This project investigates parcel price disparities across Pittsburgh neighborhoods, with a focus on quantifying and exploring location-based pricing premiums. Using parcel-level data from Allegheny County, we model how property values vary across ZIP codes after controlling for housing characteristics like size, age, style, and condition.
We employ a series of regression models—including Ordinary Least Squares (OLS), Weighted Least Squares (WLS) to address heteroskedasticity, and Analysis of Covariance (ANCOVA)—to estimate adjusted mean parcel prices for each ZIP code. These adjusted means represent what a typical parcel would cost if moved from one neighborhood to another, holding all structural and lot characteristics constant. In this way, they isolate the value of location itself, separate from the physical features of the parcel.
To explore the underlying causes of these location-based price differences, we conduct a geospatial analysis by merging adjusted price data with:
- Arrest density (as a proxy for crime)
- Public school district rankings
- ZIP code-level population data
This spatial analysis allows us to assess how crime, school quality, and geographic characteristics help explain why certain neighborhoods have higher or lower parcel prices, independent of the homes themselves. The combined statistical and spatial framework offers a rigorous approach to disentangling the effects of location on urban property values.
The data used in this project is sourced from Allegheny County, and we also use additional data from the Western Pennsylvania Regional Data Center (WPRDC) for real estate sales and property assessments.
This dataset provides transactional data from 2013 to the present. It includes sales prices, sale dates, and property identification numbers (PINs), but does not contain property characteristics (such as house size, condition, etc.).
Note: The primary key is PARID, which is equivalent to PIN (Property Identification Number).
This dataset includes property characteristics such as square footage, number of rooms, property condition, and assessment values. It provides detailed information about the physical attributes of properties, which is essential for modeling house prices.
Note: The primary key is PARID, which corresponds to the PIN (Property Identification Number), ensuring that it can be matched with transactional data.
Arrest data contains information on people taken into custody by City of Pittsburgh police officers. More serious crimes, such as felony offenses, are more likely to result in an arrest. However, arrests can occur as a result of other offenses, such as parole violations or a failure to appear for trial. All data is reported at the block/intersection level, with the exception of sex crimes, which are reported at the police zone level.
This dataset only contains information reported by the City of Pittsburgh Police. It does not contain information about incidents that solely involve other police departments operating within the city (for example, campus police or Port Authority police).
This dataset demarcates the zip code boundaries that lie within Allegheny County. If viewing this description on the Western Pennsylvania Regional Data Center’s open data portal, this dataset is harvested on a weekly basis from Allegheny County’s GIS data portal
Boundaries of school districts in Pittsburgh. School quality plays a significant role in determining the desirability of an area, and this dataset is used to examine how school district rankings impact parcel prices.
A dataset containing population figures for each ZIP code, used to understand how population density influences parcel prices in Pittsburgh. Available in the final zipcounts data set in the data folder of the repo.
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Merge: Merge both data sets together horizontally on the key of zipcodes, then remove identical columns from the merge
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Pittsburgh Specific: Since this is county-wide data, we filtered it to include only data that is within the Pittsburgh city limits (ie. City== Pittsburgh)
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Missing Values: Approximately 20% of the 90,000 observations had missing data. After inspection, these missing values were determined to be random, so they were dropped. We retained enough remaining observations for meaningful analysis.
| PROPERTYZIP.x | LOTAREA | STYLE | STORIES | YEARBLT | EXTERIORFINISH | BASEMENT | GRADEDESC | CONDITION | TOTALROOMS | BEDROOMS | FULLBATHS | HALFBATHS | HEATINGCOOLING | FIREPLACES | BSMTGARAGE | FINISHEDLIVINGAREA | PRICE | SALEYEAR | SALEDESC.x | FAIRMARKETTOTAL |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 16.8587 | 16.8633 | 16.8561 | 16.8602 | 16.8786 | 16.8633 | 16.8725 | 16.8756 | 16.8684 | 16.872 | 17.8816 | 16.8904 | 23.9331 | 20.9421 | 16.8561 | 0.304161 | 0 | 0 | 0 |
- Sale Descriptions: The sale descriptions labeled as "love and affection" were removed because they were associated with very low sale prices that did not reflect accurate market values. Upon inspection, the rate of these sales was stable across ZIP codes, so they were deemed to distort the overall analysis.
