SUMMARY This paper is concerned with the representation of a multivariate sample of size n as points P1, P2, ..., PI in a Euclidean space. The interpretation of the distance A(Pi, Pj) between the ith andjth members of the sample is discussed for some commonly used types of analysis, including both Q and R techniques. When all the distances between n points are known a method is derived which finds their co-ordinates referred to principal axes. A set of necessary and sufficient conditions for a solution to exist in real Euclidean space is found. Q and R techniques are defined as being dual to one another when they both lead to a set of n points with the same inter-point distances. Pairs of dual techniques are derived. In factor analysis the distances between points whose co-ordinates are the estimated factor scores can be interpreted as D2 with a singular dispersion matrix.

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Some distance properties of latent root and vector methods used in multivariate analysis

Advanced Statistical Methods in Biometric Research.

A multimethod, multivariate analysis of “intended” strategies provides empirical support for the presence of strategic groups based upon Porter's (1980) generic strategies. Variations in intraindus...

Porter's (1980) Generic Strategies as Determinants of Strategic Group Membership and Organizational Performance

s International, 1963, 24, 5571-5572. (University Microfilms No. 64-68,41) Maier, N. R. F. Problem solving and creativity. Belmont, Calif.: Brooks/Cole, 1970. Mendonca, J. D., & Siess, T. F. Counseling for indeci- siveness: Problem-solving and anxiety management training. Journal of Counseling Psychology, 1976, 23,.339-347. Myers, I. B. The Myers-Briggs Type Indicator: Manual. Palo Alto, Calif.: Consulting Psychologists Press, 1962. Nel, E., Helmreich, R., & Aronson, E. Opinion change in the advocate as a function of the persuasibility of his audience: A clarification of the meaning of dissonance. Journal of Personality and Social Psy- chology, 1969,12,117-124. Newell, A,, Shaw, J. C., & Simon, H. A. Elements of a theory of human problem solving. Psychological Review, 1958,65,151-166. Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K., & Bent, D. H. Statistical package for the Social Sciences (2nd ed.). New York: McGraw-Hill, 1970. Osborn, A, F. Applied imagination: Principles and procedures of creative problem-solving (3rd ed.). New York: Scribner's, 1963. Fames, S, J. Creative behavior guidebook. New York: Scribner's, 1967. Perri, M. G., & Richards, C. S. An investigation of naturally occurring episodes of self-controlled be- haviors. Journal of Counseling Psychology, 1977, 23,178-183. Platt, J. J., Scura, W. C., & Hannon, J. R. Problemsolving thinking of youthful incarcerated heroin ad- dicts. Journal of Community Psychology, 1973, 7, 278-281. Platt, J. J., & Spivack, G. Manual for the Means-Ends Problem-Solving Procedure (MEPS): A measure of interpersonal cognitive problem solving skill. Philadelphia: Department of Mental Health Sciences, Hahnemann Medical College and Hospital, 1975. Platt, J. J., Spivack, G., Altman, N., Altman, D., & Peizer, S. B. Adolescent problem-solving thinking. Journal of Consulting and Clinical Psychology, 1974, 42,787-793. Rotter, J. B. Generalized expectancies for internal versus external control of reinforcement. Psychological Monographs, 1966,80(1, Whole No. 609). Rotter, J. B. Generalized expectancies for problem solving and psychotherapy. Cognitive Therapy and Research, 1978,2,1-10. Shaftel, F. R., & Shaftel, G. Role playing for social values: Decision making in the social studies. Englewood Cliffs, N.J.: Prentice-Hall, 1967. Singer, D. G., & Kornfield, B. Conserving and consuming: A developmental study of abstract and action choices. Developmental Psychology, 1973, 8, 314. Spivack, G., & Shure, M. B. Social adjustment of young children. San Francisco: Jossey-Bass, 1974. Taylor, S. E. On inferring one's attitudes from one's behavior: Some delimiting conditions. Journal of Personality and Social Psychology, 1975, 31,

