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The vertical equity module analyzes whether properties at different price levels are assessed fairly. It detects systematic over-assessment or under-assessment at different price tiers.

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Classes

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VerticalEquityStudy

Perform vertical equity analysis and summarize the results. Attributes:
  • rows (int): Total number of rows in the input DataFrame
  • confidence_interval (float): The confidence interval (e.g. 0.95 for 95% confidence)
  • prd (ConfidenceStat): The price-related differential with confidence intervals
  • prb (ConfidenceStat): The price-related bias with confidence intervals
  • quantiles (pd.DataFrame): A DataFrame containing the median ratio with confidence intervals for all ten price quantile tiers
  • grouped_quantiles (pd.DataFrame): A DataFrame containing the median ratio with confidence intervals for location-grouped price quantile tiers

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__init__

VerticalEquityStudy(
    df_sales_in: pd.DataFrame,
    field_sales: str,
    field_prediction: str,
    field_location: str,
    confidence_interval: float = 0.95,
    iterations: int = 10000,
    seed: int = 777
)
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df_sales_in
pd.DataFrame
Input sales DataFrame
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field_sales
str
Column name for sale prices
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field_prediction
str
Column name for predicted/assessed values
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field_location
str
Column name for location grouping (e.g., neighborhood)
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confidence_interval
float
default:"0.95"
The confidence interval for bootstrap resampling (default 0.95 for 95% confidence)
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iterations
int
default:"10000"
Number of bootstrap iterations to perform
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seed
int
default:"777"
Random seed for reproducibility

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summary()

Generate a summary DataFrame of vertical equity statistics.
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return
pd.DataFrame
DataFrame containing PRD and PRB statistics with confidence intervals, statistical significance indicators, and IAAO standard compliance
The summary includes:
  • Point value for each statistic
  • Upper and lower confidence bounds
  • Statistical significance (whether confidence interval excludes neutral value)
  • IAAO recommended range compliance
  • IAAO passing range compliance

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plot_quantiles()

Plot median ratios across price quantiles to visualize vertical equity. 
plot_quantiles(
    ci_bounds: bool = False,
    ylim = None,
    grouped: bool = False
)
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ci_bounds
bool
default:"False"
If True, plots confidence interval bounds in addition to point estimates
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ylim
default:"None"
Y-axis limits. Can be:
  • None: Uses default range (0.0 to 2.0)
  • “min”: Auto-scales to data range
  • tuple of (min, max): Custom range
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grouped
bool
default:"False"
If True, uses location-grouped quantiles instead of direct price quantiles

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Metrics

The PRD measures whether assessments vary systematically with property values. Formula: 
PRD = (Mean Ratio) / (Weighted Mean Ratio)
where Weighted Mean Ratio = Sum(Assessed Values) / Sum(Sale Prices)
Interpretation:
  • PRD = 1.00: No price-related differential (perfect vertical equity)
  • PRD > 1.00: Regressive (higher-value properties are under-assessed relative to lower-value properties)
  • PRD < 1.00: Progressive (lower-value properties are under-assessed relative to higher-value properties)
IAAO Standards:
  • Recommended: 0.98 ≤ PRD ≤ 1.03
  • The same range applies for both recommended and passing
Statistical Significance: A PRD is statistically significant if its 95% confidence interval does not include 1.00.
The PRB measures systematic bias in assessments related to sale price using a more sophisticated regression approach. Formula: 
PRB = 2 × β₁ / (β₀ + β₁ × median_price)
where β₀ and β₁ are coefficients from the regression: 
(Assessed - Sale Price) = β₀ + β₁ × [(Assessed + Sale Price) / 2]
Interpretation:
  • PRB = 0: No price-related bias (perfect vertical equity)
  • PRB > 0: Regressive bias (higher-value properties are under-assessed)
  • PRB < 0: Progressive bias (lower-value properties are under-assessed)
  • PRB is expressed as a decimal (e.g., 0.05 = 5% bias)
IAAO Standards:
  • Recommended: -0.05 ≤ PRB ≤ 0.05
  • Acceptable/Passing: -0.10 ≤ PRB ≤ 0.10
Statistical Significance: A PRB is statistically significant if its 95% confidence interval does not include 0.00. Advantages over PRD:
  • More sensitive to bias at the extremes of the price range
  • Less affected by outliers
  • Preferred by IAAO for detecting vertical inequity

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Quantile Analysis

The vertical equity study divides sales into 10 quantiles (deciles) based on sale price and calculates the median assessment ratio for each quantile. Two Approaches:
  1. Direct Quantiles (quantiles attribute):
    • Properties sorted directly by sale price
    • Each property assigned to a price tier
    • Shows raw price-related patterns
  2. Grouped Quantiles (grouped_quantiles attribute):
    • Properties first grouped by location
    • Each location assigned to a price tier based on its modal quantile
    • All properties in that location inherit the tier
    • Accounts for location-based price differences
Interpretation:
  • Flat line across quantiles indicates good vertical equity
  • Upward slope indicates regressive assessment (higher-value properties over-assessed)
  • Downward slope indicates progressive assessment (lower-value properties over-assessed)
  • The plot_quantiles() method visualizes these patterns
Confidence Intervals: Bootstrap confidence intervals are calculated for each quantile’s median ratio, allowing assessment of statistical significance of differences between price tiers.

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