The analysis of change, Newton's law of gravity and association models

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.