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Other Sale Descriptions: Other sale descriptions, such as bank repossessions, could lead to lower sale prices. However, these are not equally distributed across ZIP codes and show an underlying pattern in the data. Since they provide valuable insights into the market, these observations were retained in the dataset.
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Zipcodes: Zipcodes needed to have enough observations to get a valid comparison and average price, 4 zipcodes were dropped because they had many less observations than the others (< 220)
# Count the number of observations per ZIP code
zip_counts = df["Zip"].value_counts().reset_index()
zip_counts.columns = ["Zip", "Observations"] # Rename columns
# Filter ZIP codes with at least 250 observations
filtered_zip_df = zip_counts[zip_counts["Observations"] >= 250]-
Extracting Sale Year: The sale year was extracted from the
SALEDATE.xcolumn, which contains the full date. This year is then converted into a factor for use in analysis. -
Encoding Ratings: The
GRADEDESCcolumn, which represents house ratings, was transformed into an ordered factor. This transformation ensures that the house ratings are treated as ordinal data in the statistical models. The ratings are ordered from "POOR" to "Highest Cost." -
- Create Age of House Variable: Subtract Year built from sale year
# Define the desired order of levels
rating_levels <- c("POOR", "POOR -", "POOR +", "BELOW AVERAGE", "BELOW AVERAGE -", "BELOW AVERAGE +", "AVERAGE", "AVERAGE -", "AVERAGE +", "GOOD", "GOOD -", "GOOD +", "VERY GOOD", "VERY GOOD -", "VERY GOOD +", "EXCELLENT", "EXCELLENT -", "EXCELLENT +", "Highest Cost", "Highest Cost -", "Highest Cost +")
# Encode the 'ratings' column as a factor with the specified levels
df$GRADEDESC <- factor(df$GRADEDESC, levels = rating_levels, ordered = TRUE)
# Convert the ordered factor to numeric values (ordinal encoding)
df$GRADEDESC <- as.numeric(df$GRADEDESC)The cleaned data is available for download in this repository. You can find the file under the "data" folder or in the relevant section of this project.
The initial steps involve exploring the data with summary statistics and visualizations to identify patterns and understand the structure of the data:
In this purely descriptive analysis, the average parcel prices per ZIP code are computed and visualized using a bar chart, with error bars representing the standard error of the mean (SEM) to illustrate price variability. However, this approach does not account for confounding variables such as property characteristics, neighborhood amenities, or market conditions. While useful for identifying broad trends, it does not provide a comprehensive understanding of the factors influencing parcel prices.
This research seeks to go beyond this naïve analysis by employing statistical modeling to control for key variables and offer a more rigorous, data-driven assessment of parcel price determinants.
# Calculate average price and standard error of the mean (SEM) for each ZIP code
zipcode_summary <- pittsburgh_data %>%
group_by(PROPERTYZIP.x) %>%
summarise(
avg_price = mean(PRICE, na.rm = TRUE),
sem_price = sd(PRICE, na.rm = TRUE) / sqrt(n()) # Standard error of the mean
)
# Create a plot with error bars for the average price by ZIP code
ggplot(...)Descriptive Statistics
| Statistic | N | Mean | St. Dev. | Min | Max |
|---|---|---|---|---|---|
| LOTAREA | 146,470 | 8,215.283 | 23,225.260 | 0 | 2,337,386 |
| STORIES | 146,470 | 1.742 | 0.501 | 1.000 | 4.000 |
| YEARBLT | 146,470 | 1,937.094 | 27.891 | 1,780 | 2,024 |
| BASEMENT | 146,470 | 4.753 | 0.900 | 1 | 5 |
| GRADEDESC | 146,457 | 7.834 | 1.682 | 1 | 19 |
| CONDITION | 146,470 | 3.143 | 0.796 | 1 | 8 |
| TOTALROOMS | 146,470 | 6.457 | 1.830 | 0 | 87 |
| BEDROOMS | 146,470 | 3.011 | 0.968 | 0 | 18 |
| FULLBATHS | 146,470 | 1.451 | 0.678 | 0 | 9 |
| HALFBATHS | 146,470 | 0.416 | 0.554 | 0 | 8 |
| FIREPLACES | 146,470 | 0.342 | 0.550 | 9 | |
| BSMTGARAGE | 146,470 | 0.550 | 0.737 | 0 | 6 |
| FINISHEDLIVINGAREA | 146,470 | 1,645.914 | 733.217 | 0 | 15,657 |
| PRICE | 146,470 | 184,973.500 | 270,583.300 | 0 | 10,662,000 |
| SALEYEAR | 146,470 | 2,018.022 | 3.658 | 2,012 | 2,025 |
| FAIRMARKETTOTAL | 146,470 | 139,303.800 | 0 | 2,793,400 |
A series of linear regression models are constructed to predict parcel prices based on several independent variables.
