Year: 2011
Type: article
Abstract: Introduction The problem of estimating the dimensionality of a model occurs in various forms in applied statistics. There is estimating the number of factor in factor analysis, estimating the degree of a polynomial describing the data, selecting the variables to be introduced in a multiple regression equation, estimating the order of an AR or MA time series model, and so on. In factor analysis this problem was traditionally solved by eyeballing residual eigenvalues, or by applying some other kind of heuristic procedure. When maximum likelihood factor analysis became computationally feasible the likelihoods for different dimensionalities could be compared. Most statisticians were aware of the fact that comparison of successive chi squares was not optimal in any well defined decision theoretic sense. With the advent of the electronic computer the forward and backward stepwise selection procedures in multiple regression also became quite popular, but again there were plenty of ex
Author: Jan de Leeuw
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2768042492