Strategic sampling for large choice sets in estimation and application

Use of the multinomial logit (MNL) functional form is widespread in transportation and land use demand modeling. As the state-of-the-art evolves away from aggregate forecasting and toward activity-based models and microsimulation, MNL models are being asked to accommodate increasingly large choice sets. Different strategies exist to address the challenge of estimating models with very large choice sets, but perhaps none is as commonly employed as sampling of alternatives. The effect of sampling of alternatives on parameter estimation has received considerable attention in the scientific literature. Yet comparatively little quantitative research exists that examines the issues that arise when the same sampling strategies are applied in the context of forecasting. In this study we conducted an analysis of the effect of sampling of alternatives in discrete choice models for disaggregate location choice forecasting. First, a novel measure of forecast error was defined and then used to quantify the extent of the problem as a function of sample rate, model error, and size of the universe of alternatives. Finally, we explored the potential for strategic sampling techniques to reduce the error observed under simple random sampling. In general, we found that the proportion of aggregate demand that was misallocated owing to sampling of alternatives was actually reduced as the size of the universe of alternatives increased. Additionally, simple random sampling was shown to outperform importance sampling in most scenarios. These findings suggest that error resulting from random sampling of alternatives is less of a problem for logit-based microsimulation models than previously assumed.

Utility independence versus IIA property in independent probit models

The generalized Bilal (GB) distribution can be defined as the distribution of the median of three independent random variables drawn from the Weibull distribution. Its failure rate function can be monotonic (decreasing or increasing) or upside-down bathtub-shaped. In this study, we aim to reveal some important properties of the GB distribution that have not been considered before. The findings are both theoretical and practical. From the theoretical viewpoint, we present explicit expressions for both single and product moments of order statistics from the GB distribution. The L-moments are derived as well. From the practical viewpoint, the parameter estimations are accomplished using the maximum likelihood (ML) method, which is based on two different sampling schemes: simple random sampling (SRS) and ranked set sampling (RSS) schemes. Furthermore, the asymptotic confidence intervals for the SRS and RSS estimators are discussed. For the sake of comparison and illustration, a simulation study and a real data example are presented. Concluding remarks are given at the end.

Multinomial logit models and nested logit models are limited in that they cannot accommodate unobserved variations in travelers' taste and they do not have flexible substitution patterns among alternatives because of the independence of irrelevant alternatives property. Taking this background into account, traffic demand analysts have recently used the mixed logit model in many studies. Unfortunately, most of the studies in the literature for joint analysis of revealed-preference (RP) and stated-preference (SP) data could not simultaneously resolve the two limitations just mentioned. The mixed logit framework is used to formulate an intercity travel mode choice model for joint RP-SP analysis that accommodates the following behavioral considerations: ( a) observed and unobserved heterogeneity across individuals in response to level-of-service (LOS) factors, ( b) heteroscedasticity across alternatives, and ( c) scale differences between the RP and SP choice contexts. The mixed logit formulation is estimated with the maximum simulated likelihood method that employs quasi-random Halton draws. The formulation is applied to examine the travel behavior responses of users of the HoNam, South Korea, high-speed rail to changes in travel conditions. The empirical results show that there is a significant heteroscedasticity across alternatives and a significant heterogeneity in response to LOS attributes based on both observed and unobserved individual characteristics. There is an improvement in the data-fit statistics when one introduces heterogeneity and heteroscedasticity. These results highlight the need to include heterogeneity and heteroscedasticity within the context of intercity travel mode choice modeling to assist policy decision making.

This paper develops nonparametric estimation for discrete choice models based on the mixed multinomial logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution $G$. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution $G$, to estimate choice probabilities. We provide an important theoretical support for the use of the proposed methodology by investigating consistency of the posterior distribution for a general nonparametric prior on the mixing distribution. Consistency is defined according to an $L_1$-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy-to-use blocked Gibbs sampling procedures. These procedures are based on approximations of the random probability measure by classes of finite stick-breaking processes. A simulation study is also performed to investigate the performance of the proposed methods.

