4.2 Article

Optimal designs for estimating a choice hierarchy by a general nested multinomial logit model

Journal

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 48, Issue 23, Pages 5877-5888

Publisher

TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2018.1523429

Keywords

Information matrix; nested multinomial logit model; optimal design

Funding

  1. Consejo Nacional de Ciencia y Tecnologia (CONACyT)

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In choice experiments the process of decision-making can be more complex than the proposed by the Multinomial Logit Model (MNL). In these scenarios, models such as the Nested Multinomial Logit Model (NMNL) are often employed to model a more complex decision-making. Understanding the decision-making process is important in some fields such as marketing. Achieving a precise estimation of the models is crucial to the understanding of this process. To do this, optimal experimental designs are required. To construct an optimal design, information matrix is key. A previous research by others has developed the expression for the information matrix of the two-level NMNL model with two nests: Alternatives nest (J alternatives) and No-Choice nest (1 alternative). In this paper, we developed the likelihood function for a two-stage NMNL model for M nests and we present the expression for the information matrix for 2 nests with any amount of alternatives in them. We also show alternative D-optimal designs for No-Choice scenarios with similar relative efficiency but with less complex alternatives which can help to obtain more reliable answers and one application of these designs.

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