01-10-2012, 04:47 PM
A Comparative Study on Sampling Strategies for Truck Destination Choice Model using Seoul Metropolitan Trip Data
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Abstract
One of the major issues in applying truck destination choice models with a large number of alternatives is determining how to sample a set of non-chosen traffic analysis zones (TAZs) to construct a destination choice set. Despite a large number of studies that have applied different sampling strategies, optimal strategies are still not established. The aim of this study is to investigate how the sampling strategies affect the performances of truck destination choice models. Two sampling methods (simple random sampling and stratified importance sampling) and four different sample sizes are tested using the truck trip data for the Seoul metropolitan area, which was collected by the nationwide Commodity Flow Survey (2005) of Korea. Moran’s I statistic is employed for stratified importance sampling in order to divide the whole study area into multiple strata, and Neyman allocation is utilized to determine the appropriate number of samples for each stratum. Commonly, in geographical analysis Moran’s I statistic is used to measure the spatial clustering pattern in a given area. The stratum classification varied by spatial location and employment size for each origin zone. The destination choice models are developed for each truck size, and the employment size for each origin zone is defined as a size variable. To evaluate and compare the performance of the destination choice models with respect to sampling strategies, truck trip productions are distributed by Monte Carlo simulation, and two measurements of effectiveness (MOEs) such as average trip length (ATL) and trip length distribution (TLD) are used. The results show that the models using stratified importance sampling than simple random sampling and generating small sample sizes than others performed better than others in regard to ATL and TLD, respectively.
Introduction
Destination choice models are based on random utility maximization where a decision maker's choice would be a reflection of the alternative with the highest preference or utility. One of the important issues in destination choice models is the large number of alternatives in the choice set. For example, a decision maker can potentially have hundreds of thousands of choice alternatives if a fine spatial resolution such as individual firms or retails are defined as the alternatives. It would be very challenging to consider all alternatives because of substantial efforts involved in collecting the relevant data set. The computational burden can also be an important consideration in estimation with a large number of alternatives. In this case, aggregated zones are used as the alternatives. The zones are defined on the basis of data availability and analytical considerations.
Sample Size Determination
Generally, when using a sample survey to determine if a change has taken place over time, the analyst needs to specify the level of precision and the confidence level for measuring that change. Usually, the level of precision is defined by considering the expected size of the change, and determining how much error can tolerated (Stopher and Greaves 2007).
The challenge of estimating choice models with a huge set of alternatives has led researchers to explore and apply methods to enable consistent estimation with only a subset of alternatives. However, there is no clear solution in terms of sample size for MNL models, such as the destination choice model. It should be emphasized that guidance for selecting sample sizes, including the effects of sample size, is provided even for modeling frameworks that explicitly incorporate choice set formation (Swait 2001; Nerella and Bhat 2004).
Strata Classification and Samples Allocation
The experimental design process for a stratified sampling scheme involves a number of decisions. First, a stratification variable must be prepared. Then, the number of strata must be determined. For sample allocation, the Neyman allocation has been proven to minimize the variance of the estimate for a fixed total sample size and is often used in practice. However, the number of strata can only be approximated, since the stratum variances, which are required in the computation, are typically not available. The number of strata is usually decided by the precision gain from stratification based on the number of strata increases and the cost of stratified sampling (Cochran 1977).
Stratified Importance Sampling Process
To apply stratified importance sampling for each production (origin) zone in the study area, the whole study area was divided into two strata: first and second stratum. In the first stratum, homogeneity was assumed when the Moran’s I statistic associated with employment for the TAZs in the same stratum was equal to zero. That is, there was no spatial dependency among the TAZs grouped in the first stratum according to employment size.
Conclusions
Selecting a destination involves a large number of alternatives choices. Analysts generally sample a set of non-chosen alternatives from the full choice set because sampling alternatives can prevent computational complexity. Although many studies have applied different sampling strategies, the question remains as to what are the optimal strategies in destination choice models. Thus, it is valuable to study the effect of sampling strategies on model performance in destination choice models.
Two sampling strategies were used to draw the non-chosen alternatives. One is sampling method to draw alternatives, and the other is sample size to construct model choice sets The simple random sampling and stratified importance sampling were applied as sampling methods, and sample sizes of 5, 10, 20, and 40 from the 79 full choice set were employed.
