The measurement of factor indeterminacy

Results obtained by Guttman [1955] on the determinacy of common factors have been thought to have disturbing consequences for the common factor model. It is argued that factors must be thought of as unobservable, and uniquely defined but numerically indeterminate. It follows that Guttman's measure of indeterminacy is inconsistent with the foundations of the factor model in probability theory, and the traditional measures of factor indeterminacy used by earlier writers should be reinstated. These yield no disturbing conclusions about the model.     

Factor Indeterminacy as Metrological Uncertainty: Implications for Advancing Psychological Measurement

Researchers have long been aware of the mathematics of factor indeterminacy. Yet, while occasionally discussed, the phenomenon is mostly ignored. In metrology, the measurement discipline of the physical sciences, uncertainty – distinct from both random error (but encompassing it) and systematic error – is a crucial characteristic of any measurement. This research argues that factor indeterminacy is uncertainty. Factor indeterminacy fundamentally threatens the validity of psychometric measurement, because it blurs the linkage between a common factor and the conceptual variable that the factor represents. Acknowledging and quantifying factor indeterminacy is important for progress in reducing this component of uncertainty in measurement, and thus improving psychological measurement over time. Based on our elaborations, we offer a range of recommendations toward achieving this goal.     

Parceling Cannot Reduce Factor Indeterminacy in Factor Analysis: A Research Note

Parceling—using composites of observed variables as indicators for a common factor—strengthens loadings, but reduces the number of indicators. Factor indeterminacy is reduced when there are many observed variables per factor, and when loadings and factor correlations are strong. It is proven that parceling cannot reduce factor indeterminacy. In special cases where the ratio of loading to residual variance is the same for all items included in each parcel, factor indeterminacy is unaffected by parceling. Otherwise, parceling worsens factor indeterminacy. While factor indeterminacy does not affect the parameter estimates, standard errors, or fit indices associated with a factor model, it does create uncertainty, which endangers valid inference.

     

Radical interpretation and the permutation principle

Davidson has claimed that to conclude that reference is inscrutable, one must assume that If some theory of truth ... is satisfactory in the light of all relevant evidence ... then any theory that is generated from the first theory by a permutation will also be satisfactory in the light of all relevant evidence. However, given that theories of truth are not directly read off the world, but rather serve as parts of larger theories of behavior, this assumption is far from self-evident. A proper understanding of the role truth theories play in theories of interpretation makes the inscrutability of reference much less wide-spread than Davidson suggests, and, as a result, the radical interpretation methodology is much less likely to saddle its defenders with counterintuitive cases of indeterminacy than is commonly supposed.     

Descriptive axioms for common factor theory,image theory and component theory

Through an extension of work by Guttman, common factor theory, image theory, and component theory are derived from distinct minimum subsets of assumptions chosen out of a set of five possible assumptions. It is thence shown that the problem of indeterminacy of factor scores in the common factor model is precisely reflected in the problem of the non-orthogonality of anti-images. Indeed, image scores are determinate for the same reason that the usual estimates of factor scores are determinate, and image scores cannot be used as though they were factor scores for the same reason that factor score estimates cannot be used as though they were factor scores.     

Indeterminacy in the social sciences

It is maintained that a principle of indeterminacy exists in the social sciences which bears some resemblance to the Heisenberg principle in the realm of physics. In the social sciences, however, the principle is grounded not on physical interference, but on the capacity of human beings to alter their behavior on the basis of changing conceptions of their social condition, and so the contention of writers like Nagel ‘that no distinct principle of explanation is involved’ must be rejected. The paper concludes with a brief consideration of the causes of social indeterminacy, which suggests that the phenomenon is ineradicable.     

Coming Full Circle in the History of Factor Indeterminancy

Nearly 70 years ago, eminent mathematician Edwin Bidwell Wilson attended a dinner at Harvard where visitor Charles Spearman discussed the "two-factor theory" of intelligence and his just-released book The Abilities of Man. Wilson, having just discovered factor indeterminacy, attempted to explain to Spearman and the assembled guests that Spearman's two-factor theory might have a non-uniqueness problem. Neither Spearman nor the guests could follow Wilson's argument, but Wilson persisted, first through correspondence, later through a series of publications that spanned more than a decade, involving Spearman and several other influential statisticians in an extended debate. Many years have passed since the Spearman-Wilson debates, yet the fascinating statistical, logical, and philosophical issues surrounding factor indeterminacy are very much alive. Equally fascinating are the sociological issues and historical questions surrounding the way indeterminacy has periodically vanished from basic textbooks on factor analysis. In this article, I delineate some of these historical-sociological issues, and respond to a critique from some recent commentators on the history of factor indeterminacy.     

