Redundancy analysis an alternative for canonical correlation analysis

A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.A Fortran IV program for the method of redundancy analysis described in this paper can be obtained from the author upon request.     

CPCA: A program for principal component analysis with external information on subjects and variables

A program is described for principal component analysis with external information on subjects and variables. This method is calledconstrained principal component analysis (CPCA), in which regression analysis and principal component analysis are combined into a unified framework that allows a full exploration of data structures both within and outside known information on subjects and variables. Many existing methods are special cases of CPCA, and the program can be used for multivariate multiple regression, redundancy analysis, double redundancy analysis, dual scaling with external criteria, vector preference models, and GMANOVA (growth curve models).     

Bayesian Mixture Model of Extended Redundancy Analysis

Psychometrika - Extended redundancy analysis (ERA), a generalized version of redundancy analysis (RA), has been proposed as a useful method for examining interrelationships among multiple sets of...     

The effect of affine transformation on redundancy analysis

Canonical redundancy analysis provides an estimate of the amount of shared variance between two sets of variables and provides an alternative to canonical correlation. The proof that the total redundancy is equal to the average squared multiple correlation coefficient obtained by regressing each variable in the criterion set on all variables in the predictor set is generalized to the case in which there are a larger number of criterion than predictor variables. It is then shown that the redundancy for the criterion set of variables is invariant under affine transformation of the predictor variables, but not invariant under transformation of the criterion variables.     

A Redundancy Analysis for the Inwald Personality Inventory and the MMPI

A redundancy analysis between two psychological preemployment screening inventories was conducted with 2,438 male correction officer candidates. One canonical variate accounted for the majority of overlapping variance. When cross-validated, redundancy indices were. 17 for the Inwald Personality Inventory (IPI) and. 15 for the Minnesota Multiphasic Personality Inventory (MMPI). Three areas of overlap—control over actions, external control, and restlessness—were suggested. Less pathological behavioral patterns predictive of future job performance appeared measured only by the IPI. These results, combined with results from predictive validity studies, provide evidence that pathology is not sufficient for identifying "high risk" candidates.     

Regularized Partial and/or Constrained Redundancy Analysis

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in multiple regression analysis for some time, especially when predictor variables are nearly collinear, and the ordinary least squares estimator is poorly determined. The ridge estimation method was extended to PRA, CRA, and PCRA, where the reduced rank ridge estimates of regression coefficients were obtained by minimizing the ridge least squares criterion. It was shown that in all cases they could be obtained in closed form for a fixed value of ridge parameter. An optimal value of the ridge parameter is found by G-fold cross validation. Illustrative examples were given to demonstrate the usefulness of the method in practical data analysis situations. We thank Jim Ramsay for his insightful comments on an earlier draft of this paper. The work reported in this paper is supported by Grants 10630 from the Natural Sciences and Engineering Research Council of Canada to the first author.     

A redundancy analysis for the Inwald Personality Inventory and the MMPI

A redundancy analysis between two psychological preemployment screening inventories was conducted with 2,438 male correction officer candidates. One canonical variate accounted for the majority of overlapping variance. When cross-validated, redundancy indices were. 17 for the Inwald Personality Inventory (IPI) and. 15 for the Minnesota Multiphasic Personality Inventory (MMPI). Three areas of overlap-control over actions, external control, and restlessness-were suggested. Less pathological behavioral patterns predictive of future job performance appeared measured only by the IPI. These results, combined with results from predictive validity studies, provide evidence that pathology is not sufficient for identifying "high risk" candidates.     

Selective attention and secondary message analysis: A reconsideration of Broadbent's filter model of selective attention

If the type of channel sharing which Broadbent (1958) hypothesized for low information messages also occurs with high information verbal messages, then his filter model is an adequate model of the selective attention process. Analysis which proceeds by a hierarchy of tests and the fluctuating redundancy of primary prose messages can together account for the characteristics of secondary message detection. This hypothesis was tested using four levels of redundancy in the primary message, and two types of secondary message targets, requiring analysis to two different levels in the hierarchy of tests for detection. It was predicted that there should be more target detection as redundancy increased, and more detection of the targets requiring the lower level of analysis than of those requiring the higher. The predictions were confirmed with the exception that the higher level targets were detected with equal frequency at all levels of redundancy. A possible reason for this is suggested.     

Coactivation in the perception of redundant targets

Reaction time (RT) to redundant stimuli was investigated while controlling for distraction effects and response competition. In Experiment 1, a redundancy gain was found for 2 target letters with identical features (redundant) compared to trials in which 2 different targets shared the same response assignment (compatible) indicating coactivation of stimulus inputs. No difference in RTs was found between compatible displays and displays containing 2 targets with different responses (incompatible), suggesting (with other evidence) that letters were serially processed. In Experiment 2, a redundancy gain was again found. Unlike in Experiment 1, incompatible displays produced response competition, indicating a redundancy gain with parallel processing. Three forms of redundancy gains operating under specific conditions are discussed.     

Formal assessment of reliability specifications in embedded cyber-physical systems

Reliability has become an integral component of the design intent of embedded cyber-physical systems. Safety-critical embedded systems are designed with specific reliability targets, and design practices include the appropriate allocation of both spatial and temporal redundancies in the implementation to meet such requirements. With increasing complexity of such systems and considering the large number of components in such systems, redundancy allocation requires a formal scientific basis. In this work, we profess the analysis of the redundancy requirement upfront with the objective of making it an integral part of the specification. The underlying problem is one of synthesizing a formal specification with built-in redundancy artifacts, from the formal properties of the error-free system, the error probabilities of the control components, and the reliability target. We believe that upfront formal analysis of redundancy requirements is important in budgeting the resource requirements from a cost versus reliability perspective. Several case-studies from the automotive domain highlight the efficacy of our proposal.     

