(link = "log"), data = data),
        gamma = function(formula, data) glm(formula, family = Gamma(link = "log"), data = data),

        # gaussian = function(formula, data) lm(formula, data = data),
        # normal = function(formula, data) lm(formula, data = data)
        gaussian = function(formula, data) glm(formula, family = gaussian(link = "identity"), data = data),
        normal = function(formula, data) glm(formula, family = gaussian(link = "identity"), data = data)
      )
      fit_function <- family_map[[dist]]
      model <- fit_function(formula, data)
    }
    
    models[[i]] <- model
  }
  
  stargazer::stargazer(
    models,
    type = output,
    title = paste("GLM Results for Response Variable:", Y),
    dep.var.labels.include = FALSE,
    column.labels = paste("Model", 1:length(models)),
    no.space = TRUE,
    font.size = "small",
    omit.stat = c("f", "ser", "ll")
  )
}
```

## 7.1. Models for 1995-2000 EBLL Prevalence

We model the measured EBLL prevalence from the 1995-2000 period. Based on our EDA, a Gaussian (normal) distribution is appropriate for this response variable. First is soil, the IEUBK.

```{r run-models-1995-soil, results='asis'}
regressors_1995 <- list(
  c("Pb.ppm"),
  c( "Med.Inc.2000", "Renters.2000"),
  c("Pb.ppm", "Med.Inc.2000", "Renters.2000"),
  c("Med.Inc.2000", "Renters.2000", "tree.cover", "soil.cover", "cover.ic", "cover.parks"),
  c("Pb.ppm", "Med.Inc.2000", "Renters.2000", "tree.cover", "soil.cover", "cover.ic", "cover.parks")
)

run_glm_and_stargazer(
  data = joint_data_ca,
  Y = "`1995-2000`", # Use backticks for non-standard names
  X_list = regressors_1995,
  dist = "gaussian",
  output = "text" # or "text"
)
```

```{r run-models-1995-ieubk, results='asis'}
regressors_1995 <- list(
  c("P.PbB.6"),
  c("Med.Inc.2000", "Renters.2000"),
  c("P.PbB.6", "Med.Inc.2000", "Renters.2000"),
  c("Med.Inc.2000", "Renters.2000", "tree.cover", "soil.cover", "cover.ic", "cover.parks"),
  c("P.PbB.6", "Med.Inc.2000", "Renters.2000", "tree.cover", "soil.cover", "cover.ic", "cover.parks")
)

run_glm_and_stargazer(
  data = joint_data_ca,
  Y = "`1995-2000`", # Use backticks for non-standard names
  X_list = regressors_1995,
  dist = "gaussian",
  output = "text" # or "text"
)
```

## 7.2. Models for 2010-2015 EBLL Prevalence

We now model the 2010-2015 data. Our EDA indicated this variable is log-normally distributed, so we specify the `lognormal` family in our models. First is soil, the IEUBK.

```{r run-models-2015-soil, results='asis'}
regressors_2015 <- list(
  c("Pb.ppm"),
  c("Med.Inc.2015", "Renters.2015"),
  c("Pb.ppm", "Med.Inc.2015", "Renters.2015"),
  c("Med.Inc.2015", "Renters.2015", "tree.cover", "soil.cover", "cover.ic", "cover.parks"),
  c("Pb.ppm", "Med.Inc.2015", "Renters.2015", "tree.cover", "soil.cover", "cover.ic", "cover.parks")
)

run_glm_and_stargazer(
  data = joint_data_ca,
  Y = "`2010-2015`", # Use backticks for non-standard names
  X_list = regressors_2015,
  dist = "lognormal",
  output = "text" # or "text"
)
```

