Understanding Unbiased Dimensions: The Use of Repertory-Grid Methodology

1978 ◽  
Vol 10 (10) ◽  
pp. 1137-1150 ◽  
Author(s):  
C J Palmer
Keyword(s):  
Multidimensional Scaling ◽  
Principal Components Analysis ◽  
Principal Components ◽  
Repertory Grid ◽  
Grid Data ◽  
Number Of Components ◽  
Verbal Labels ◽  
Components Analysis ◽  
Component Scores ◽  
Grid Test

The unbiased nature of the dimensions derived from multidimensional scaling poses a problem of interpretation. Subjective labelling by the researcher assumes that his judgments correspond to those of the respondents and is unsatisfactory. Identification of the dimensions needs to be based upon information gathered from the respondents themselves and in terms of the manner by which they were originally construed. Such information can be derived from the use of the repertory-grid test, which, like multidimensional scaling, requires subjects to make judgments of similarity between objects. The repertory-grid test also provides verbal labels for the distinctions that are made. A principal-components analysis of the repertory-grid data provides a number of components which are shown to be equivalent to the dimensions derived from multidimensional scaling. The use of component scores that relate to the verbal labels allows the dimensions to be identified in terms of the evaluations and perceptions of the respondents.

Non-Graphical Solutions for Cattell’s Scree Test

Methodology ◽  
2013 ◽  
Vol 9 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Gilles Raîche ◽  
Theodore A. Walls ◽  
David Magis ◽  
Martin Riopel ◽  
Jean-Guy Blais
Keyword(s):  
Factor Analysis ◽  
Principal Components Analysis ◽  
Simulation Study ◽  
Principal Components ◽  
Correlation Matrix ◽  
Numerical Solutions ◽  
Number Of Components ◽  
Components Analysis ◽  
Low Dimensional ◽  
Scree Test

Most of the strategies that have been proposed to determine the number of components that account for the most variation in a principal components analysis of a correlation matrix rely on the analysis of the eigenvalues and on numerical solutions. The Cattell’s scree test is a graphical strategy with a nonnumerical solution to determine the number of components to retain. Like Kaiser’s rule, this test is one of the most frequently used strategies for determining the number of components to retain. However, the graphical nature of the scree test does not definitively establish the number of components to retain. To circumvent this issue, some numerical solutions are proposed, one in the spirit of Cattell’s work and dealing with the scree part of the eigenvalues plot, and one focusing on the elbow part of this plot. A simulation study compares the efficiency of these solutions to those of other previously proposed methods. Extensions to factor analysis are possible and may be particularly useful with many low-dimensional components.

Delineation of climatic regions in Maine

1992 ◽  
Vol 22 (6) ◽  
pp. 801-811 ◽  
Author(s):  
R.D. Briggs ◽  
R.C. Lemin Jr.
Keyword(s):  
Cluster Analysis ◽  
Principal Components Analysis ◽  
Principal Components ◽  
Multivariate Analyses ◽  
The State ◽  
Climatic Zones ◽  
Climatic Regions ◽  
Weather Stations ◽  
Components Analysis ◽  
Component Scores

As part of a project to develop a productivity-oriented site classification system for spruce and fir in Maine, multivariate analyses of meteorological data were used to partition the state into homogeneous climatic zones. Data were obtained for 63 weather stations reporting both temperature and precipitation in Maine during the period 1954–1983. Monthly means were computed for each variable over the period of record and summarized by four 3-month seasons. Eighty-two percent of the variation in the 37 variables was accounted for by the first three principal components. Cluster analysis identified eight homogeneous groups of weather stations. Results from the principal components analysis were spatially extrapolated across the state using stepwise regression to define the relationship between the first two principal components and the location variables latitude, longitude, and elevation. Principal component scores were predicted across the state along a grid composed of township line intersections. The Triangulated Irregular Network of ARCINFO, a geographic information system software package, was used to spatially summarize the predicted component scores into climagraphic maps. The combined results from cluster analysis and spatial extrapolation of the principal components analysis suggested the presence of four broad climatic regions, which were further subdivided into nine climatic zones. Overlap among the four regions and nine zones was evaluated with a jackknifed classification of a linear discriminant function. Ninety-four percent of the weather stations were correctly classified by climatic region, whereas 76% were correctly classified by climatic zone. The high degree of correspondence between climatic zones and biophysical regions reinforced results of the multivariate analyses.

Diagnoses Generated by Numerical Taxonomic Methods Applied to Standard Blood Variables

1980 ◽  
Vol 19 (04) ◽  
pp. 205-209
Author(s):  
L. A. Abbott ◽  
J. B. Mitton
Keyword(s):  
Liver Cirrhosis ◽  
Renal Disease ◽  
Principal Components Analysis ◽  
Discriminant Function ◽  
Principal Components ◽  
Discriminant Function Analysis ◽  
Chronic Renal Disease ◽  
Function Analysis ◽  
Infectious Hepatitis ◽  
Components Analysis

Data taken from the blood of 262 patients diagnosed for malabsorption, elective cholecystectomy, acute cholecystitis, infectious hepatitis, liver cirrhosis, or chronic renal disease were analyzed with three numerical taxonomy (NT) methods : cluster analysis, principal components analysis, and discriminant function analysis. Principal components analysis revealed discrete clusters of patients suffering from chronic renal disease, liver cirrhosis, and infectious hepatitis, which could be displayed by NT clustering as well as by plotting, but other disease groups were poorly defined. Sharper resolution of the same disease groups was attained by discriminant function analysis.

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