The max model includes all potential predictors of house price, such as LOTAREA, STYLE, YEARBLT, GRADEDESC, CONDITION, and more.
The null model includes only an intercept, essentially predicting the mean price without any independent variables.
The best model is selected using a stepwise selection process. This function selects the best predictors based on AIC (Akaike Information Criterion), which balances model fit and complexity. This model will give us an intial jumping off point for future transformations and analysis.
best_model = step(min_model, direction = "both", scope = max_model)
Non-Linearity (Residuals vs Fitted Plot)
- Residuals show a pattern rather than being randomly scattered around zero.
- Indicates that the model may be missing important non-linear relationships.
Non-Normality of Residuals (Normal Q-Q Plot)
- The Q-Q plot shows heavy deviations in both tails.
- Suggests the residuals are not normally distributed, which may impact hypothesis testing.
Heteroscedasticity (Scale-Location Plot)
- Residual spread is not uniform across fitted values.
- Variance increases for certain values, violating homoscedasticity.
High-Leverage & Influential Points (Residuals vs Leverage Plot)
- Observations with high leverage are identified (e.g., 143203, 760650).
- These points may disproportionately impact the model.
Dependent Variables
To address non-normality in the regression, we first examine the distributions of the dependent variables. Numeric variable distributions are represented in blue, while categorical variables are shown in orange. Variables exhibiting non-normality typically display right skewness. To mitigate this, we will apply a logarithmic transformation to these variables in an effort to normalize their distributions and improve the model’s assumptions.
Independent Variable
In regression analysis, it is common to apply a logarithmic transformation to price because price data often follow a skewed distribution, with a few extreme values pulling the distribution to the right. This can violate the assumption of normality, which is important for many statistical tests and models. The logarithmic transformation helps to compress the scale of high values, making the distribution more symmetric and closer to normal. This also helps stabilize the variance and reduce the influence of outliers, leading to more reliable regression results. Additionally, applying a log transformation often interprets coefficients more meaningfully, as changes in the log-transformed variable can be interpreted in terms of percentage changes rather than absolute changes.
High leverage points can distort regression estimates, reduce accuracy, and violate key assumptions by skewing coefficients, lead to heteroscedasticity, non-normal residuals, and misleading p-values. Removing these points ensures a more robust, reliable, and generalizable model. Using diagnostics like Cook’s Distance, we can identify and exclude them for a more stable and meaningful parcel price analysis. From the Residuals vs. Leverage plot, we identified the following influential data points with high Cook’s Distance: 306, 3722, 12370.
The threshold used for identifying influential observations is:
influence <- influence.measures(model)
high_influence <- which(influence$infmat[, "cook.d"] > 4/(nrow(df)-length(model$coefficients)-2))
df <- df[-high_influence, ]Multicollinearity occurs when independent variables in a regression model are highly correlated, leading to unstable coefficient estimates and inflated standard errors. To assess multicollinearity, we use the Generalized Variance Inflation Factor (GVIF), which extends the traditional VIF to categorical variables with multiple levels.
