Regression Diagnostics by Period using REPS"

In REPS: Hedonic and Multilateral Index Methods for Real Estate Price Statistics

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(REPS)
data("data_constraxion")

Introduction

The calculate_regression_diagnostics() function in REPS provides regression diagnostics by period. It is designed for panel or repeated cross-section data (e.g. property transactions over time) to evaluate the quality of period-specific log-linear regressions.

For each period, it:

• Fits a log-linear regression model: log(price) ~ covariates
• Computes diagnostics:
• Shapiro-Wilk p-value (normality)
• Adjusted R-squared (linearity)
• Durbin-Watson test (autocorrelation)
• Breusch-Pagan test (heteroscedasticity)

These diagnostics help assess model quality over time, identifying periods with issues like non-normality, low fit, heteroscedasticity, or autocorrelation.

Required Data

Your dataset should include:

• A period variable (e.g. quarterly/annual codes)
• A dependent variable (typically price)
• One or more numerical independent variables (e.g. floor area)
• Optionally, categorical independent variables (e.g. neighbourhood codes)

# Example dataset (you should already have this loaded)
head(data_constraxion)

# We log transform the floor_area again (see vignette on calculating price index as why)
dataset <- data_constraxion
dataset$floor_area <- log(dataset$floor_area)

Using calculate_regression_diagnostics()

Example:

diagnostics <- calculate_regression_diagnostics(
  dataset = dataset,
  period_variable = "period",
  dependent_variable = "price",
  numerical_variables = c("floor_area", "dist_trainstation"),
  categorical_variables = c("dummy_large_city", "neighbourhood_code")
)

head(diagnostics)

Visualizing Diagnostics

For convenient visualization:

plot_regression_diagnostics(diagnostics)

This generates a 3x2 grid of plots:

• Normality (p-value Shapiro-Wilk)
• Linearity (Adjusted R-squared)
• Autocorrelation (Durbin-Watson statistic)
• Autocorrelation (p-value Durbin-Watson)
• Heteroscedasticity (p-value Breusch-Pagan)

Example:

knitr::include_graphics("diagnostics_plot.png")

Interpreting the Output

The hedonic price index relies on a log-linear regression model, which assumes that certain statistical conditions hold. The diagnostics plot provides an overview of how well these assumptions are met across different periods.

Each subplot corresponds to a specific model assumption:

Row 1: Normality and Linearity

• Shapiro-Wilk test (left plot)
• Shows p-values for the normality of residuals.

• A p-value below 0.05 (dashed red line) indicates a potential violation of the normality assumption.

• Adjusted R-squared (right plot)

• Reflects the explanatory power of the regression model.
• Values below 0.6 (dashed red line) may indicate a weak linear relationship.

Row 2: Independence

• Durbin-Watson statistic (left plot)
• Tests for autocorrelation in residuals.
• Ideal value is around 2.

• Values outside the 1.75–2.25 range (dashed lines) suggest potential autocorrelation.

• Durbin-Watson p-value (right plot)

• Indicates whether autocorrelation is statistically significant.
• p > 0.05: no significant evidence of autocorrelation.
• p ≤ 0.05: residuals may not be independent.

Row 3: Homoscedasticity

• Breusch-Pagan p-value
• Tests whether residuals have constant variance.
• A p-value below 0.05 (dashed red line) suggests heteroscedasticity (non-constant variance).

Summary

The calculate_regression_diagnostics() and plot_regression_diagnostics() functions in REPS enable:

• Period-by-period regression checking
• Easy comparison of assumptions over time
• Detection of problematic periods

They support robust, high-quality hedonic price index modeling by systematically checking regression assumptions.

REPS documentation built on March 16, 2026, 5:08 p.m.