In factor analysis, factor contributions of latent variables are assessed conventionally by the sums of the squared factor loadings related to the variables. First, the present paper considers issues in the conventional method. Second, an alternative entropy-based approach for measuring factor contributions is proposed. The method measures the contribution of the common factor vector to the manifest variable vector and decomposes it into contributions of factors. A numerical example is also provided to demonstrate the present approach.
A path analysis method for causal systems based on generalized linear models is proposed by using entropy. A practical example is introduced, and a brief explanation of the entropy coefficient of determination is given. Direct and indirect effects of explanatory variables are discussed as log odds ratios, i.e., relative information, and a method for summarizing the effects is proposed. The example dataset is re-analyzed by using the method.
Karl Pearson's work strongly influenced the development of Italian statistics in the early 20th century. This paper reports some Italian contributions following Pearson's thought, which are probably less known outside Italy; for other Italian work, which was more successful internationally, just a brief description is given. Pearsonian topics are divided into three categories: curve systems, interpolation and correlation. For the first category, the contribution by F. De Helguero and F. Insolera is outlined. The former worked on dimorphic curves and developed a new family as a modification of the normal model; the latter dealt primarily with the problems arising when Pearson's curve system is applied to data that do not meet its basic assumptions. For interpolation, we recall a remarkable work by C. Gini, where Pearson's idea of minimizing geometrical distances of points from an interpolating line is discussed and extended. Contributions by G. Pietra and G. Bortolotti are discussed. Regarding correlation, where the Italian contribution was large, the paper focuses on the work by C.E. Bonferroni and G. Parenti, who extended Pearson's product-moment correlation "r" and Pearson's correlation ratio η to the general case of polynomial dependence. A discussion on the correct interpretation of η by Parenti is reported. Copyright (c) 2009 The Author. Journal compilation (c) 2009 International Statistical Institute.
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