International Choice Modelling Conference, International Choice Modelling Conference 2017

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Quasi-Monte Carlo and Gaussian quadrature: Efficient choice experiment designs for climate change adaptation measures in Kenya
MARY NTHAMBI

Last modified: 28 March 2017

Abstract


Stated choice models involve the use of choice situations containing two or more policy alternatives and a current situation option. Alternatives are products of statistical combination of attributes and attribute levels through a process known as experimental design. Experimental design can either be efficient or orthogonal but recent studies have given more attention to efficient designs due to their non-linearity and logistic capabilities as compared to orthogonal designs which are for linear models. Efficient designs are important in stated choice studies because they play a very major role in determining how true parameter estimates generated from discrete choice models are. They are generated using discrete choice models which include; multinomial logit (MNL), nested logit (NL) and mixed multinomial logit (ML) models. They require prior parameter estimates which if known with certainty produce fixed efficient designs, otherwise, the designs generated are known as Bayesian designs.

Bayesian efficient designs are estimated using three main methods; (a) pseudo-random Monte Carlo (PMC) simulation, (b) quasi-Monte Carlo simulation, and (c) Gaussian quadrature (Bliemer et al., 2008). Bliemer et al., (2008) establishes that performance of Gaussian quadrature is better than quasi-Monte Carlo simulations and that PMC performs the least, using multinomial logit model (MNL). Other studies that support these assertions include Bhat, (2001) and Bhat, (2003) but in the context of efficient experimental designs Bliemer et al., (2008) takes a perfect lead. However, in the works of Bliemer et al., (2008) and, Bliemer and Rose, (2010) a number of gaps can be identified.

First, Bliemer et al., (2008) assumes that the performance of quasi-Monte Carlo simulation and Gaussian quadrature for Bayesian multinomial logit model (MNL) holds also for nested and mixed logit models. This stands to be confirmed for mixed logit models due to the assumptions of independent and identically distributed (IID) error terms and independence of irrelevant alternatives (IIA) assumptions that the multinomial logit model makes. Mixed logit models relax these assumptions by allowing error terms to vary across alternatives, choice sets to correlate and preferences to vary (Bliemer et al., 2010) among respondents’ choices.

Second, Bliemer and Rose, (2010) generates fixed efficient designs using multinomial logit and mixed logit models. However, the authors do not take into account Bayesian priors but assumes that parameters are known with certainty a priori, thus compares the multinomial logit model, cross-sectional mixed logit and panel mixed logit models. A similar study using Bayesian priors is needed because Bayesian efficient designs are better because they take into account erroneous measurement of prior parameters and models.

Third, the findings from Bliemer and Rose (2010) show that the panel mixed logit models and multinomial logit model performance is similar. However, it does not show the number of draws where the performance of the two models is likely to converge. The performance of the multinomial, cross-sectional mixed logit and panel mixed logit model across choice sets is also another gap that needs to be filled.

Fourth, some previous studies have concentrated on efficient designs based on the D-error (Bliemer et al., 2009; Bliemer and Rose, 2010) efficiency measure except Bliemer and Rose, (2005), and  Rose and Bliemer, (2013) who focus on S-efficient designs (Rose and Bliemer, 2013). However, S-efficient rather than D-efficient experimental designs from a rural developing country perspective may be more preferable. This could be true considering discrete choice modelling studies challenges in developing countries especially among rural communities where illiteracy levels, poverty levels and poor road infrastructure can be an impediment for large sample size surveys. Sample size and the number of choice cards presented to an individual are key considerations for choice studies and S-efficient designs could provide insights to challenges of choice studies in developing countries.

Given the above analysis of gaps, this paper bases its work on the framework of Bliemer et al., (2008) and Bliemer and Rose (2010). In summary, the objectives of this paper are three fold; (i) compare the performance of quasi-Monte Carlo simulations (Halton and Sobol sequences) and Gaussian quadrature for multinomial logit model, cross-sectional mixed logit and panel mixed logit model (ii) compare the sample sizes and the minimum and maximum t-ratios for multinomial logit, cross-sectional mixed logit and panel mixed logit models and, (iii) assess the number of draws where multinomial logit and panel mixed logit models are likely to converge.

To meet the above objectives, this paper uses a case study of Makueni County, Kenya, which in a broader perspective is an attempt to value the preferences of climate change adaptation measures among farmers in rural areas. The study involves two sets of unlabeled efficient experimental designs. The priors for the first set of efficient designs are estimated from preference rankings from data collected during 6 focused group discussions and 17 stakeholder interviews held in the study area. The resulting efficient designs include 12 choices sets with 4 alternatives each generated using Bayesian priors and blocked into three, with 4 choice cards per block. The reason for Bayesian priors are based on the high variability and uncertainty of two parameter estimates. To obtain priors for the second set of efficient designs, three survey versions are administered to a total of 60 households in the study area and data is analyzed using NLOGIT5. The priors and attribute levels are then used to create utility functions in NGENE software to generate 15 unlabeled efficient designs across 12, 18 and 24 choice sets for the three models. The minimum number of Sobol and Halton draws are 1200 while the maximum is 42,000 draws.

Although, data analysis is still in progress, results generated so far show similar performance for multinomial logit and panel mixed logit models and convergence tendencies at given number of draws. Further, multinomial logit model produces very small unrealistic sample sizes and panel mixed logit model produces reasonable sample sizes, thus prompting the question; why not panel mixed logit models for developing countries designs?

Keywords: Multinomial logit, cross-sectional, panel, quasi-Monte Carlo, Gaussian Quadrature


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