Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach : Volume 2 Multivariate Statistical Modeling

Often a statistical analysis involves use of a set of alternative models for the data. A "model-selection criterion" is a formula which provides a figure-of­ merit for the alternative models. Generally the alternative models will involve different numhers of parameters. Model-selection criteria take into account hoth the goodness-or-fit of a model and the numher of parameters used to achieve that fit. 1.1. SETS OF ALTERNATIVE MODELS Thus the focus in this paper is on data-analytic situations ill which there is consideration of a set of alternative models. Choice of a suhset of explanatory variahles in regression, the degree of a polynomial regression, the number of factors in factor analysis, or the numher of dusters in duster analysis are examples of such situations. 1.2. MODEL SELECTION VERSUS HYPOTHESIS TESTING In exploratory data analysis or in a preliminary phase of inference an approach hased on model-selection criteria can offer advantages over tests of hypotheses. The model-selection approach avoids the prohlem of specifying error rates for the tests. With model selection the focus can he on simultaneous competition between a hroad dass of competing models rather than on consideration of a sequence of simpler and simpler models. Front Matter....Pages i-xiii Summary of Contributed Papers to Volume 2....Pages 1-35 Some Aspects of Model-Selection Criteria....Pages 37-67 Mixture-Model Cluster Analysis Using Model Selection Criteria and a New Informational Measure of Complexity....Pages 69-113 Information and Entropy in Cluster Analysis....Pages 115-147 Information-Based Validity Functionals for Mixture Analysis....Pages 149-170 Unsupervised Classification with Stochastic Complexity....Pages 171-182 Modelling Principal Components with Structure....Pages 183-198 Aic-Replacements for Some Multivariate Tests of Homogeneity with Applications in Multisample Clustering and Variable Selection....Pages 199-232 High Dimensional Covariance Estimation: Avoiding the ‘Curse of Dimensionality’....Pages 233-253 Categorical Data Analysis by AIC....Pages 255-269 Longitudinal Data Models with Fixed and Random Effects....Pages 271-292 Multivariate Autoregressive Modeling for Analysis of Biomedical Systems with Feedback....Pages 293-317 A Simulation Study of Information Theoretic Techniques and Classical Hypothesis Tests in One Factor Anova....Pages 319-346 Roles of Fisher Type Information in Latent Trait Models....Pages 347-378 A Review of Applications of Aic in Psychometrics....Pages 379-403 Back Matter....Pages 405-417 Often a statistical analysis involves use of a set of alternative models for the data. A "model-selection criterion" is a formula which provides a figure-ofƯ merit for the alternative models. Generally the alternative models will involve different numhers of parameters. Model-selection criteria take into account hoth the goodness-or-fit of a model and the numher of parameters used to achieve that fit. 1.1. SETS OF ALTERNATIVE MODELS Thus the focus in this paper is on data-analytic situations ill which there is consideration of a set of alternative models. Choice of a suhset of explanatory variahles in regression, the degree of a polynomial regression, the number of factors in factor analysis, or the numher of dusters in duster analysis are examples of such situations. 1.2. MODEL SELECTION VERSUS HYPOTHESIS TESTING In exploratory data analysis or in a preliminary phase of inference an approach hased on model-selection criteria can offer advantages over tests of hypotheses. The model-selection approach avoids the prohlem of specifying error rates for the tests. With model selection the focus can he on simultaneous competition between a hroad dass of competing models rather than on consideration of a sequence of simpler and simpler models These three volumes comprise the proceedings of the US/Japan Conference, held in honour of Professor H. Akaike, on the `Frontiers of Statistical Modeling: an Informational Approach'. The major theme of the conference was the implementation of statistical modeling through an informational approach to complex, real-world problems. Volume 1 contains papers which deal with the Theory and Methodology of Time Series Analysis. Volume 1 also contains the text of the Banquet talk by E. Parzen and the keynote lecture of H. Akaike. Volume 2 is devoted to the general topic of Multivariate Statistical Modeling, and Volume 3 contains the papers relating to Engineering and Scientific Applications. For all scientists whose work involves statistics.