In a mode choice model, a positive coefficient for travel cost is counterintuitive because travel cost is typically expected to have a negative impact on utility (higher cost should decrease the likelihood of choosing a mode). Here are some possible reasons for this issue:

1. Data Issues

* Incorrect Cost Data: If the travel cost variable is incorrectly recorded or has errors (e.g., costs are miscalculated or misrepresented), it could lead to a misleading positive coefficient.

* Reverse Coding Issue: If travel cost is coded in a way where higher values represent cheaper modes due to subsidies or incentives, this could flip the expected sign.

* Outliers in Data: A few extreme values in the cost variable may distort the coefficient estimation.

2. Model Specification Issues

* Omitted Variable Bias: If an important variable (e.g., income, subsidies, travel time) is omitted, the cost coefficient might pick up its effect, leading to an unexpected sign.

* Correlation with Other Variables: If travel cost is highly correlated with another variable (e.g., comfort, reliability), the model might assign part of the other variable’s effect to travel cost.

* Interaction Effects: If there is an interaction effect between cost and another variable (e.g., income or trip purpose), it might lead to an unexpected positive coefficient.

3. Behavioral Explanations

* High-Cost Modes Are Preferred: If high-cost modes are associated with higher service quality (e.g., first-class train, business-class flights), travelers might prefer them despite higher costs.

* Subsidized Modes or Reimbursements: If travel costs are reimbursed (e.g., corporate travel expenses) or subsidized, travelers might not be sensitive to cost.

*Luxury vs. Necessity Behavior: Some travelers may view cost as a proxy for convenience or prestige, leading to a preference for more expensive modes.

How to Fix It?

· Check your data for errors or incorrect coding.

· Include missing variables (e.g., income, travel time, subsidies).

· Examine multicollinearity by checking correlations between variables.

· Consider alternative model specifications to capture interaction effects.