Smallest space analysis of intelligence and achievement tests.

Abstract

Smallest Space Analysis is more parsimonious than factor analysis in the sense that it usually renders a space of fewer dimensions. Interpretation of such a space is facilitated by an a priori definitional system for the variables being studied. A reanalysis of the intercorrelation matrix in a previous study by H6ger by means of the Guttman-Lingoes SSA-I computer program shows how a certain definitional structure of the test variables is reflected in a two-space. Contiguous regions in this space represent the task of the subject-rule-inferring, rule-applying, and school achievementand the language of presentation of the item: verbal, digital, and figural. The six orthogonal common factors extracted by Ho'ger's factor analysis can be represented as six points in a two-space simultaneously with the tests. These results add further confirmation to the utility of the faceted definition of intelligence and the radex hypothesis for the structure of test interrelationships.The present paper illustrates a new method of analysis of the intercorrelations within a battery of n tests, which is suggested as more parsimonious than factor analysis: smallest space analysis. SMALLEST SPACE ANALYSIS AS MORE PAR-SIMONIOUS THAN FACTOR ANALYSISAmong the nonmetric computer programs developed recently by Guttman and Lingoes, a suitable one for analyzing correlation matrices is the G-L SSA-I (for further information see Guttman, in press;Lingoes, 1965Lingoes, , 1966. Each test is represented as a point hi a Euclidean space, and two points are closer together as the correlation between the corresponding tests increases. More explicitly, if ry is the observed correlation between tests i and j, and if dy is the calculated distance between these two tests for the smallest space, then the calculations are aimed at preserving the following inequalities: da < fai whenever r tj > r k i (V,^=l,2,---,ra). [1] Order among the correlations is thus preserved

Modeling the construct validity of the Berlin Intelligence Structure Model

“…However, Guttman's initial prediction failed in empirical analyses since the complex tests were located in the center of the radex (Schlesinger & Guttman, 1969). Therefore, the complexity facet was replaced by a rule task facet: tests of rule-inference are located in the center of the radex, followed by tests of rule-application; tests for learning or achievement are located at the periphery of the radex (Guttman & Levy, 1991;Schlesinger & Guttman, 1969). The most complex tasks of the BIS are probably the reasoning tasks, the simplest tasks are surely the speed tasks.…”

“…Guttman predicted that complex tests would be located at the periphery of the radex because complex tests would have fewer components in common with each other than simple tests as they diverge in different directions of complexity. However, Guttman's initial prediction failed in empirical analyses since the complex tests were located in the center of the radex (Schlesinger & Guttman, 1969). Therefore, the complexity facet was replaced by a rule task facet: tests of rule-inference are located in the center of the radex, followed by tests of rule-application; tests for learning or achievement are located at the periphery of the radex (Guttman & Levy, 1991;Schlesinger & Guttman, 1969).…”

Factor analysis versus multi-dimensional scaling: binary choice roll-call voting and the US Supreme Court

“…There is, for instance, a long history of the comparison of these analytic approaches in psychology and education research, primarily through the work of Louis Guttman (1958Guttman ( , 1966Guttman ( , 1982Guttman ( , 1954aGuttman ( , 1954bLingoes and Guttman, 1967;Schlesinger and Guttman, 1969; but see also, e.g. Guttman and Shoham, 1982;Levin et al, 1983;Masolavty et al, 2001).…”

Structural Analysis of the Motivation-Evaluating Rating Scale for Chronic Schizophrenics

“…It should be noted that, in many cases, SSA is found to produce a smaller space than factor analysis of the same material (6,13). Looking at our map ( fig.…”