Since GVIF depends on the degrees of freedom (Df) of a variable, we compute
| GRADEDESC | 1.839543 | 1 | 1.356298 |
| log(FINISHEDLIVINGAREA + 0.001) | 3.509536 | 1 | 1.873376 |
| SALEDESC.x | 1.274342 | 25 | 1.004860 |
| HEATINGCOOLING | 1.777424 | 15 | 1.019357 |
| STYLE | 2813.159214 | 28 | 1.152372 |
| FULLBATHS | 3.333085 | 9 | 1.069171 |
| log(LOTAREA + 0.001) | 39.207922 | 1 | 6.261623 |
| HALFBATHS | 1.549149 | 7 | 1.031759 |
| CONDITION | 1.118446 | 1 | 1.057566 |
| FIREPLACES | 1.486511 | 8 | 1.025087 |
| log(TOTALROOMS + 0.001) | 4.141634 | 1 | 2.035100 |
| EXTERIORFINISH | 1.110825 | 1 | 1.053957 |
| BEDROOMS | 6.372283 | 13 | 1.073827 |
| STORIES | 15.339543 | 10 | 1.146280 |
| AGE | 3.318723 | 1 | 1.821736 |
# 3. Check for multicollinearity using VIF
vif_values <- vif(model)
print(vif_values)By applying weights based on the fitted values from an initial model, WLS minimizes the influence of high-variance observations, providing more accurate estimates of the regression coefficients. In OLS regression, the ordinary least squares method minimizes the sum of squared residuals under the assumption that the variance of residuals is constant across all levels of the independent variables (homoscedasticity). However, when there is heteroscedasticity (non-constant variance of residuals), OLS estimates become inefficient, and the standard errors of the coefficients may be biased.
To address this, Weighted Least Squares (WLS) regression applies a weight to each observation, which accounts for the varying variability in the data. The weights are typically the inverse of the variance of each observation, and they down-weight observations that have larger residuals (i.e., higher variance) and up-weight those with smaller residuals (i.e., lower variance).
The weights are computed as the inverse of the fitted values from an initial OLS regression model:
Full Model
lm(LOG_PRICE ~ ..., data = df, weights = 1 / sqrt(fitted(model)))
The Box-Cox transformation is applied to the dependent variable (PRICE) to identify an optimal transformation (lambda) that improves the model’s normality. The test revealed that the optimal value of (PRICE^2) would be the most effective. However, to handle the skewness effectively, we applied the square root transformation instead, which is a commonly used method for right-skewed data such as parcel prices. we compared the square root version to the squared version, and the square root version diagnostic was significantly better than the squared.
The general formula for the Box-Cox transformation is as follows:
Moving forward, we will proceed with both the Weighted Least Squares (WLS) model and the Lambda-transformed model. While neither approach is perfect, each provides unique strengths in capturing different segments of the parcel market. The Lambda-transformed model better accounts for lower-end parcel prices, while the WLS model more effectively captures higher-end parcel prices. By comparing the results of both models and identifying consistent patterns, we can enhance the robustness of our analysis. Interpreting each model through the lens of its strengths allows us to achieve a more comprehensive and reliable assessment of parcel prices in Pittsburgh.
ANCOVA is performed to compare the mean prices of homes across different ZIP codes, adjusting for other variables in the model. The significance of sale year and zip code tells us that there is significant variation in parcel prices from these variables, controlling for all other property and land characteristics from our previous models. Moving forward, we will calculate adjusted means for both the transformed model and the wls model, to get a complete picture of Pricing patterns.
| Variable | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|---|---|---|---|---|
| as.factor(PROPERTYZIP.x) | 37 | 12011 | 325 | 246.582 | < 2e-16 |
| as.factor(SALEYEAR) | 13 | 7691 | 592 | 449.356 | < 2e-16 |
| ... | .. | .... | ... | ....... | ....... |
| Residuals | 140620 | 185128 | 1 |
# Perform ANOVA to compare to see if zip and year still have a significant impact on House Prices Even After Accounting for Other Confounding Variables
anova_results <- aov(model)
# Display the ANCOVA table
summary(anova_results)Finally, adjusted means for the parcel prices across ZIP codes are calculated, accounting for nuisance variables like GRADEDESC, SALEDESC.x, and HEATINGCOOLING. These adjusted means are visualized to identify which ZIP codes are the most and least expensive.
While the adjusted average parcel prices across various Pittsburgh ZIP codes show clear trends, it is important to interpret the data with caution:
Overlapping Confidence Intervals
The overlapping error bars in the visualizations for the top and bottom ZIP codes indicate that, while the prices for these areas differ, the variation within these neighborhoods makes it difficult to confidently state that one ZIP code is definitively the most expensive or on the other hand the cheapest.
Significant Price Differences Between Highest and Lowest ZIP Codes:
The red line in the visualization represents the upper limit of the confidence interval for the lowest-priced ZIP code. This means that, while there is overlap in some of the adjusted mean prices, those ZIP codes whose lower confidence interval does not cross the red line can be considered significantly different in terms of pricing from the lowest-priced neighborhood.