According to Weibull distribution timing truncation test, considering that it is difficult to have a strictly defined complete failure samples in engineering practice, so the life sampling schemes of censored failure samples are discussed. Here, we have considered random right censored samples with different censored ratios. Compared with other sampling studies, this paper is not limited to explore more sampling theories, but uses SPSS software to give the specific operation processes of three sampling schemes: simple random sampling, two-stage sampling and Bayes sampling considering the minimum total cost, as well as the discussion on the verification analysis of the sampling accuracy. In order to simplify the estimation of Weibull distribution parameters, the estimated parameters are obtained by the probability plot analysis of Minitab software, thus the error between the sample’s MTBF (Mean Time Between Failure) and the overall MTBF is calculated. The sensitivity of Weibull distribution parameters is obtained by Minitab software. Finally, according to the accuracy of the three sampling schemes with different censored ratios, the optimal life sampling decision is obtained, which may provide sampling reference for the decision makers.

Ranked set sampling (RSS) is an efficient sampling method when ranking observations is easier than precise measurement. Unlike simple random sampling (SRS), RSS can reduce costs. The unit Xgamma distribution (UXGD), defined over the interval (0,1), effectively captures the characteristics of negatively skewed datasets. This study aims to comprehensively compare several estimation methods, including maximum likelihood, Anderson‐Darling, Kolmogorov, ordinary least squares, Anderson‐Darling left tail second order, Cramer‐von‐Mises, left tail Anderson‐Darling, weighted least squares, maximum product spacing, right tail Anderson‐Darling, and five types of minimum spacing distance for the UXGD parameter under both RSS and SRS techniques. Through extensive simulations, we evaluate the performance of these estimators using multiple criteria under both designs. We rank the estimators based on their performance under both sampling schemes. Simulation findings indicate that the maximum product spacing and maximum likelihood estimation methods are superior to alternative approaches for assessing the estimated quality of RSS and SRS, respectively. It is interesting to note that for both SRS and RSS datasets, the estimates revealed by our model satisfy the consistency property. With an increase in the sample size, the estimates approach the true parameter values. Furthermore, the results highlight the efficiency gains of RSS over SRS, as evidenced by improved accuracy metrics. Two real‐world applications, including COVID‐19 data from the United Kingdom and France, demonstrate the practical utility of our findings.

SummaryAs field sampling is time consuming, it is necessary to develop efficient sampling techniques to obtain accurate estimates of the weed seedbank in soil. The relative efficiency between sampling schemes depends on the spatial variability in weed seed density across agricultural fields. Spatial variability of the weed seed density was characterized by theoretical correlograms. A systematic sampling (square grill) scheme was considered and it was found that, taking into account spatial variability, this sampling scheme was more efficient than simple random sampling. As a result, the sample size can be reduced in comparison with that given in previous studies, where spatial correlation was ignored. The reduction depends on the correlation structure defined as a function of the ratio, τ, between the nugget effect and the sill of the variogram. The maximum reduction of the sample size, without loss of either precision or confidence level corresponds to the case where there is no nugget effect, τ = 0. The opposite extreme case, where the reduction is nil, corresponds to the case of a pure nugget effect τ = 1. The abaci based on given expressions are provided to determine the sample size in species whose spatial pattern can be fitted either to a Poisson or to a negative binomial distribution.

Statisticians along with other scientists have made significant computational advances that enable the estimation of formerly complex statistical models. The Bayesian inference framework combined with Markov chain Monte Carlo estimation methods such as the Gibbs sampler enable the estimation of discrete choice models such as the multinomial logit (MNL) model. MNL models are frequently applied in transportation research to model choice outcomes such as mode, destination, or route choices or to model categorical outcomes such as crash outcomes. Recent developments allow for the modification of the potentially limiting assumptions of MNL such as the independence from irrelevant alternatives (IIA) property. However, relatively little transportation-related research has focused on Bayesian MNL models, the tractability of which is of great value to researchers and practitioners alike. This paper addresses MNL model specification issues in the Bayesian framework, such as the value of including prior information on parameters, allowing for nonlinear covariate effects, and extensions to random parameter models, so changing the usual limiting IIA assumption. This paper also provides an example that demonstrates, using route-choice data, the considerable potential of the Bayesian MNL approach with many transportation applications. This paper then concludes with a discussion of the pros and cons of this Bayesian approach and identifies when its application is worthwhile.

