Factor Analysis in the 1980's and the 1990's: Some Old Debates and Some New Developments

Abstract

A number of years have passed since my active involvement (Steiger & Schonemann, 1978; Steiger, 1979a, 1979b) in the “factor indeterminacy controversy.” In that period, factor analysis has become more firmly entrenched than ever as a multivariate method, enjoying wide use as a data reduction technique, as a “measurement model” for true scores in structural modeling, and as an exploratory data analysis tool. At the same time, the typical computing environment has changed radically, making the cost of execution time and computer memory a negligible issue in factor analytic practice. Though many would argue that research interest in factor analysis has declined substantially since the heyday of Thurstone and Tucker, there have been some interesting new lines of technical development, most of which have come laterally from the closely related field of structural equation modeling. There have also been some new twists on the old debates about the relative merits of factor analysis and component analysis. In this paper, I will attempt to review these developments and place them in perspective. This perspective is, of course, a personal one, even in matters of notation. One person might call the matrix F a “factor pattern.” Another might call it a “factor matrix.” To reduce potential communication problems, I begin in Section 2 with a review of basic theory and terminology, that will hopefully make this account reasonably self-contained and comprehensible. In Section 3, I attempt to summarize significant developments in the last 15 years. At this stage, I try to be descriptive rather than judgmental and my account emphasizes more recent developments. For an alternative view of developments from 1940 until the mid-eighties, see Mulaik (1986). Finally, in Section 4, I summarize, freely injecting my views and biases on the state of the art, and speculating about future trends and important unanswered questions. I must apologize in advance for concentrating, in this account, on traditional linear factor analysis and component analysis. Space considerations made me choose not to attempt to discuss interesting work by Ramsay, Takane, McDonald, Bartholomew, and others on non-linear (and other) variations on the factor-analytic theme. I was also forced to omit a review of the profound, and extremely interesting discussion in Behavioral and Brain Sciences of Jensen’s (1985) article on black-white intelligence differences. This article, the commentaries, and the followup discussion in Multivariate Behavioral Research (Volume 27, Number 2), especially “Guttman’s last paper” (Guttman, 1992) should be considered required reading for the sophisticated social scientist.

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