The development and implications of a personal problem-solving inventory

This field study explores the nature of entrepreneurial strategy making (ESM) and its relationship with strategy, environment and performance. In the first phase, we assess the independence of entrepreneurially oriented strategy-making processes through factor analysis. The second phase, using moderated hierarchical regression anlaysis, investigates the relative predictive power of two approaches for exploring the ESM–performance relationship: contingency and configuration. Findings from a sample of 32 firms competing in a wide variety of industries indicate that configurational approaches that align ESM, strategy, and environment have greater predictive power than contingency approaches. However, not all high performing configurations are consistent with normative theory. Thus, alternate theories linking entrepreneurial strategy making to competitive advantage should be developed and tested. © 1997 John Wiley & Sons, Ltd.

Entrepreneurial strategy making and firm performance: tests of contingency and configurational models

Factor analysis aims to explain observed relations among numerous variables in terms of simpler relations. The simplification may consist of producing a set of classificatory categories, or creating a smaller number of hypothetical variables. Such resolution is so central to all scientific work that we must pause in a moment to ask about the relation of factor analysis to investigatory methods in general. However, it may be said forthwith that its most valuable functions lie in the biological and behavioral sciences, where a great array of phenomena are multiply determined and where the conceptual independent variables are not easily located and agreed upon. For example, in the behavioral sciences, a student of delinquency or mental disorder may have doubts whether there is such a single thing as delinquency or mental disorder and must have an open mind as to where the important causal influences lie in the bewildering array of possibilities. In such a situation he may take a set of variables, each semantically entitled to be called a form of delinquency, and measure each on members of a population and then seek for the functional unities by computing correlation coefficients for each pair of variables over the list of people concerned. Into this correlation matrix-as we designate the square matrix of coefficients shown in Table 1 below-he may also introduce measures of putative causal influences, seeking in the subsequent factor analysis to find those underlying 'hypothetical variables' or factors among them which are of -theoretical importance. Or again a biologist concerned with nutrition might correlate-over many animals, each fed in a different wayvarious signs of health and disease and various ingredients in the food. The vitamins, for example, might historically have been located-perhaps more economically of research time than they were-as factors each with a certain pattern of deficiency signs and of relative presence in various foods.

A Biometrics Invited Paper. Factor Analysis: An Introduction to Essentials I. The Purpose and Underlying Models

If, as the extensive findings with simple structure, supported by the few presently available confactor rotations, suggest, oblique factors are the rule in nature, with orthogonality as a special, rather rare, case, it behoves us to outline more fully the implications of the oblique model, for it has certain important new properties. Two main consequences appear, both unknown in the orthogonal case: (1) The correlations of a factor with its variables, on the one hand, and its loadings on them on the other, which fuse into the same values in orthogonal factors, here become recognizably and importantly different; (2) From factoring the correlations among factors one can derive second and higher order factor systems which do not exist in the orthogonal case. The differentiation of a correlation and a loading can be shown geometrically in Figure 3, which also brings out the distinction between reference vectors and factors. The reference vector is the perpendicular to a hyperplane, and it is by examination of the projections formed by correlations with the reference vector that we perform rotations for simple structure. The corresponding factor is the line of intersection of the hyperplanes of all the reference vectors other than the one perpendicular to the hyperplane. Corresponding reference vectors and factors are shown in Figure 3, whence one sees that where the former are positively correlated the latter are inversely correlated. In the orthogonal case, reference vectors and factors are one and the same. As Figure 3 shows, the lines of projection of variables on factor axes, as in all nmathematical oblique representation, must run parallel, in getting projections on one factor, to the other factor axis. Thus, as is easily seen, the correlations of variables with a reference vector are

Raymond B. Cattell

Papers

A Biometrics Invited Paper. Factor Analysis: An Introduction to Essentials I. The Purpose and Underlying Models

Factor analyis: an introduction to essentials. ii. the role of factor analysis in research.