Despite the overlapping error within the groups of ZIP codes (highest price and lowest priced), we can confidently say that there is a significant difference in price when comparing the highest and lowest priced neighborhoods, holding all house and land features constant. The clear price gap between these groups indicates that the factors driving high prices in areas like 15232 are substantially different from those in areas like 15235, even after accounting for property features such as size, age, and condition.
grid <- ref_grid(model_transformed, nuisance = c("GRADEDESC", "SALEDESC.x", "HEATINGCOOLING", "STYLE",
"FULLBATHS", "CONDITION", "FIREPLACES", "EXTERIORFINISH",
"BEDROOMS", "STORIES", "YEARBLT"))
adjusted_means_transformed <- emmeans(grid, ~ PROPERTYZIP.x)
The adjusted average parcel prices across various Pittsburgh ZIP codes reveal important insights into the parcel market dynamics:
Parallel Trends Across ZIP Codes
Both the top three highest and lowest ZIP codes in terms of parcel prices, including 15232, 15217, 15222 (high-priced areas), and 15204, 15210, 15235 (lower-priced areas), show fairly parallel trends over time. Despite differences in their price levels, all these areas have experienced similar effects from broader market forces such as inflation and fluctuations in the parcel market. Influence of Timing and Inflation:
This suggests that, although the price points differ across neighborhoods, the overall trend of increasing parcel prices (with occasional fluctuations) has been a common experience for both high-end and more affordable areas. This trend reflects a generalized market shift rather than isolated changes in individual neighborhoods. Seeing this parallel trend validates our previous adjusted means because regardless of the adjusted mean year held constant, the ranking remains the same.
adjusted_means_transformed <- emmeans(grid, ~ PROPERTYZIP.x * SALEYEAR)
| Metric | Value |
|---|---|
| Max CI Difference | $426965.34 |
| Min CI Difference | $170959.97 |
| Average Predicted Price Difference | $426965.34 |
# Find the highest and lowest 'emmean' values
max_emmean = df_cleaned['adjusted_price'].max()
min_emmean = df_cleaned['adjusted_price'].min()
# Calculate the difference between the highest and lowest 'emmean' values
emmean_difference = max_emmean - min_emmean# Find the rows with the highest and lowest 'emmean'
max_emmean_row = df_cleaned.loc[df_cleaned['adjusted_price'] == max_emmean]
min_emmean_row = df_cleaned.loc[df_cleaned['adjusted_price'] == min_emmean]
# Get the lower_ci of the row with the lowest emmean and the upper_ci of the row with the highest emmean
lower_ci_lower_emmean = min_emmean_row['lower_ci'].values[0] # lower_ci of the lower emmean
upper_ci_higher_emmean = max_emmean_row['upper_ci'].values[0] # upper_ci of the higher emmean
# Calculate the difference
price_difference = upper_ci_higher_emmean - lower_ci_lower_emmeanThe estimated price difference between the most expensive and least expensive ZIP codes in Pittsburgh is $298,940.92, with a confidence interval ranging from $170,959.96 to $426,965.34. This significant disparity highlights the substantial variation in parcel prices across different areas.
The most expensive ZIP codes include 15232, 15217, 15222, 15201, and 15213, indicating neighborhoods with higher market valuations. In contrast, the least expensive ZIP codes, such as 15235, 15210, 15204, 15221, and 15214, reflect areas with lower parcel prices. While there is a significant difference between the low house price zip codes and the high house price zip codes, the top 3-5 of each respective group's confidence intervals overlap so much that we can not identify a most or least expensive zip code with confidence.
This estimated difference holds all house characteristics constant, meaning it represents the price change if the same house were hypothetically moved from one ZIP code to another. In other words, if you took a house from an inexpensive ZIP code and placed it in an expensive ZIP code, this is the price difference we would expect to see, purely based on location.
Both the highest- and lowest-priced ZIP codes have followed parallel trends over time. This suggests that parcel prices across Pittsburgh, regardless of their starting points, have been shaped by overarching market forces rather than isolated neighborhood-specific changes. Furthermore, this parallel trend reinforces the validity of our adjusted mean estimates, as the ranking of ZIP codes remains consistent regardless of the adjustment year.
