Skewed Measurement Error Can Bias Regressions Even When Small

📌 What’s the problem?

Classical measurement error in a dependent variable in linear regression only reduces precision. Nonclassical measurement error, however, can produce biased estimates and weak inference. One common form of nonclassical error is skewed (one-sided) measurement error, which is likely in many political science outcomes.

🧾 What this study investigates

Focus is on skewed measurement error in the dependent variable and how even relatively small amounts of skew—especially when the error is heteroskedastic—can distort estimates from ordinary linear regression.

🔬 How the issue is explored

• Examined the theoretical bias that skewed, nonclassical measurement error introduces in linear regression estimates.
• Assessed two potential remedies: the stochastic frontier model and Nonlinear Least Squares (NLS).
• Used simulations and three replication exercises to evaluate how these methods perform under realistic conditions.

📈 Key findings

• Classical measurement error: mainly a loss of precision.
• Skewed (nonclassical) measurement error: can generate biased parameter estimates and reduce inferential power.
• Heteroskedastic skewed error amplifies bias, so even modest skew can have substantial effects.
• Alternative estimation strategies (stochastic frontier, NLS) were evaluated as potential solutions; simulations and replications underscore the importance of explicitly accounting for skew when it is plausible.

🔎 Why it matters

Ignoring skewed or one-sided measurement error in political science outcomes risks producing misleading estimates and underpowered tests. Careful diagnostics and consideration of estimation approaches that allow for skew and heteroskedastic error are important for credible inference.