Pitfalls in Regression Analysis

Pitfalls in Regression Analysis

Multicollinearity

• Occurs when two or more independent variables are highly correlated, making it difficult to separate their individual effects on the dependent variable.
• Identification methods:
  • Calculate Variance Inflation Factor (VIF) for each independent variable; VIF above 10 suggests significant multicollinearity.
  • Check pairwise correlation coefficients between independent variables; correlations above 0.8 indicate potential multicollinearity.
• Remedies:
  • Remove or combine highly correlated variables.
  • Apply Principal Component Analysis (PCA) to reduce dimensionality while retaining variance.

Heteroscedasticity

• Occurs when the variance of residuals is not constant across all levels of the independent variables.
• Identification methods:
  • Plot residuals against predicted values or independent variables; funnel shape or systematic pattern suggests heteroscedasticity.
  • Perform Breusch-Pagan test; significant p-value indicates heteroscedasticity.
• Remedies:
  • Use heteroscedasticity-robust standard errors to correct for non-constant variance.
  • Apply transformations like logarithms to stabilize variance of residuals.
  • Apply Weighted Least Squares (WLS) to give different weights to observations, stabilizing variance.

Autocorrelation

• Occurs when residuals are correlated across observations, typically in time series data.
• Identification methods:
  • Calculate Durbin-Watson statistic; values significantly different from 2 suggest autocorrelation.
  • Plot residuals over time; patterns indicate autocorrelation.
• Remedies:
  • Adjust standard errors using Newey-West standard errors to account for autocorrelation.
  • Include lagged dependent or independent variables in the model.

Omitted Variable Bias

• Occurs when a relevant variable is left out of the model, leading to biased and inconsistent coefficient estimates.
• Identification methods:
  • Use theory and domain knowledge to identify potentially omitted variables.
  • Perform specification tests like the Ramsey RESET test to detect omitted variable bias.
• Remedies:
  • Add the omitted variables to the model if data is available.

Endogeneity

• Occurs when an independent variable is correlated with the error term, often due to omitted variable bias, measurement error, or simultaneity.
• Identification method:
  • Compare OLS and IV estimates using the Hausman test; significant differences indicate endogeneity.
• Remedies:
  • Use Instrumental Variables (IV) regression with instruments that are correlated with the endogenous variable but uncorrelated with the error term.

Model Misspecification

• Occurs when the functional form of the model is incorrect (e.g., omitting quadratic terms when the relationship is non-linear).
• Identification methods:
  • Check for systematic patterns in residuals.
  • Perform goodness-of-fit tests like the Ramsey RESET test to identify misspecification.