While this analysis provides insight into price variation across ZIP codes, it does not yet explain why these differences exist. Moving forward, we will analyze geospatial data to explore the underlying factors driving these disparities, such as crime rates and school quality. Combining Adjusted Mean Data (from our above analysis) with geospatial data to allow us to develop a more comprehensive understanding of the forces shaping Pittsburgh’s parcel market.
The aim of this analysis is to understand why certain ZIP codes in Pittsburgh have higher parcel prices than others by analyzing factors such as crime rates, school district quality, and other socioeconomic factors. By combining spatial, demographic, and geographic data, this project provides a comprehensive analysis of the key drivers behind property value disparities across Pittsburgh.
The analysis requires integrating data from various sources with different structures. The key merging steps are:
- Merge Parcel Prices with ZIP Codes: Merge the
zipcode_avg_pricedataset (which contains average prices by ZIP code) with thezipsGeoDataFrame to analyze how prices vary geographically. - Merge Crime Data: Perform a spatial join between the crime data (arrest incidents) and the ZIP code boundaries to calculate arrest density in each ZIP code.
- School District Data Integration: Using fuzzy matching, align the school district rankings to the corresponding ZIP codes.
- Population Data Merge: Merge population data with arrest counts to normalize arrest density by population, allowing for a more accurate comparison of crime rates across neighborhoods.
- Merge Parcel Prices with ZIP Codes: Merge the
zipcode_avg_pricedataset (from the above eemaean analysis) with thezipsGeoDataFrame to analyze how prices vary geographically. Be sure to treat the zip code column of each data frame as an integer to ensure a proper merge.
# Step 3: Merge the GeoDataFrame with the price data (based on ZIP code)
zips_with_prices = zips.merge(zipcode_avg_price, left_on='ZIP', right_on='PROPERTYZIP.x')- Check Coordinate Type: Check the coordinate format of the geojson provided by Allegheny County. We will need to ensure compatibility with other geojsons and to understand possible distortions when viewing the zip code area. The coordinate system in this file is
crs="EPSG:4326"
Crime is often a significant factor affecting property values. Areas with higher crime rates typically see lower property values due to safety concerns. Crime data in this project comes from Pittsburgh’s public crime reporting system, which provides details on incidents, including arrests, and the locations (latitude and longitude) of these events.
- Geo-spatial Join: Crime data, which contains coordinates for each incident, is joined with the ZIP code boundaries using GeoPandas. This spatial join links each crime incident to a specific ZIP code.
# Step 3: Convert the DataFrame to a GeoDataFrame
gdf = gpd.GeoDataFrame(df, geometry=gpd.points_from_xy(df['X'], df['Y']), crs="EPSG:4326")
# Ensure Compatability
zipcodes_gdf = zipcodes_gdf.set_crs("EPSG:4326")-
Arrest Density Calculation: The number of arrests in each ZIP code is divided by the population of the ZIP code to calculate arrest density—the number of arrests per square meter. High arrest density in a ZIP code typically correlates with lower property values, which is expected based on general urban real estate trends.
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Crime Rate and Parcel Prices: Once the arrest density is calculated, it is merged with the Adjusted Parcel price data. This allows us to explore how areas with higher crime rates (higher arrest density) correlate with lower property values.
# Step 5: Perform a spatial join to assign ZIP codes to incident features
incidents_with_zip = gpd.sjoin(gdf, zipcodes_gdf, how="left", predicate="intersects")
# Step 6: Count the number of incidents (arrests) per ZIP code
zipcode_counts = incidents_with_zip.groupby('ZIP').agg(num_incidents=('ARRESTLOCATION', 'count')).reset_index()
# Step 7: Merge the ZIP code boundary GeoDataFrame with the incident count data
zips_with_incidents = zipcodes_gdf.merge(zipcode_counts, left_on='ZIP', right_on='ZIP', how='left')
- Higher crime rates are generally associated with lower property prices.
- Crime hotspots in Pittsburgh, where arrest density is high, show a marked decrease in average parcel prices compared to safer neighborhoods.
- Neighborhoods with low crime rates tend to have higher property values, highlighting the importance of safety as a key factor in homebuying decisions.
The quality of local schools is often a significant factor in determining real estate prices, as many homebuyers are willing to pay a premium for access to high-performing school districts. For this project, school district boundaries were mapped using the GeoJSON file for school districts in Allegheny County, Pittsburgh.
