The analysis of change, Newton's law of gravity and association models
The analysis of change, Newton's law of gravity and association models
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变化分析、牛顿万有引力定律和关联模型
DOI：
10.1111/j.1467-985x.2007.00498.x
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
M. Rooij
中科院分区：
文献类型：
--
作者：
M. Rooij
牛顿引力定律指出，宇宙中两个物体之间的作用力等于两个物体质量的乘积除以两个物体之间距离的平方。在论文的第一部分中，表明具有“万有引力定律”解释的模型适用于纵向分类数据的分析，其中将行为或选择从一个类别改变到另一个类别的人数是力的度量，目标是获得两个类别的质量估计值以及它们之间的距离估计值。为了更好地描述数据，引入了动态质量和动态位置。结果表明，广义引力定律与Goodman的RC（M）缔合模型是等价的.在本文的第二部分中，模型被推广到两种三向数据。第一种情况是当有多个双向表时，在第二种情况下，我们在三个时间点上进行更改。条件关联模型和部分关联模型分别与三向距离模型（如INDSCAL模型）和三元距离模型相关。
Summary. Newton's law of gravity states that the force between two objects in the universe is equal to the product of the masses of the two objects divided by the square of the distance between the two objects. In the first part of the paper it is shown that a model with a ‘law‐of‐gravity’ interpretation applies well to the analysis of longitudinal categorical data where the number of people changing their behaviour or choice from one category to another is a measure of force and the goal is to obtain estimates of mass for the two categories and an estimate of the distance between them. To provide a better description of the data dynamic masses and dynamic positions are introduced. It is shown that this generalized law of gravity is equivalent to Goodman's RC(M) association model. In the second part of the paper the model is generalized to two kinds of three‐way data. The first case is when there are multiple two‐way tables and in the second case we have change over three points of time. Conditional and partial association models are related to three‐way distance models, like the INDSCAL model, and triadic distance models respectively.