Equity Studies

Understanding horizontal and vertical equity in mass appraisal

Overview

Equity in mass appraisal means treating all property owners fairly. OpenAVM Kit provides tools to measure and ensure both horizontal equity (similar properties assessed similarly) and vertical equity (consistent treatment across value levels).

Equity analysis ensures that assessment models don’t systematically favor or penalize certain property types or value ranges.

Types of Equity

Horizontal Equity

Definition: Properties with similar characteristics should have similar assessment ratios.

Measurement: Coefficient of Horizontal Dispersion (CHD) within clusters of comparable properties.

Vertical Equity

Definition: Assessment ratios should be consistent across different value levels.

Measurement: Price-Related Differential (PRD) and Price-Related Bias (PRB).

Horizontal Equity Analysis

The Clustering Approach

Horizontal equity requires identifying groups of similar properties:

from openavmkit.horizontal_equity_study import (
    mark_horizontal_equity_clusters,
    HorizontalEquityStudy
)

# Mark clusters based on location and characteristics
df = mark_horizontal_equity_clusters(
    df,
    settings,
    verbose=True,
    id_name="he_id"
)

# Analyze equity within clusters
study = HorizontalEquityStudy(
    df,
    field_cluster="he_id",
    field_value="prediction"
)

Configuration

Define clustering criteria in settings:

analysis:
  horizontal_equity:
    enabled: true
    location: neighborhood  # Primary geographic grouping
    fields_categorical:
      - property_class
      - bedrooms
      - bathrooms
    fields_numeric:
      - year_built: 10      # Bin by decade
      - living_area_sf: 500 # Bin by 500 sqft

HorizontalEquitySummary

The summary provides distribution statistics across all clusters:

summary = study.summary

print(f"Total Rows: {summary.rows:,}")
print(f"Total Clusters: {summary.clusters:,}")
print(f"Median CHD: {summary.median_chd:.2f}")
print(f"5th percentile CHD: {summary.p05_chd:.2f}")
print(f"95th percentile CHD: {summary.p95_chd:.2f}")

Attributes:

• rows: Total number of properties analyzed
• clusters: Number of comparable property groups
• min_chd: Best-performing cluster
• max_chd: Worst-performing cluster
• median_chd: Typical cluster performance
• p05_chd, p25_chd, p75_chd, p95_chd: Percentile distributions

Coefficient of Horizontal Dispersion (CHD)

CHD is calculated as COD within each cluster:

import numpy as np
from openavmkit.utilities.stats import calc_cod

# For each cluster
for cluster_id in df["he_id"].unique():
    df_cluster = df[df["he_id"] == cluster_id]
    values = df_cluster["prediction"].values
    
    # CHD is the COD within the cluster
    chd = calc_cod(values)
    print(f"Cluster {cluster_id}: CHD = {chd:.2f}")

Cluster Summary

Each cluster has detailed statistics:

from openavmkit.horizontal_equity_study import HorizontalEquityClusterSummary

# Access individual cluster summaries
for cluster_id, cluster_summary in study.cluster_summaries.items():
    print(f"Cluster: {cluster_summary.id}")
    print(f"  Count: {cluster_summary.count}")
    print(f"  CHD: {cluster_summary.chd:.2f}")
    print(f"  Min: ${cluster_summary.min:,.0f}")
    print(f"  Median: ${cluster_summary.median:,.0f}")
    print(f"  Max: ${cluster_summary.max:,.0f}")

Attributes:

• id: Cluster identifier
• count: Number of properties in cluster
• chd: Coefficient of Horizontal Dispersion
• min: Minimum value in cluster
• max: Maximum value in cluster
• median: Median value in cluster

Multi-Level Equity Analysis

OpenAVM Kit supports specialized equity clusters:

from openavmkit.horizontal_equity_study import mark_horizontal_equity_clusters_per_model_group_sup

# Mark general, land, and improvement equity clusters
sup = mark_horizontal_equity_clusters_per_model_group_sup(
    sup,
    settings,
    verbose=True,
    do_land_clusters=True,    # For vacant land equity
    do_impr_clusters=True     # For improvement equity
)

This creates three cluster types:

• General clusters (he_id): Overall horizontal equity
• Land clusters (land_he_id): Equity for land values
• Improvement clusters (impr_he_id): Equity for building values

Land Equity Configuration

analysis:
  land_equity:
    location: neighborhood
    fields_categorical:
      - zoning
      - land_use
    fields_numeric:
      - lot_size_sf: 5000

When analyzing land equity, you should provide at least a location field to ensure meaningful clusters.

