A STUDY OF COLEMAN'S LINEAR MODEL FOR ATTRIBUTES.

The sociologist who has accumulated data on a subject is soon faced with the problem of interpreting these data. He then must reorganize, combine, eventually reduce them. For this he uses mathematical models. If his variables are real numbers, he can choose among a variety of standard statistical models which most frequently involve linear structures, as these are the most easily worked out. The simplest probabilistic model involving attributes is the multinomial model, where the basic assumption is that the probability that an event belongs to a certain class depends only on this class. Statisticians have long been interested in multinomial models and have provided with a certain number of results. One approach has been to assimilate the linear model for proportions with an analysis-of-variance model, which also involves attributes. The theory of tests concerning multinomial models is largely based on tests of the chi-square type. The aim of this article is to discuss a statistical treatment for the estimations of the parameters, regions of confidence and tests of hypotheses.