ResidualsVisualInspection

Provides a comprehensive visual analysis of residuals for regression models utilizing various plot types.

Purpose: The main purpose of this metric is to visualize and analyze the residuals (the differences between the observed and predicted values) of a regression problem. It allows for a graphical exploration of the model’s errors, helping to identify statistical patterns or anomalies that may indicate a systematic bias in the model’s predictions. By inspecting the residuals, we can check how well the model fits the data and meets the assumptions of the model.

Test Mechanism: The metric generates four common types of residual plots which are: a histogram with kernel density estimation, a quantile-quantile (Q-Q) plot, a residuals series dot plot, and an autocorrelation function (ACF) plot.

• The residuals histogram with kernel density estimation visualizes the distribution of residuals and allows to check if they are normally distributed.
• Q-Q plot compares the observed quantiles of the data to the quantiles of a standard normal distribution, helping to assess the normality of residuals.
• A residuals dot plot indicates the variation in residuals over time, which helps in identifying any time-related pattern in residuals.
• ACF plot visualizes the correlation of an observation with its previous observations, helping to pinpoint any seasonality effect within residuals.

Signs of High Risk:

• Skewness or asymmetry in the histogram or a significant deviation from the straight line in the Q-Q plot, which indicates that the residuals aren’t normally distributed.
• Large spikes in the ACF plot, indicating that the residuals are correlated, in violation of the assumption that they are independent.
• Non-random patterns in the dot plot of residuals, indicating potential model misspecification.

Strengths:

• Visual analysis of residuals is a powerful yet simple way to understand a model’s behavior across the data set and to identify problems with the model’s assumptions or its fit to the data.
• The test is applicable to any regression model, irrespective of complexity.
• By exploring residuals, we might uncover relationships that were not captured by the model, revealing opportunities for model improvement.

Limitations:

• Visual tests are largely subjective and can be open to interpretation. Clear-cut decisions about the model based solely on these plots may not be possible.
• The metrics from the test do not directly infer the action based on the results; domain-specific knowledge and expert judgement is often required to interpret the results.
• These plots can indicate a problem with the model but they do not necessarily reveal the nature or cause of the problem.
• The test assumes that the error terms are identically distributed, which might not always be the case in real-world scenarios.