Dynamic factor models

摘要

Factor models in social science originate from the need to condense large-scale statistical data on many variables into a much smaller number of indices or "common factors", with as little loss of information as possible. These indices are more oftenthan not considered latent, even though one may also test for an hypothetically prescribed simple structure involving a number of observed variables as candidate common factors. In both cases, being latent or not, factors are conceived to reduce the dimension of the statistical model. As is well explained by Bartholomew (1987), a second approach to factor models is more theoretical and arises naturally in social science contexts where one wants to think about some quantities for which no measuring instrument exists. Business sentiment, quality of life, and general intelligence are such hypothetical variables that may be extracted as common factors from a set of answers to a questionnaire used in a sample survey. Actually, Factor Analysis was invented by psychologists for measurement of general intelligence. In the beginning of the twentieth century, in the study of human abilities, psychologists, including Butt and Spearman, were concerned with the fact that people performing well in one test of mental ability also tended to do well in others. This motivated the hypothesis of a common latent factor, called general intelligence. Of course, the scores on different items were not perfectly correlated but it could be hypothesized that the variation in performance from one item to another was only due to additional random elements, called specific because they were mutually independent. In other words, one common factor was able to summarize the dependence between a number of scores. In the 1930s, Thurstone and his associates in Chicago proposed to replace Spearman's single general factor by a limited number of common factors representing different abilities.