Logit Function

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M Abdalla - One of the best experts on this subject based on the ideXlab platform.

  • modeling repeated multinomial route choices under advanced traveler information system generalized estimating equations with polytomous Logit Function
    Transportation Research Record, 2004
    Co-Authors: Mohamed Abdelaty, M Abdalla
    Abstract:

    Correlated multinomial route choice data were modeled under an advanced traveler information system (ATIS). A travel simulator was used as a dynamic data collection tool. The simulator uses realistic network and real historical traffic volumes. It provides five levels of ATIS and accounts for types of delay. A 25-node and 40-link network was used. Sixty-three qualified subjects performed a total of 539 trial days. Forty-four distinct routes were chosen. The multinomial generalized estimating equation (MGEE) methodology was used with a generalized polytomous Function and an exchangeable correlation structure. MGEEs account for the serial correlation between repeated choices made by the same subject as well as the correlation due to the overlapping between alternatives. The modeling results show that drivers can identify and follow the shortest path when they are provided with advice-free traffic information on all the network links. In addition, it is shown that the odds of choosing a certain shortest-path route, whether the drivers are advised or not, vary from route to route, depending on the characteristics of the route itself. It was proved that the proposed model could account for a correlation in the multinomial repeated route choices with simple computational effort, even for a large number of alternatives.

Birgit Trauble - One of the best experts on this subject based on the ideXlab platform.

  • robustness of statistical methods when measure is affected by ceiling and or floor effect
    PLOS ONE, 2019
    Co-Authors: Matus Simkovic, Birgit Trauble
    Abstract:

    Goals and methods A simulation study investigated how ceiling and floor effect (CFE) affect the performance of Welch’s t-test, F-test, Mann-Whitney test, Kruskal-Wallis test, Scheirer-Ray-Hare-test, trimmed t-test, Bayesian t-test, and the “two one-sided tests” equivalence testing procedure. The effect of CFE on the estimate of group difference and on its confidence interval, and on Cohen’s d and on its confidence interval was also evaluated. In addition, the parametric methods were applied to data transformed with log or Logit Function and the performance was evaluated. The notion of essential maximum from abstract measurement theory is used to formally define CFE and the principle of maximum entropy was used to derive probability distributions with essential maximum/minimum. These distributions allow the manipulation of the magnitude of CFE through a parameter. Beta, Gamma, Beta prime and Beta-binomial distributions were obtained in this way with the CFE parameter corresponding to the logarithm of the geometric mean. Wald distribution and ordered logistic regression were also included in the study due to their measure-theoretic connection to CFE, even though these models lack essential minimum/maximum. Performance in two-group, three-group and 2 × 2 factor design scenarios was investigated by fixing the group differences in terms of CFE parameter and by adjusting the base level of CFE. Results and conclusions In general, bias and uncertainty increased with CFE. Most problematic were occasional instances of biased inference which became more certain and more biased as the magnitude of CFE increased. The bias affected the estimate of group difference, the estimate of Cohen’s d and the decisions of the equivalence testing methods. Statistical methods worked best with transformed data, albeit this depended on the match between the choice of transformation and the type of CFE. Log transform worked well with Gamma and Beta prime distribution while Logit transform worked well with Beta distribution. Rank-based tests showed best performance with discrete data, but it was demonstrated that even there a model derived with measurement-theoretic principles may show superior performance. Trimmed t-test showed poor performance. In the factor design, CFE prevented the detection of main effects as well as the detection of interaction. Irrespective of CFE, F-test misidentified main effects and interactions on multiple occasions. Five different constellations of main effect and interactions were investigated for each probability distribution, and weaknesses of each statistical method were identified and reported. As part of the discussion, the use of generalized linear models based on abstract measurement theory is recommended to counter CFE. Furthermore, the necessity of measure validation/calibration studies to obtain the necessary knowledge of CFE to design and select an appropriate statistical tool, is stressed.

Mohamed Abdelaty - One of the best experts on this subject based on the ideXlab platform.

