Let A be a matrix with its Moore-Penrose pseudo-inverse † . It is proved that, after re-ordering the columns of , projector P = I − has block-diagonal form, that there permutation Π such T diag ( S 1 2 … k ) further each block i corresponds to cluster are linearly dependent other. clustering algorithm provided allows partition into clusters where in correlate only within same cluster. Some appl...

The quadratic assignment procedures for inference on multiple-regression coefficients(MRQAP) has become popular in social network analysis. These tests have been developed to assess the sizes of a set of multiple-regression coefficients. However, research practitioners often use these tests to assess the size of individual multiple-regression coefficients. Although this might be a harmless exte...

This paper presents a procedure for coefficient estimation in a multivariate regression model of reduced rank in the presence of multicollinearity. The procedure permits the prediction of the dependent variables taking advantage of both Partial Least Squares (PLS) and Singular Value Decomposition (SVD) methods, which is denoted by PLSSVD. Global variability indices and prediction error sums are...

The backfitting algorithm commonly used in estimating additive models is used to decompose the component shares explained by a set of predictors on a dependent variable in the presence of linear dependencies (multicollinearity) among the predictors. Multicollinearity of independent variables affects the consistency and efficiency of ordinary least squares estimates of the parameters. We propose...

In Multiple linear regression models, problems arise when serious multicollinearity or influential outliers are present in the data. Failure to include significant quadratic or cross-product terms result in model specification error. Simple scatter plots are most of the time not effective in revealing the complex relationships of predictor variables or data problems in multiple linear regressio...

Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc...

In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust reg...

Econometrics textbooks generally conclude that in regression, because the calculation of path estimate variances includes a variance inflation factor (VIF) that reflects correlations between “independent” constructs, multicollinearity should not cause false positives except in extreme cases. However, textbook treatments of multicollinearity assume perfect measurement – rare in behavioral resear...