Indeterminacy and the principle of need

The principle of need—the idea that resources should be allocated according to need—is often invoked in priority setting in the health care sector. In this article, I argue that a reasonable principle of need must be indeterminate, and examine three different ways that this can be dealt with: appendicizing the principle with further principles, imposing determinacy, or empowering decision makers. I argue that need must be conceptualized as a composite property composed of at least two factors: health shortfall and capacity to benefit. When one examines how the different factors relate to each other, one discovers that this is sometimes indeterminate. I illustrate this indeterminacy in this article by applying the small improvement argument. If the relation between the factors are always determinate, the comparative relation changes by a small adjustment. Yet, if two needs are dissimilar but of seemingly equal magnitude, the comparative relation does not change by a small adjustment of one of the factors. I then outline arguments in favor of each of the three strategies for dealing with indeterminacy, but also point out that all strategies have significant shortcomings. More research is needed concerning how to deal with this indeterminacy, and the most promising path seems to be to scrutinize the position of the principle of need among a plurality of relevant principles for priority setting in the health care sector.     

Reaction to Mortality: An Interdisciplinary Organizing Principle for the Human Sciences

Ernest Becker's theory about death denial is one example of depth psychological theory. Because very important features of Becker's theory have now successfully and singularly met the rigorous empirical testing of Terror Management Theory (TMT), it must be concluded that the theory of death denial stands apart from and above alternative depth psychological theories in explaining human behavioral and attitudinal motivation. Nevertheless, TMT only touches the surface of Becker's theory in the round. This essay looks at how Becker's wider theories of death denial are applied to (1) personal psychological, (2) social psychological, (3) political, and (4) spiritual aspects of human experience and suggests that what Becker has given us is an organizing principle, a theory of considerable integrative, explanatory, and interpretive power, for a broadly interdisciplinary social science of human behavior.     

Self‐esteem and anomie: An integration of Adler and Merton as a theory of deviance

The purpose of this paper is to show that while anomie theory on the social level offers a valid explanation of deviance, in order to understand the phenomenon in its entirety, we must consider the individual level as well. The psycho‐dynamic dimension of individual action is a crucial component of deviant behavior and one which must be integrated into a broader theory of overall deviance. With this in mind we will attempt to integrate the social and the psychological by incorporating the Adlerian and Mertonian models in order to create a more dynamic theory of deviance.     

Attribution bias: On the inconclusiveness of the cognition-motivation debate

Social psychologists have given considerable theoretical and research attention to whether motivational variables bias the attributions people make for behavior. Some theorists maintain that motivational constructs must be invoked to explain certain attributional phenomena; other theorists maintain that information-processing variables can adequately explain these phenomena. The present article critically examines existing cognitive and motivational approaches to attribution and analyzes the assumptions underlying the cognition-motivation debate. We argue that cognitive and motivational theories are currently empirically indistinguishable. In particular, its is possible to construct information-processing explanations for virtually all evidence for motivated bias. We conclude by examining the implications of this indeterminacy of cognitive and motivational explanations. Future research in the area can most profitably be addressed to improving the specificity of cognitive and motivational theories rather than to resolving the between-theory confrontation.     

绿色消费的许可效应：绿色让我们更不道德？

绿色消费属于道德范畴,消费者在助推绿色社会发展中的作用日益受到重视。然而,绿色消费会降低指定性道德约束或增强禁止性道德选择,消费者会变得不再绿色甚至自私(如享乐、撒谎或偷窃),这便是绿色消费的许可效应。从时间维度上来说,绿色消费许可效应的产生包括启动效应-绿色消费-许可效应三个阶段。有关该效应的理论解释是道德自我调节。从根本上来说,化解该效应需要消费者养成绿色生活方式,它包括两个路径：一方面,从绿色行为到绿色自我,抽象化表征行为,将绿色行为与自我概念相连接,采用自下而上加工方式实现;另一方面,从绿色自我到绿色行为,基于价值观-行为一致性原则,会促进个体产生更多绿色消费以及节俭和利他,采用的是自上而下加工。文章最后指出未来一些研究方向。     

Epistemicism and the Combined Spectrum

Derek Parfit's combined‐spectrum argument seems to conflict with epistemicism, a viable theory of vagueness. While Parfit argues for the indeterminacy of personhood, epistemicism denies indeterminacy. But, we argue, the linguistically based determinacy that epistemicism supports lacks the sort of normative or ontological significance that concerns Parfit. Thus, we reformulate his argument to make it consistent with epistemicism. We also dispute Roy Sorensen's suggestion that Parfit's argument relies on an assumption that fuels resistance to epistemicism, namely, that ‘the magnitude of a modification must be proportional to its effect.’     