Improvement Equity Configuration

analysis:
  impr_equity:
    location: neighborhood
    fields_categorical:
      - property_class
      - construction_quality
    fields_numeric:
      - year_built: 10
      - living_area_sf: 500

Vertical Equity Analysis

Vertical equity examines consistency across property value levels:

VerticalEquityStudy Class

from openavmkit.vertical_equity_study import VerticalEquityStudy

# Create vertical equity study
study = VerticalEquityStudy(
    df_sales,
    field_sales="sale_price",
    field_prediction="prediction",
    field_location="neighborhood",
    confidence_interval=0.95,
    iterations=10000
)

Key Metrics

The study calculates:

PRD (Price-Related Differential):

print(f"PRD: {study.prd.value:.3f}")
print(f"95% CI: [{study.prd.low:.3f}, {study.prd.high:.3f}]")

PRB (Price-Related Bias):

print(f"PRB: {study.prb.value:.3f}")
print(f"95% CI: [{study.prb.low:.3f}, {study.prb.high:.3f}]")

Summary Output

df_summary = study.summary()
print(df_summary)

Output includes:

• Point values for PRD and PRB
• Confidence interval bounds
• Statistical significance indicators
• IAAO compliance flags

Price Quantile Analysis

Vertical equity studies divide sales into price tiers:

# Analyze median ratio by price quantile
df_quantiles = study.quantiles

print(df_quantiles[["quantile", "ratio", "ratio_low", "ratio_high"]])

Output:

   quantile  ratio  ratio_low  ratio_high
0        10  1.042      1.028       1.056
1        20  1.035      1.022       1.048
2        30  1.028      1.016       1.040
...

Grouped Quantiles

Grouped quantiles assign entire neighborhoods to price tiers:

# Use grouped quantiles for geographic consistency
df_grouped = study.grouped_quantiles

This prevents neighborhoods from being split across multiple price tiers.

Visualization

Plot vertical equity:

# Plot median ratio by price tier
study.plot_quantiles(
    ci_bounds=True,    # Show confidence intervals
    ylim=(0.9, 1.1),   # Y-axis limits
    grouped=False      # Use direct quantiles
)

Ideal vertical equity shows a flat line around 1.0 across all price tiers, indicating consistent assessment levels.

Interpreting Results

Horizontal Equity Benchmarks

Median CHD	Assessment Quality
< 5.0	Excellent
5.0-10.0	Good
10.0-15.0	Acceptable
> 15.0	Needs improvement

Vertical Equity Benchmarks

PRD Standards:

• Excellent: 0.98-1.03
• Acceptable: 0.95-1.05
• Needs improvement: Outside acceptable range

PRB Standards:

• Excellent: -0.05 to +0.05
• Acceptable: -0.10 to +0.10
• Needs improvement: Outside acceptable range

Statistical Significance

Use confidence intervals to determine significance:

prd = study.prd

if prd.low <= 1.00 <= prd.high:
    print("PRD is not statistically different from 1.00")
else:
    if prd.value > 1.00:
        print("Statistically significant REGRESSIVITY detected")
    else:
        print("Statistically significant PROGRESSIVITY detected")

Statistically significant inequity requires model adjustment. Don’t ignore systematic bias, even if metrics are close to targets.

Addressing Inequity

For Horizontal Inequity (High CHD)

1. Add more property characteristics to differentiate similar properties
2. Refine clustering criteria for better comparable groups
3. Check data quality in high-CHD clusters
4. Consider local market factors not captured by the model

For Vertical Inequity (PRD/PRB issues)

1. Check for non-linear relationships in value
2. Add value-based features or interactions
3. Use stratified models for different value ranges
4. Apply post-modeling adjustments to correct bias

Complete Workflow

from openavmkit.data import SalesUniversePair
from openavmkit.horizontal_equity_study import (
    mark_horizontal_equity_clusters_per_model_group_sup,
    HorizontalEquityStudy
)
from openavmkit.vertical_equity_study import VerticalEquityStudy

# Step 1: Mark horizontal equity clusters
sup = mark_horizontal_equity_clusters_per_model_group_sup(
    sup,
    settings,
    verbose=True
)

# Step 2: Analyze horizontal equity
he_study = HorizontalEquityStudy(
    sup.universe,
    field_cluster="he_id",
    field_value="prediction"
)

print("\nHorizontal Equity Summary:")
print(he_study.summary.print())

# Step 3: Analyze vertical equity
df_sales = get_hydrated_sales_from_sup(sup)
ve_study = VerticalEquityStudy(
    df_sales,
    field_sales="sale_price",
    field_prediction="prediction",
    field_location="neighborhood"
)

print("\nVertical Equity Summary:")
print(ve_study.summary())

# Step 4: Visualize
ve_study.plot_quantiles(ci_bounds=True)

Best Practices

1. Define Meaningful Clusters

   Use location, property type, and key characteristics to create comparable groups

2. Analyze Both Dimensions

   Horizontal and vertical equity are equally important for fair assessment

3. Use Confidence Intervals

   Bootstrap methods provide robust statistical inference

4. Monitor Over Time

   Track equity metrics across assessment cycles

5. Address Systematic Issues

   Statistically significant inequity requires model refinement

Next Steps

Ratio Studies

Learn about COD, PRD, and ratio study metrics

SHAP Analysis

Understand model predictions with SHAP values