Why Multinomial Logit Coefficients Mislead: Focus on Predicted Probabilities

🔎 What the Problem Is

Multinomial logit (MNL) models estimate effects on nominal—rather than ordered—outcomes. Because coefficients in MNL are calculated relative to a chosen reference (or “baseline”) category, those coefficients change when the baseline changes. Many researchers recognize this point in principle but nonetheless use MNL coefficients the same way they use coefficients from models with ordered dependent variables, especially focusing on statistical significance of coefficients.

🧭 How This Issue Was Examined

• Emphasizes the conceptual difference between nominal and ordered outcomes in commonly used econometric methods.
• Highlights how the choice of reference category alters coefficient estimates without changing the underlying predicted probabilities.
• Traces how routine reliance on coefficient significance can produce statistics that do not correspond to the actual quantities of interest for the research question.

📌 Key Consequences

• Reporting and interpreting MNL coefficients as if they were invariant can lead to misleading inferences.
• Statistical significance of coefficients may not reflect statistical or substantive significance of the outcome probabilities that matter to the question at hand.
• As a result, researchers can report statistics that do not match the correct quantities of interest and thereby reach flawed conclusions.

💡 Why This Matters—and What Should Be Done

• Inference and interpretation should be oriented toward predicted probabilities (and comparisons of those probabilities) that directly match the substantive research question.
• Both substantive significance (how large or meaningful a probability change is) and statistical significance (whether that change is reliably different from zero) should be assessed for predicted probabilities rather than for baseline-dependent coefficients.

This note argues for shifting analytic attention from baseline-dependent coefficients to the predicted probabilities of interest to ensure correct substantive and statistical inference with multinomial logit models.