  • modeling repeated multinomial route choices under advanced traveler information system generalized estimating equations with polytomous Logit Function
    Transportation Research Record, 2004
    Co-Authors: Mohamed Abdelaty, M Abdalla
    Abstract:

    Correlated multinomial route choice data were modeled under an advanced traveler information system (ATIS). A travel simulator was used as a dynamic data collection tool. The simulator uses realistic network and real historical traffic volumes. It provides five levels of ATIS and accounts for types of delay. A 25-node and 40-link network was used. Sixty-three qualified subjects performed a total of 539 trial days. Forty-four distinct routes were chosen. The multinomial generalized estimating equation (MGEE) methodology was used with a generalized polytomous Function and an exchangeable correlation structure. MGEEs account for the serial correlation between repeated choices made by the same subject as well as the correlation due to the overlapping between alternatives. The modeling results show that drivers can identify and follow the shortest path when they are provided with advice-free traffic information on all the network links. In addition, it is shown that the odds of choosing a certain shortest-path route, whether the drivers are advised or not, vary from route to route, depending on the characteristics of the route itself. It was proved that the proposed model could account for a correlation in the multinomial repeated route choices with simple computational effort, even for a large number of alternatives.

Srinivas Peeta - One of the best experts on this subject based on the ideXlab platform.

  • promoting zero emissions vehicles using robust multi period tradable credit scheme
    Transportation Research Part D-transport and Environment, 2019
    Co-Authors: Mohammad Miralinaghi, Srinivas Peeta
    Abstract:

    Abstract This study designs a robust multi-period tradable credit scheme (TCS) to incentivize travelers to shift from internal combustion engine vehicles (ICEVs) to zero-emissions vehicles (ZEVs) over a long-term planning horizon to reduce vehicular emissions. The need for robust design arises because of uncertainty in forecasting travel demand over a planning horizon in the order of several years. The robust multi-period TCS design is formulated as a bi-level model. In the upper level, the central authority (CA) determines the TCS parameters (credit allocation and charging schemes) by vehicle type to minimize the worst-case vehicular emissions rate, i.e. the maximum vehicular emissions rate under the possible travel demand scenarios. The upper-level model is a mixed-integer nonlinear program. In the lower level, travelers minimize their generalized travel costs under the TCS parameters obtained in the upper level. These parameters are used to determine the vehicle type choice, between ICEVs and ZEVs, using a binomial Logit Function, and influence route selection based on the difference in credits charged on links for these two vehicle types. The lower-level model is a mathematical program with equilibrium constraints. The bi-level model is solved using a cutting plane method. Numerical experiments illustrate that the incentive to shift to ZEVs is fostered by allocating more credits and charging fewer credits to ZEV travelers compared to ICEV travelers. Further, the proposed TCS design reduces volatility in the realized vehicular emissions rates under different travel demand scenarios compared to a TCS design that does not consider demand uncertainty.

Henry P. Stott - One of the best experts on this subject based on the ideXlab platform.

  • Cumulative prospect theory's Functional menagerie
    Journal of Risk and Uncertainty, 2006
    Co-Authors: Henry P. Stott
    Abstract:

    Many different Functional forms have been suggested for both the value Function and probability weighting Function of Cumulative Prospect Theory (Tversky and Kahneman, 1992). There are also many stochastic choice Functions available. Since these three components only make predictions when considered in combination, this paper examines the complete pattern of 256 model variants that can be constructed from twenty Functions. All these variants are fit to experimental data and their explanatory power assessed. Significant interaction effects are observed. The best model has a power value Function, a risky weighting Function due to Prelec (1998), and a Logit Function.

  • Cumulative prospect theory's Functional menagerie
    Journal of Risk and Uncertainty, 2006
    Co-Authors: Henry P. Stott
    Abstract:

    Many different Functional forms have been suggested for both the value Function and probability weighting Function of Cumulative Prospect Theory (Tversky and Kahneman, 1992). There are also many stochastic choice Functions available. Since these three components only make predictions when considered in combination, this paper examines the complete pattern of 256 model variants that can be constructed from twenty Functions. All these variants are fit to experimental data and their explanatory power assessed. Significant interaction effects are observed. The best model has a power value Function, a risky weighting Function due to Prelec (1998), and a Logit Function. © Springer Science + Business Media, LLC 2006.