Derivation of Aggregation Rules in the Generalized Nested Logit Model to Avoid the Aggregation Problem(Theory and Methodology)

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  • GNLにおける集計問題を回避するための集計ルールの導出(理論・技術)
  • GNLにおける集計問題を回避するための集計ルールの導出
  • GNL ニ オケル シュウケイ モンダイ オ カイヒ スル タメ ノ シュウケイ ルール ノ ドウシュツ

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This paper derives conditions of aggregation rules in the generalized nested logit (GNL) model to avoid the aggregation problem. In respect to control of increasing parameters, it is useful for researchers to reduce the number of nests or alternatives in the GNL model. Therefore, aggregation rules in the GNL model are important for researchers to reduce time to analyze models or estimate their parameters. First, we demonstrate two simple aggregation rules (the arithmetical mean and the geometric mean of definite utilities in nests) that cannot solve the aggregation problem using actual scan panel data. Second, we derive the three following aggregation rules of the GNL model to avoid the aggregation problem: 1) aggregation of nests which results in three conditions in the brand choice model, 2) aggregation of alternatives which results in two conditions in the same model, and 3) aggregation of nests which results in six conditions in the traffic mode choice model. Finally, we conduct comparison analysis of aggregation rules among the multinomial logit (MNL), nested logit (NL) and GNL models in two cases: 1) aggregation of nests, and 2) aggregation of alternatives in the brand choice model. As a result of this comparison, it is indicated that 1) the relationship among aggregation rules in the MNL, the NL and the GNL models is consistent with the relationship among choice probabilities in these models, and 2) in limited but many cases, each definite utility component has maximum and minimum values.

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