[attachment=34956]
Abstract
One of the major issues in applying truck destination choice models with a large number of alternatives is determining how to sample a set of non-chosen traffic analysis zones (TAZs) to construct a destination choice set. Despite a large number of studies that have applied different sampling strategies, optimal strategies are still not established. The aim of this study is to investigate how the sampling strategies affect the performances of truck destination choice models. Two sampling methods (simple random sampling and stratified importance sampling) and four different sample sizes are tested using the truck trip data for the Seoul metropolitan area, which was collected by the nationwide Commodity Flow Survey (2005) of Korea. Moran’s I statistic is employed for stratified importance sampling in order to divide the whole study area into multiple strata, and Neyman allocation is utilized to determine the appropriate number of samples for each stratum. Commonly, in geographical analysis Moran’s I statistic is used to measure the spatial clustering pattern in a given area. The stratum classification varied by spatial location and employment size for each origin zone. The destination choice models are developed for each truck size, and the employment size for each origin zone is defined as a size variable. To evaluate and compare the performance of the destination choice models with respect to sampling strategies, truck trip productions are distributed by Monte Carlo simulation, and two measurements of effectiveness (MOEs) such as average trip length (ATL) and trip length distribution (TLD) are used. The results show that the models using stratified importance sampling than simple random sampling and generating small sample sizes than others performed better than others in regard to ATL and TLD, respectively.
Introduction
Destination choice models are based on random utility maximization where a decision maker's choice would be a reflection of the alternative with the highest preference or utility. One of the important issues in destination choice models is the large number of alternatives in the choice set. For example, a decision maker can potentially have hundreds of thousands of choice alternatives if a fine spatial resolution such as individual firms or retails are defined as the alternatives. It would be very challenging to consider all alternatives because of substantial efforts involved in collecting the relevant data set. The computational burden can also be an important consideration in estimation with a large number of alternatives. In this case, aggregated zones are used as the alternatives. The zones are defined on the basis of data availability and analytical considerations.
Sample Size Determination
Generally, when using a sample survey to determine if a change has taken place over time, the analyst needs to specify the level of precision and the confidence level for measuring that change. Usually, the level of precision is defined by considering the expected size of the change, and determining how much error can tolerated (Stopher and Greaves 2007).
The challenge of estimating choice models with a huge set of alternatives has led researchers to explore and apply methods to enable consistent estimation with only a subset of alternatives. However, there is no clear solution in terms of sample size for MNL models, such as the destination choice model. It should be emphasized that guidance for selecting sample sizes, including the effects of sample size, is provided even for modeling frameworks that explicitly incorporate choice set formation (Swait 2001; Nerella and Bhat 2004).
Strata Classification and Samples Allocation
The experimental design process for a stratified sampling scheme involves a number of decisions. First, a stratification variable must be prepared. Then, the number of strata must be determined. For sample allocation, the Neyman allocation has been proven to minimize the variance of the estimate for a fixed total sample size and is often used in practice. However, the number of strata can only be approximated, since the stratum variances, which are required in the computation, are typically not available. The number of strata is usually decided by the precision gain from stratification based on the number of strata increases and the cost of stratified sampling (Cochran 1977).
Stratified Importance Sampling Process
To apply stratified importance sampling for each production (origin) zone in the study area, the whole study area was divided into two strata: first and second stratum. In the first stratum, homogeneity was assumed when the Moran’s I statistic associated with employment for the TAZs in the same stratum was equal to zero. That is, there was no spatial dependency among the TAZs grouped in the first stratum according to employment size.
Conclusions
Selecting a destination involves a large number of alternatives choices. Analysts generally sample a set of non-chosen alternatives from the full choice set because sampling alternatives can prevent computational complexity. Although many studies have applied different sampling strategies, the question remains as to what are the optimal strategies in destination choice models. Thus, it is valuable to study the effect of sampling strategies on model performance in destination choice models.
Two sampling strategies were used to draw the non-chosen alternatives. One is sampling method to draw alternatives, and the other is sample size to construct model choice sets The simple random sampling and stratified importance sampling were applied as sampling methods, and sample sizes of 5, 10, 20, and 40 from the 79 full choice set were employed.