Leveraging Heteroskedastic Extreme Value Frameworks to Specify Nested Tree Structures in Weibit Choice Models

Abstract

This study explores the application of the Heteroscedastic Extreme Value (HEV) framework to specify nesting structures in Weibit choice models. While the HEV framework has effectively defined nested tree structures in Logit choice models, its potential in Weibit models has not yet been investigated. The nested Weibit (NW) model uniquely addresses heterogeneous covariance between alternatives, unlike the nested Logit (NL) model, which maintains fixed covariance. However, establishing nest specifications within the NW model presents an ongoing empirical challenge. By implementing the HEV Weibit (HEVW) model, we leverage its capacity to estimate individual variances, yielding distinct shape parameters for each alternative in a choice set. This variance analysis can unveil tree structures that may not be immediately evident to analysts relying on intuitive configurations. We demonstrate how to specify these nested structures in Weibit choice models based on HEVW model results, supported by empirical findings from London mode choice behavior.