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A Bayesian semiparametric latent variable model for binary, ordinal and continuous response

机译:二元,序数和连续响应的贝叶斯半参数潜变量模型

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摘要

This thesis discusses a latent variable model (LVM) which is based on a Bayesian approach and is estimated by Markov chain Monte Carlo methods (MCMC). The model extends classic factor analysis by allowing not only for gaussian metric manifest variables, but also for binary and ordinal indicators which are very common in many areas of application (e.g. psychology, sociology). Furthermore, a semiparametric predictor is introduced which describes the influence of covariates on the latent variables. The predictor may contain parametric effects, smooth functions of metric covariates (modeled by random walks and P-splines), spatial effects (modeled by Markov random fields) and interactions of metric and categorical covariates. The integration of temporal effects is easily possible. Consequently, the influence of covariates on the latent variables can be analyzed in much more detail than with currently available methods.One emphasis of this work is the development of an efficient MCMC algorithm with good estimation properties (in particular concerning the cutpoints of ordinal indicators) and its implementation in the standard software package R. Another focus lies on the demonstration of the model's applicability using data from an internet survey.Several models with differently structured predictors are analyzed and first ideas for model selection are presented.
机译:本文讨论了基于贝叶斯方法并通过马尔可夫链蒙特卡洛方法(MCMC)估计的潜在变量模型(LVM)。该模型不仅允许使用高斯度量清单变量,还允许使用在许多应用领域(例如心理学,社会学)中非常常见的二进制和有序指标,从而扩展了经典因子分析。此外,引入了半参数预测器,该预测器描述了协变量对潜在变量的影响。预测变量可能包含参数效应,度量协变量的平滑函数(由随机游动和P样条曲线建模),空间效应(由Markov随机场建模)以及度量和分类协变量的交互作用。时间效应的整合很容易实现。因此,与现有方法相比,可以更详细地分析协变量对潜在变量的影响。这项工作的重点是开发一种具有良好估计属性的有效MCMC算法(尤其是关于序数指标的切点)另一个重点是使用来自互联网调查的数据论证该模型的适用性。分析了具有不同结构的预测变量的几个模型,并提出了模型选择的第一个思路。

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    Raach Alexander;

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  • 年度 2006
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