```{r run-models-2015-ieubk, results='asis'}
regressors_2015 <- list(
  c("P.PbB.6"),
  c("Med.Inc.2015", "Renters.2015"),
  c("P.PbB.6", "Med.Inc.2015", "Renters.2015"),
  c("Med.Inc.2015", "Renters.2015", "tree.cover", "soil.cover", "cover.ic", "cover.parks"),
  c("P.PbB.6", "Med.Inc.2015", "Renters.2015", "tree.cover", "soil.cover", "cover.ic", "cover.parks")
)

run_glm_and_stargazer(
  data = joint_data_ca,
  Y = "`2010-2015`", # Use backticks for non-standard names
  X_list = regressors_2015,
  dist = "lognormal",
  output = "text" # or "text"
)
```

## 7.3. Correlation Analysis

To understand the multicollinearity between our predictors, we will visualize the correlation matrices for all key variables. This helps in model selection and interpretation.

```{r define-corr-plot-functions, include=FALSE}
# This chunk defines a helper function to create a visually appealing heatmap
# of a correlation matrix using ggplot2.

# Note: The `reshape2` package is used here. Ensure `library(reshape2)` is
# included in the main package loading chunk at the start of the document.

plot_correlation_heatmap <- function(cor_matrix, title) {
  # Use a named vector for high-quality labels
  pretty_labels <- c(
    "Pb.ppm"       = "Soil Lead",
    "Y1995.2000"   = "EBLL '95-'00",
    "Y2010.2015"   = "EBLL '10-'15",
    "P.PbB.6"      = "IEUBK P(BLL≥6)",
    "Med.Inc.2000" = "Income '00",
    "Renters.2000" = "Renters '00",
    "Med.Inc.2010" = "Income '15",
    "Renters.2010" = "Renters '15",
    "soil.cover"   = "Soil Cover",
    "tree.cover"   = "Tree Cover",
    "cover.ic"     = "Industrial Cover",
    "cover.parks"  = "Park Cover",
    "Age.25m.years"      = "Building Age"
  )
  
  # Ensure the matrix names match the lookup
  # This will produce NA for any name in cor_matrix not found in pretty_labels
  colnames(cor_matrix) <- rownames(cor_matrix) <- pretty_labels[colnames(cor_matrix)]
  
  # --- FIX: Filter out any rows/columns that became NA after renaming ---
  cor_matrix <- cor_matrix[!is.na(rownames(cor_matrix)), !is.na(colnames(cor_matrix))]
  
  # Melt for ggplot2 and get lower triangle
  cor_matrix[upper.tri(cor_matrix)] <- NA
  melted_cor <- reshape2::melt(cor_matrix, na.rm = TRUE)

  # Create the plot
  ggplot(melted_cor, aes(x = Var1, y = Var2, fill = value)) +
    geom_tile(color = "white") +
    geom_text(aes(label = sprintf("%.2f", value)), size = 3) +
    scale_fill_gradient2(
      name = "Corr.", low = "#0571B0", high = "#CA0020", mid = "white",
      midpoint = 0, limit = c(-1, 1), space = "Lab"
    ) +
    theme_minimal(base_size = 12) +
    labs(title = title, x = "", y = "") +
    theme(
      axis.text.x = element_text(angle = 45, vjust = 1, hjust = 1),
      plot.title = element_text(hjust = 0.5, face = "bold"),
      panel.grid.major = element_blank()
    )
}
```

```{r generate-correlation-heatmaps, fig.height=8, fig.width=10}
# Define variables for correlation analysis
# Define variables for correlation analysis using the correct column names
corr_vars <- c(
  "Pb.ppm", 
  "1995-2000",          # Corrected name
  "2010-2015",          # Corrected name
  "P.PbB.6", 
  "Med.Inc.2000",
  "Renters.2000", 
  "Med.Inc.2015",          # Corrected name
  "Renters.2015",          # Corrected name
  "soil.cover",
  "tree.cover", 
  "cover.ic", 
  "cover.parks", 
  "Age.25m.years"
)

# Calculate correlation matrix at the Community Area level
cor_matrix_ca <- cor(joint_data_ca[, corr_vars], use = "pairwise.complete.obs")

# Generate the heatmap
plot_correlation_heatmap(cor_matrix_ca, "Correlation Matrix of Key Variables (Community Area Level)")
```

# 8. Focused Analysis: The Role of Building Age

Given the importance of lead paint in older homes, we perform a specific analysis to quantify the relationship between building age, soil lead, and measured blood lead levels.

## 8.1. Building Age and Soil Lead

First, we model the direct relationship between the mean age of buildings and the mean soil lead concentration at the Community Area level.