This study investigates a range of parameter estimation methods for the Half-Logistic Inverse Rayleigh Distribution (HLIRD) under two distinct sampling frameworks: ranked set sampling (RSS) and simple random sampling (SRS). The estimation techniques considered include maximum likelihood estimation, ordinary and weighted least squares, and the maximum and minimum product of spacings methods. Model adequacy is evaluated using five goodness-of-fit criteria: the Anderson–Darling (AD) statistic, its right- and left-tail variants, the second-order left-tail AD statistic, and the Cramér–von Mises statistic. An extensive simulation study is conducted to thoroughly evaluate and compare the performance of the proposed estimators while maintaining a fixed total number of observations across both sampling schemes. The practical relevance of the proposed methods is further illustrated through an application to a real dataset consisting of 69 carbon fiber specimens, with tensile strength measurements (in GPa) recorded at a gauge length of 20 mm. The numerical results demonstrate that estimators based on RSS consistently outperform their SRS counterparts across all considered performance measures, including mean squared error, bias, and mean absolute relative error. Overall, the findings highlight the advantages of employing RSS for parameter estimation of the HLIRD, particularly due to its superior efficiency in small-sample scenarios.

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are studied under second order approximation. In third paper some estimators are proposed in two-phase sampling and their properties are studied in the presence of non-response. In fourth chapter a family of median based estimator is proposed in simple random sampling. In fifth paper some difference type estimators are suggested in simple random sampling and stratified random sampling and their properties are studied in presence of measurement error.

Forest measurements, especially in natural forests are cumbersome and complex. 100% enumeration is costly and inefficient. This study sought to find out reliable, efficient and cost-effective sampling schemes for use in tropical rain forest (TRF), moist montane forest (MMF) and dry woodland forest (DWF) in Kenya. Forty-eight sampling schemes (each combining sampling intensity (5, 10, 20, 30%), plot size (25, 50, 100, 400 m2) and sampling technique (simple random sampling, systematic sampling along North-South and along East-West orientations) were generated for testing estimates of forest attributes such as regeneration through simulation using R-software. Sampling error and effort were used to measure efficiency of each sampling scheme in relation to actual values. Though forest sites differed in biophysical characteristics, cost of sampling increased with decreasing plot size regardless of the forest type and attribute. Accuracy of inventory increased with decreasing plot size. Plot sizes that captured inherent variability were 5mx5m for regeneration and trees ha-1 across forest types but varied between forest types for basal area. Different sampling schemes were ranked for relative efficiency through simulation techniques, using regeneration as an example. In many instances systematic sampling-based sampling schemes were most effective. Sub-sampling in one-hectare forest unit gave reliable results in TRF (e.g. SSV-5mx5m-30%) and DWF (e.g. SSV-10mx10m-30%) but not in MMF (5mx5m-100%). One-hectare-complete-inventory method was found inevitable for regeneration assessment in montane forest.

When genetically modified (GM) maize is planted in an open field, it may cross-pollinate with the nearby non-GM maize under certain airflow conditions. Suitable sampling methods are crucial for tracing adventitious GM content. By using field data and bootstrap simulation, we evaluated the performance of common sampling schemes to determine the adventitious GM content in small maize fields in Taiwan. A pollen dispersal model that considered the effect of field borders, which are common in Asian agricultural landscapes, was used to predict the cross-pollination (CP) rate. For the 2009–1 field data, the six-transect (Tsix), JM method for low expected flow (JM[L]), JM method for high expected flow (JM[H]), and V-shaped transect (TV) methods performed comparably to simple random sampling (SRS). Tsix, TV, JM(L), and JM(H) required only 13% or less of the sample size required by SRS. After the simulation and verification of the 2009–2 and 2010–1 field data, we concluded that Tsix, TV, JM(L), and systematic random sampling methods performed equally as well as SRS in CP rate predictions. Our findings can serve as a reference for monitoring the pollen dispersal tendencies of maize in countries with smallholder farming systems.

Surface Fuel Sampling Strategies: Linking Fuel Measurements and Fire Effects

ABSTRACTLogistic regression is the most popular technique available for modeling dichotomous-dependent variables. It has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient logistic regression analysis based on moving extreme ranked set sampling (MERSSmin) scheme with ranking based on an easy-to-available auxiliary variable known to be associated with the variable of interest (response variable). The paper demonstrates that this approach will provide more powerful testing procedure as well as more efficient odds ratio and parameter estimation than using simple random sample (SRS). Theoretical derivation and simulation studies will be provided. Real data from 2011 Youth Risk Behavior Surveillance System (YRBSS) data are used to illustrate the procedures developed in this paper.