论文标题
基于建模的可视化：理论，方法和应用
Unfolding-Model-Based Visualization: Theory, Method and Applications
论文作者
论文摘要
多维展开方法被广泛用于可视化项目响应数据。这样的方法将项目受访者和项目同时介绍到低维的欧几里得空间上，其中受访者和项目由理想点表示，人人，项目项目和个人项目相似性由欧几里得距离之间的距离捕获。在本文中，我们从统计角度研究了多维展开的可视化。我们将多维展开呈现为估计问题，在该问题中，受访者和项目理想点被视为要估计的参数。然后，提出了估计器以同时估计这些参数。提供了渐近理论，用于恢复理想点，从基于模型的可视化的有效性上散发出灯。为参数估计提出了交替的投影梯度下降算法。我们提供了两个说明性的例子，一个示例用于用户的电影评级，另一个关于参议院滚动电话投票。
Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal points, with person-person, item-item, and person-item similarities being captured by the Euclidian distances between the points. In this paper, we study the visualization of multidimensional unfolding from a statistical perspective. We cast multidimensional unfolding into an estimation problem, where the respondent and item ideal points are treated as parameters to be estimated. An estimator is then proposed for the simultaneous estimation of these parameters. Asymptotic theory is provided for the recovery of the ideal points, shedding lights on the validity of model-based visualization. An alternating projected gradient descent algorithm is proposed for the parameter estimation. We provide two illustrative examples, one on users' movie rating and the other on senate roll call voting.
