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Variance-component-based nested logit specifications: Improved formulation, and practical microsimulation of random disturbance terms

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  • Bunch, David S.
  • Rocke, David M.

Abstract

The initial motivation leading to the results in this paper was a problem most choice modeling researchers may have not considered: how to simulate random disturbance terms from nested logit (NL) models. We develop an approach using results from Cardell (1997), who proved the existence of a probability distribution (C(λ)) that could be used to formulate NL models based on statistically independent variance components. These components can be interpreted as unobserved preference heterogeneity for the choice ‘dimensions’ used to define NL tree structures. Simulation aside, we consider this formulation to have other practical advantages for empirical work, but it does not appear to have penetrated the literature (possibly due to notational obstacles). We use notation from Daly (2001) to implement an equivalent representation, which also establishes mathematical equivalence between Cardell (1997) and other important results in the NL literature.

Suggested Citation

  • Bunch, David S. & Rocke, David M., 2016. "Variance-component-based nested logit specifications: Improved formulation, and practical microsimulation of random disturbance terms," Journal of choice modelling, Elsevier, vol. 21(C), pages 30-35.
    • Handle: RePEc:eee:eejocm:v:21:y:2016:i:c:p:30-35
    DOI: 10.1016/j.jocm.2016.04.001
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    References listed on IDEAS

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    1. Daly, Andrew, 2001. "Alternative tree logit models: comments on a paper of Koppelman and Wen," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 717-724, September.
    2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555.
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    6. Cardell, N. Scott, 1997. "Variance Components Structures for the Extreme-Value and Logistic Distributions with Application to Models of Heterogeneity," Econometric Theory, Cambridge University Press, vol. 13(2), pages 185-213, April.
    7. Daly, Andrew & Bierlaire, Michel, 2006. "A general and operational representation of Generalised Extreme Value models," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 285-305, May.
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