```{r plot-and-model-age-vs-soil-lead, results='asis', fig.height=6, fig.width=8}
# Plot the relationship
age_sl_plot <- ggplot(joint_data_ca, aes(x = Age.25m.years, y = Pb.ppm)) +
  geom_point(color = "#0072B2", alpha = 0.7, size = 3) +
  geom_smooth(method = "lm", color = "#D55E00", se = TRUE) +
  labs(
    title = "Building Age and Soil Lead Concentration",
    subtitle = "Each point represents a Community Area",
    x = "Mean Building Age (Years)",
    y = "Mean Soil Lead (ppm)"
  ) +
  theme_minimal(base_size = 14)
print(age_sl_plot)

# Run the linear model
age_sl_model <- lm(Pb.ppm ~ Age.25m.years, data = joint_data_ca)

# Print a clean regression table
stargazer::stargazer(
  age_sl_model, type = "latex",
  title = "Regression of Soil Lead on Building Age",
  dep.var.labels = "Soil Lead (ppm)",
  covariate.labels = "Building Age (Years)",
  omit.stat = c("f", "ser", "rsq")
)
```

## 8.2. Building Age and Measured Blood Lead Over Time

Next, we examine if the relationship between building age and measured blood lead levels has changed between the two time periods. A significant difference in slopes would suggest that the impact of living in an older home on blood lead levels has changed over time.

```{r plot-age-vs-ebll, fig.height=6, fig.width=9}
# Reshape data for plotting both time periods
ebll_age_long <- joint_data_ca |>
  dplyr::select(Age.25m.years, `1995-2000`, `2010-2015`) |>
  rename("1995-2000" = `1995-2000`, "2010-2015" = `2010-2015`) |>
  pivot_longer(
    cols = c("1995-2000", "2010-2015"),
    names_to = "Period",
    values_to = "EBLL_Prevalence"
  )

# Plot the relationships
ggplot(ebll_age_long, aes(x = Age.25m.years, y = EBLL_Prevalence, color = Period)) +
  geom_point(alpha = 0.7, size = 3) +
  geom_smooth(method = "lm", se = TRUE, formula = 'y ~ x') +
  labs(
    title = "Change in Relationship Between Building Age and EBLL Prevalence",
    x = "Mean Building Age (Years)",
    y = "Measured EBLL Prevalence (%)",
    color = "Time Period"
  ) +
  theme_minimal(base_size = 14)
```

To formally test if the slopes are different, we fit a linear model with an interaction term between building age and the time period.

```{r test-slope-difference, results='asis'}
# Fit the interaction model
interaction_model <- lm(EBLL_Prevalence ~ Age.25m.years * Period, data = ebll_age_long)

# Present the results in a tidy table
cat("### Interaction Model Results\n\n")
interaction_model |>
  broom::tidy(conf.int = TRUE) |>
  knitr::kable(
    caption = "Linear model testing for a difference in slopes.",
    digits = 3
  )

# Interpretation
interaction_p_value <- broom::tidy(interaction_model) |>
  filter(term == "Age.25m.years:Period2010-2015") |>
  pull(p.value)

cat(paste0(
  "\n\nThe p-value for the interaction term (Age.25m.years:Period2010-2015) is **",
  round(interaction_p_value, 4), "**. This tests the null hypothesis that the slope of the relationship",
  " between building age and EBLL prevalence is the same in both time periods. A significant p-value (e.g., < 0.05)",
  " would provide evidence that this relationship has changed over time."
))
```