- Fuzzy Matching: Because the names of school districts in the external dataset may not exactly match those in the ZIP code data, fuzzy matching techniques were used to align school district names to the correct ZIP codes.
def fuzzy_match(row, choices, threshold=80):
match = process.extractOne(row, choices, scorer=fuzz.partial_ratio)
if match and match[1] >= threshold:
return match[0]
return None
# Extract the school district names from the df DataFrame for matching
df_school_districts = df['School District'].tolist()
# Perform fuzzy matching on the 'SCHOOLD' column of zip_school_join
zip_school_join['Matched School District'] = zip_school_join['SCHOOLD'].apply(
fuzzy_match, args=(df_school_districts, 80))- Merging School District Boundaries: After the fuzzy matching, the school district boundaries were merged with the ZIP codes to associate each ZIP code with its corresponding school district.
- School District Rankings: School district rankings were then linked to each ZIP code. Since the zipcodes and school district lines do not perfectly match up we average the rank of each school within the zipcode. A higher ranking (indicating a better-performing school district) is associated with a higher price for homes in that ZIP code, as families often prioritize access to quality education.
# Group by 'ZIP' and calculate the average rank for each ZIP code
zip_avg_rank = merged_df.groupby('ZIP')['Rank'].mean().reset_index()- Rank Inversion: To ensure better clarity in interpretation, the school district ranking values were inverted, so that a higher value represented a better-ranked school district.
zip_avg_rank['Inverted Rank'] = max_rank - zip_avg_rank['Rank'] + 1
- Better-performing school districts correlate with higher parcel prices. Homebuyers are often willing to pay more for properties located in areas with highly-ranked schools.
- Areas with high-ranked schools (such as Mt. Lebanon, Fox Chapel, and Pine-Richland) exhibit higher property values, making school district quality a significant factor in the parcel price equation.
- Neighborhoods with poor-performing schools tend to have more affordable parcels, which might be due to lower demand for homes in those areas.
- Certain neighborhoods in Pittsburgh, even without the best-ranked schools or lowest crime rates, maintain higher property values due to geographic features such as proximity to the city center or desirable scenic views.
In this alternative analysis, we aim to isolate the underlying value of the location by subtracting the fair market value of the house's physical structure (which includes the appraised value of the building and the lot) from the actual house price. This analysis is based on the assumption that the price of a house can be decomposed into two main components:
- Fair Market Value (FMV): The FMV is assumed to reflect the appraised value of both the land and the building itself. For this analysis, we subtract this value from the house price to estimate the pure location value.
- Location Value: This value represents the premium placed on a property's location — factors such as proximity to schools, amenities, transportation, and other location-based advantages or disadvantages are not reflected by the FMV.
- Subtract Fair Market Value: We subtract the fair market value (FMV) of the house (which is the combined appraised value of the building and the land) from the price of the house. This leaves us with the location value, which captures how much the area or neighborhood contributes to the house price, independent of its physical structure.
-
Group Differences by ZIP Code: After calculating the location value for each house, we group the location value differences by ZIP code to identify whether different areas command different underlying values that are not captured by the physical structure of the house itself.
-
Analysis Objective: By comparing the location value across different ZIP codes, we can explore whether certain regions have significantly higher or lower underlying values, independent of the size or condition of the houses themselves. This allows us to assess how much value the neighborhood or location adds to the overall house price.
Without controlling for the types of houses and other factors, we can see that over time the difference fluctuates much more than in our main analysis. This suggests that, when ignoring the influence of other variables such as house size, condition, and location, the differences in house prices across time appear more volatile. However, without accounting for these other factors, the confidence intervals of differences between ZIP codes become much smaller. This indicates that while the raw differences may appear larger, this indicates that the types of houses are similar within zip codes, but can vary widely between zip codes. This is why other confounding factors are important. When controlling for these factors, the differences between ZIP codes become less pronounced but more reliable.
This project leverages the following R libraries:
- tidyverse: For data manipulation and visualization.
- car: For regression diagnostics and VIF (Variance Inflation Factor).
- ggplot2: For creating visualizations.
- MASS: For statistical modeling functions.
- readxl: For reading Excel files (if needed).
- softImpute: For matrix factorization techniques (if any missing values).
- stargazer: For presenting summary statistics and regression results.
- gridExtra: For arranging multiple plots in a grid.