Abstract not found

SUMMARY Regression problems with a number of related response variables are typically analyzed by separate multiple regressions. This paper shows how these regressions can be visualized jointly in a biplot based on reduced-rank regression. Reduced-rank regression combines multiple regression and principal components analysis and can therefore be carried out with standard statistical packages. The proposed biplot highlights the major aspects of the regressions by displaying the least-squares approximation of fitted values, regression coefficients and associated t-ratio's. The utility and interpretation of the reduced-rank regression biplot is demonstrated with an example using public health data that were previously analyzed by separate multiple regressions.

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis, The plot of structure correlations is shown to be optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biptots may be interpreted. Key words: biplot, canonical correlation analysis, canonical weight, interbattery factor analy-sis, partial analysis, redundancy analysis, regression coefficient, reduced rank regression, struc-ture correlations.

We propose a new approach to the multivariate analysis of data sets with known sampling site spatial positions. A between-sites neighbouring relationship must be derived from site positions and this relationship is introduced into the multivariate analyses through neighbouring weights (number of neighbours at each site) and through the matrix of the neighbouring graph. Eigenvector analysis methods (e.g., principal component analysis, correspondence analysis) can then be used to detect total, local and global structures. The introduction of the D-centring (centring with respect to the neighbouring weights) allows us to write a total variance decomposition into local and global components, and to propose a unified view of several methods. After a brief review of the matrix approach to this problem, we present the results obtained on both simulated and real data sets, showing how spatial structure can be detected and analysed. Freely available computer programs to perform computations and graphical displays are proposed.

This paper contains a discussion of partial least squares (PLS) path modeling with latent constructs as a general method for research on educational achievement. To the extent that such research requires the analysis of comparatively large and complex models under mild supplementary assumptions, PLS is an extremely flexible and powerful tool for statistical model building. The formal specification, estimation, and evaluation of PLS models is described with special emphasis on the features that distinguish PLS from other methods for path analysis. This specifically concerns distribution-free least squares estimation and distribution-free model evaluation using jackknife techniques. 1