Use of composite likelihood methods for the estimation of probit models

使用复合似然法估计概率模型

• 批准号: 356500581
• 负责人: Professor Dr. Dietmar Bauer
• 金额: --
• 依托单位: Lehrstuhl für Ökonometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/356500581?language=en
• 关键词: Use; composite; likelihood; methods; estimation

Mobility demand models are usually based on discrete choice models with often a large number of choice alternatives. The predominant model classes are constituted by the multinomial logit (MNL) and -probit (MNP) models. For different flavors of (mixed) MNL model numerically and statistically efficient estimation algorithms exist based on the (simulated) maximum likelihood paradigm which, however, show disadvantages with respect to the representation of correlation between the random utility terms for different alternatives as well as the choice of the mixing distributions. For large data sets a large number of simulations are needed in order to ensure consistency and asymptotic efficiency of the estimators. MNP models on the other hand in particular in a panel context provide good modeling capabilities, however, lead to numerically demanding estimation problems as these necessitate the evaluation of high dimensional Gaussian cumulative distribution functions (CDF). As an alternative the group around Chandra Bhat proposed the "maximum composite marginal likelihood" (MaCML) approach linking two ideas: the likelihood is replaced by a so called "composite marginal likelihood" (CML) and second the Gaussian CDF is analytically approximated. Bhat's proposal has up to now only been motivated by a number of simulation exercises. A thorough theoretical investigation is currently not available. Investigating simple examples it can be verified easily that the MaCML approach does not guarantee consistent estimation. Also the particular choice of the approximation method used by Bhat as well as the chosen CML has been criticised. Thus this project will deal with a detailed investigation of the properties of estimator on the basis of the MaCML idea, examining the effects of the choice of the CML function and the CDF approximation with respect to (i) the asymptotic bias, (ii) the relative efficiency and (iii) the properties of model selection procedures based on the MaCML estimation. It is the main goal of this project to develop numerically efficient and statistically sound estimation procedures (including adequate initialisation routines) for MNP-models in panel data settings showing a large number of alternatives. The methods developed within the project will be used to investigate the determinants of the choice of so called motifs (representations of the trips of a day of an individual as directed graphs). In a number of different data sets in different cities it has been shown that out of a potentially large number of motifs people only choose one out of 17 motifs. Currently there is little knowledge as to the determinants underlying this choices as well as the dependence on sociodemographic characteristics. Additionally the temporal evolution of the relative frequency of choice are unknown. This knowledge is of importance for the development of activity based mobility demand models.

移动需求模型通常基于离散的选择模型，通常具有大量的选择方案。主要的模型类由多项Logit(MNL)和-Probit(MNP)模型构成。对于不同风格的(混合)MNL模型，基于(模拟的)最大似然范式存在着数值和统计上有效的估计算法，但在表示不同备选方案的随机效用项之间的相关性以及混合分布的选择方面存在不足。对于大数据集，为了保证估计器的一致性和渐近效率，需要进行大量的仿真。另一方面，特别是在面板环境中的MNP模型提供了良好的建模能力，然而，由于这些问题需要评估高维高斯累积分布函数(CDF)，因此导致了数值上要求很高的估计问题。作为另一种选择，Chandra Bhat周围的小组提出了将两个想法联系在一起的“最大合成边际似然”(MaCML)方法：用所谓的“合成边际似然”(CML)代替似然；第二，对高斯CDF进行解析近似。到目前为止，哈特的提议只是受到了一些模拟演习的推动。目前还没有全面的理论调查。通过简单的例子，可以很容易地验证MaCML方法不能保证一致的估计。此外，BHAT使用的近似方法的特殊选择以及所选的CML也受到了批评。因此，本项目将在MaCML思想的基础上详细研究估计量的性质，考察CML函数和CDF近似的选择对于(I)渐近偏差、(Ii)相对效率和(Iii)基于MaCML估计的模型选择过程的性质的影响。本项目的主要目标是为显示大量备选方案的面板数据环境中的MNP模型开发数字高效和统计合理的估计程序(包括足够的初始化例程)。在该项目中开发的方法将被用来调查选择所谓的主题(以有向图表示个人一天的旅行)的决定因素。在不同城市的一些不同的数据集中，已经表明，在潜在的大量主题中，人们只从17个主题中选择了一个。目前，对于这种选择背后的决定因素以及对社会人口特征的依赖，人们知之甚少。此外，选择的相对频率的时间演变是未知的。这些知识对于开发基于活动的移动需求模型非常重要。