Structural Indeterminacy

The threat of ontological deflationism (the view that disagreement about what there is can be non-substantive) is averted by appealing to realism about fundamental structure—or so tells us Ted Sider. In this paper, the notion of structural indeterminacy is introduced as a particular case of metaphysical indeterminacy; then it is argued that structural indeterminacy is not only compatible with a metaphysics of fundamental structure, but it can even safeguard it from a crucial objection; finally, it is shown that, if there are instances of structural indeterminacy, a hitherto unacknowledged variety of ontological deflationism will arise. Unless structure is shown to be determinate, ontological deflationism remains a live option. Furthermore, I will consider whether structural indeterminacy could be challenged by adopting a naturalistic epistemology of structure; the question is answered in the negative on the basis of a formal result concerning theory choice. Finally, I submit a new way of articulating the epistemology of structure, which hinges on the very possibility of structural indeterminacy.     

Another View of Translation Manuals and the Study of Science

The article argues for the possibility of translation manuals having an implicit internal structure. This structure is composed of specific methodological assumptions and techniques. Using the (N)-type and (G)-type distinction developed by Fuller for the study of scientific behavior, it is shown that these are incomplete characterizations of translation manuals. A more complete characterization must involve an analysis of how the presence or absence of methodological rules influences the interpretation of specific research questions. It is further argued that while Quine's original indeterminacy thesis cannot be completely rejected, in some cases it can be modified to reflect the importance of the methodological constraints. Finally, it is suggested that the more critical analysis of translation manuals will benefit the on-going debates in the study of scientific behavior.     

Underdetermination and Meaning Indeterminacy: What is the Difference?

The first part of this paper discusses Quine’s views on underdetermination of theory by evidence, and the indeterminacy of translation, or meaning, in relation to certain physical theories. The underdetermination thesis says different theories can be supported by the same evidence, and the indeterminacy thesis says the same component of a theory that is underdetermined by evidence is also meaning indeterminate. A few examples of underdetermination and meaning indeterminacy are given in the text. In the second part of the paper, Quine’s scientific realism is discussed briefly, along with some of the difficulties encountered when considering the ‘truth’ of different empirically equivalent theories. It is concluded that the difference between underdetermination and indeterminacy, while significant, is not as great as Quine claims. It just means that after we have chosen a framework theory, from a number of empirically equivalent ones, we still have further choices along two different dimensions.     

Autistic Heterogeneity: Linking Uncertainties and Indeterminacies

Autism is a highly uncertain entity and little is said about it with any degree of certainty. Scientists must, and do, work through these uncertainties in the course of their work. Scientists explain uncertainty in autism research through discussion of epistemological uncertainties which suggest that diverse methods and techniques make results hard to reconcile, ontological uncertainties which suggest doubt over taxonomic coherence, but also through reference to autism’s indeterminacy which suggests that the condition is inherently heterogeneous. Indeed, indeterminacy takes two forms—an inter-personal form which suggests that there are fundamental differences between individuals with autism and an intra-personal form which suggests that no one factor is able to explain all features of autism within a given individual. What is apparent in the case of autism is that scientists put uncertainty and indeterminacy into discussion with one another and, rather than a well-policed epistemic-ontic boundary, there is a movement between, and an entwinement of, the two. Understanding scientists’ dialogue concerning uncertainty and indeterminacy is of importance for understanding autism and autistic heterogeneity but also for understanding uncertainty and ‘uncertainty work’ within science more generally.     

Semi-sparse PCA

It is well known that the classical exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy problem. A new alternative model is proposed, which gives determinate factors and can be seen as a semi-sparse principal component analysis (PCA). An alternating algorithm is developed, where in each step a Procrustes problem is solved. It is demonstrated that the new model/algorithm can act as a specific sparse PCA and as a low-rank-plus-sparse matrix decomposition. Numerical examples with several large data sets illustrate the versatility of the new model, and the performance and behaviour of its algorithmic implementation.

     

Psychological Empowerment and Workforce Agility

Unpredictable, dynamic, and constantly changing environments require an ‘agile organization.’ The notion of an agile workforce has been discussed as critical to creating an agile organization. Despite the increasing recognition that workforce agility is critical to achieve competitiveness, the concept of workforce agility has not yet been systematically studied. The current research has been proposed on the assumption that employee cognition can support agile attitude and behavior. The research has been conceptualized considering psychological empowerment as an important employee cognition capable of promoting workforce agility. Following the Spreitzer, psychological empowerment, in the form of meaningfulness, self-determination, competence, and impact, has been proposed as facilitators of workforce agility. Our result supports the conceptualization implicit in the literature and suggests that psychological empowerment must be considered as an important aspect of an organization’s effort to foster workforce agility. Further, from among the psychological empowerment variables, impact is the most influential variable followed by self-determination, meaning and competence on workforce agility. While the study result agrees with few cognitive theories such as self-determination theory, job characteristics theory, and sense-making theory, the result has important managerial implications.