Optimal Design for a Three – Level Nested Multinomial Logit Model in Discrete Choice Experiments (original) (raw)

On Locally D-optimal Design for Nested Logit Model (Two Nests)

Discrete choice experiments play an important role in psychology and market research when measuring the consumer's preferences. Usually, the choice behavior is modeled by a multinomial response, where the probabilities of the preferences are given by a logistic model. The resulting "independence of irrelevant alternatives" property of this model, may lead to counter-intuitive results. To avoid these pitfalls, "nested multinomial logit models" have been introduced that allow correlations between the utilities of similar alternatives. In this paper, we consider some choice sets each with the same number of alternatives to obtain locally D-optimal design. In this situation, according to the number of alternatives in each nest there are some classes to define design. Afterward, a design which is produced by combination of designs (related to classes) will be defined and we obtain locally Doptimal deign for it.

Locally D-Optimal Design for a Logit Model in Discrete Choice Experiment

Communications in Statistics - Theory and Methods, 2013

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Efficient stated choice experiments for estimating nested logit models

Transportation Research Part B: Methodological, 2009

The allocation of combinations of attribute levels to choice situations in stated choice (SC) experiments can have a significant influence upon the resulting study outputs once data is collected. Recently, a small but growing stream of research has looked at using what have become known as efficient SC experimental designs to allocate the attribute levels to choice situations in a manner designed to produce better model outcomes. This research stream has shown that the use of efficient SC designs can lead to improvements in the reliability of parameter estimates derived from discrete choice models estimated on SC data for a given sample size. Unlike orthogonal designs, however, efficient SC experiments are generated in such a manner that their efficiency is related to the econometric model that is most likely to be estimated once the choice data is collected. To date, most of the research on efficient SC designs has assumed an MNL model format. In this paper, we generate efficient SC experiments for nested logit models and compare and contrast these with designs specifically generated assuming an MNL model form. We find that the overall efficiency of the design is maximized only when the model assumed in generating the design is the model that is fitted during estimation.

Models and optimal designs for conjoint choice experiments including a no-choice option

2007

In a classical conjoint choice experiment, respondents choose one profile from each choice set that has to be evaluated. However, in real life the respondent does not always make a choice: often he/she does not prefer any of the alternatives offered. Therefore, including a no-choice option in a choice set makes a conjoint choice experiment more realistic. In the literature three different models are used to analyze the results of a conjoint choice experiment with a no-choice option: the no-choice multinomial logit model, the extended no-choice multinomial logit model and the nested no-choice multinomial logit model. We develop optimal designs for each of these models using the D-optimality criterion and the modified Fedorov algorithm. We compare the optimal designs with a reference design that was constructed ignoring the no-choice option and we discuss the impact of the different designs and models on the precision of estimation and the predictive accuracy based on a simulation study.

Fast algorithms to generate individualized designs for the mixed logit choice model

Transportation Research Part B: Methodological, 2014

The mixed logit choice model has become the common standard to analyze transport behavior. Moreover, more and more transport studies start to make use of stated preference data to obtain precise knowledge on travelers' preferences. Accounting for the individual-specific coefficients in the mixed logit choice model, this research advocates an individualized design approach to generate these stated choice experiments. Individualized designs are sequentially generated for each person separately, using the answers from previous choice sets to select the next best set in a survey. In this way they are adapted to the specific preferences of an individual and therefore more efficient than an aggregate design. In order for individual sequential designs to be practicable, the speed of designing an additional choice set in an experiment is obviously a key issue. This paper introduces three design criteria used in optimal test design, based on Kullback-Leibler information, and compares them with the well known D-efficiency criterion to obtain individually adapted choice designs for the mixed logit choice model. Being equally efficient to D-efficiency and at the same time much faster, the Kullback-Leibler criteria are well suited for the design of individualized choice experiments.

Characterization and Optimal Designs for Discrete Choice Experiments

2019

In discrete choice experiments, a choice design involves n attributes (factors) with i-th attribute at li levels, and there are N choice sets each of size m. Demirkale, Donovan and Street (2013) considered the setup of symmetric factorials (li = l) and obtainedD-optimal choice designs under main effects model in the absence of two or higher order interaction effects. They provide some sufficient conditions for a design to be D-optimal. In this paper, we first derive a modified Information matrix of a choice design for estimating the factorial effects of a l1 × l2 × · · · × ln choice experiment. For a 2 choice experiment, following Singh, Chai and Das (2015), under the broader main effects model (both in the presence and in the absence of two-factor interactions) we give a simple necessary and sufficient condition for the Information matrix to be diagonal. Furthermore, we characterize the structure of the choice sets which gives maximum trace of the Information matrix. Our characteri...

Efficient conjoint choice designs in the presence of respondent heterogeneity

2007

The authors propose a fast and efficient algorithm for constructing D-optimal conjoint choice designs for mixed logit models in the presence of respondent heterogeneity. With this new algorithm, the construction of semi-Bayesian D-optimal mixed logit designs with large numbers of attributes and attribute levels becomes practically feasible. The results from the comparison of eight designs (ranging from the simple locally D-optimal design for the multinomial logit model and the nearly orthogonal design generated by Sawtooth (CBC) to the complex semi-Bayesian mixed logit design) across wide ranges of parameter values show that the semi-Bayesian mixed logit approach outperforms the competing designs not only in terms of estimation efficiency but also in terms of prediction accuracy. In particular, it was found that semi-Bayesian mixed logit designs constructed with large heterogeneity parameters are most robust against the misspecification of the values for the mean of the individual l...

A Comparison of Criteria to Design Efficient Choice Experiments

Journal of Marketing Research, 2006

To date, no attempt has been made to design efficient choice experiments by means of the G-and V-optimality criteria. These criteria are known to make precise response predictions, which is exactly what choice experiments aim to do. In this article, the authors elaborate on the G-and V-optimality criteria for the multinomial logit model and compare their prediction performances with those of the D-and A-optimality criteria. They make use of Bayesian design methods that integrate the optimality criteria over a prior distribution of likely parameter values. They employ a modified Fedorov algorithm to generate the optimal choice designs. They also discuss other aspects of the designs, such as level overlap, utility balance, estimation performance, and computational effectiveness.

D-optimal designs for multinomial logistic models

The Annals of Statistics, 2020

We consider optimal designs for general multinomial logistic models, which cover baseline-category, cumulative, adjacent-categories, and continuation-ratio logit models, with proportional odds, non-proportional odds, or partial proportional odds assumption. We derive the corresponding Fisher information matrices in three different forms to facilitate their calculations, determine the conditions for their positive definiteness, and search for optimal designs. We conclude that, unlike the designs for binary responses, a feasible design for a multinomial logistic model may contain less experimental settings than parameters, which is of practical significance. We also conclude that even for a minimally supported design, a uniform allocation, which is typically used in practice, is not optimal in general for a multinomial logistic model. We develop efficient algorithms for searching D-optimal designs. Using examples based on real experiments, we show that the efficiency of an experiment can be significantly improved if our designs are adopted.