Relationships between redundancy analysis,canonical correlation,and multivariate regression

This paper attempts to clarify the nature of redundancy analysis and its relationships to canonical correlation and multivariate multiple linear regression. Stewart and Love introduced redundancy analysis to provide non-symmetric measures of the dependence of one set of variables on the other, as channeled through the canonical variates. Van den Wollenberg derived sets of variates which directly maximize the between set redundancy. Multivariate multiple linear regression on component scores (such as principal components) is considered. The problem is extended to include an orthogonal rotation of the components. The solution is shown to be identical to van den Wollenberg's maximum redundancy solution.This research was supported in part by U.S. Environmental Protection Agency contract 68-02-3402. The author gratefully acknowledges the stimulation of Maurice Tatsuoka and Beth Dawson-Saunders in first interesting him in redundancy analysis, as well as a useful change suggested by Warren Sarle.     

Effects of response task and accessory stimuli on redundancy gain: tests of the hemispheric coactivation model

Two experiments tested predictions of the hemispheric coactivation model for redundancy gain (J. O. Miller, 2004). Simple reaction time was measured in divided attention tasks with visual stimuli presented to the left or right of fixation or redundantly to both sides. Experiment 1 tested the prediction that redundancy gain--the decrease in reaction time when 2 stimuli are presented rather than 1--should increase when the response requires a greater degree of bilateral control by both hemispheres. In different blocks, the response was made with the left hand, the right hand, or both hands simultaneously. In accordance with the model, redundancy gain was larger with bimanual than with unimanual responses. Experiment 2 tested and found support for the prediction that redundancy gain should decrease when both hemispheres are activated by an irrelevant auditory accessory stimulus. Thus, the results support the hemispheric coactivation model.     

Interpreting canonical correlation analysis through biplots of structure correlations and weights

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the 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 biplots may be interpreted.     

Canonical/redundancy factoring analysis

The interrelationships between two sets of measurements made on the same subjects can be studied by canonical correlation. Originally developed by Hotelling [1936], the canonical correlation is the maximum correlation betweenlinear functions (canonical factors) of the two sets of variables. An alternative statistic to investigate the interrelationships between two sets of variables is the redundancy measure, developed by Stewart and Love [1968]. Van Den Wollenberg [1977] has developed a method of extracting factors which maximize redundancy, as opposed to canonical correlation.A component method is presented which maximizes user specified convex combinations of canonical correlation and the two nonsymmetric redundancy measures presented by Stewart and Love. Monte Carlo work comparing canonical correlation analysis, redundancy analysis, and various canonical/redundancy factoring analyses on the Van Den Wollenberg data is presented. An empirical example is also provided.Wayne S. DeSarbo is a Member of Technical Staff at Bell Laboratories in the Mathematics and Statistics Research Group at Murray Hill, N.J. I wish to express my appreciation to J. Kettenring, J. Kruskal, C. Mallows, and R. Gnanadesikan for their valuable technical assistance and/or for comments on an earlier draft of this paper. I also wish to thank the editor and reviewers of this paper for their insightful remarks.     

A Metaphilosophical Analysis of the Core Idea of Deflationism

In this paper, I give a metaphilosophical analysis of the core idea of deflationism by discussing some basic conceptual and methodological issues involved in the debate between deflationism and substantivism. In so doing, I argue for three positive points. First, the crux of the dispute between deflationism and substantivism is whether or not truth is substantive in its metaphysical nature and in its explanatory role in philosophical enterprises, rather than whether or not a minimal approach regarding conceptual resources is taken to explain truth; a minimal approach itself is philosophically innocent. Second, there is no intrinsic connection between the core idea of deflationism and the Tarski-style equivalence thesis, which is often identified as implying or supporting the former. Third, there are some unbridged fundamental gaps between the core idea of deflationism and various redundancy theses; these redundancy theses cannot be identified as the former, nor can they be used to justify the former on their own.     

On the optimality of the simultaneous redundancy transformations

The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.     

On the relationship between Fortier's simultaneous linear prediction and van den Wollenberg's redundancy analysis

The purpose of this note is to show that Van den Wollenberg's method of redundancy analysis is a special case of a simultaneous linear prediction method offered by Fortier.     

Pattern redundancy and detection in very short-term memory

A tachistoscopically presented target letter is detected better in a background of redundant items than in nonredundant material. The present experiment extended this finding by showing that detection rate increased systematically across three levels of background letter redundancy. A conclusion based on the earlier findings was that a serial process of letters in memory could not account for the effects of background redundancy on detection accuracy. Contrary to this conclusion, the present analysis showed that detection for semiredundant displays was successfully predicted by two variants of a serial process model. One model assumed that the scan of a letter is faster when the letter is the same as any prior letter scanned in the matrix. The other model assumes that nonredundant letters are processed serially and that redundant letters are processed all at once, i.e., in parallel.     

Visual recognition under conditions of high and low discrimination redundancy

The purpose of this investigation was to measure the minimum interval for recognition under conditions of high and low discrimination redundancy. The minimum interval for recognition is the briefest interval between two stimuli at which the first stimulus can be processed. Two sets of four digits were used. Digits were selected so that one set exhibited high discrimination redundancy and the other low discrimination redundancy. Ten Ss viewed digits with high discrimination redundancy, and 10 Ss viewed digits with low discrimination redundancy. The minimum interval for recognition for Ss tested with high discrimination redundancy was nearly twice as large as the minimum interval for recognition of the digits with low discrimination redundancy.