Asymptotic biases in exploratory factor analysis and structural equation modeling

Formulas for the asymptotic biases of the parameter estimates in structural equation models are provided in the case of the Wishart maximum likelihood estimation for normally and nonnormally distributed variables. When multivariate normality is satisfied, considerable simplification is obtained for the models of unstandardized variables. Formulas for the models of standardized variables are also provided. Numerical examples with Monte Carlo simulations in factor analysis show the accuracy of the formulas and suggest the asymptotic robustness of the asymptotic biases with normality assumption against nonnormal data. Some relationships between the asymptotic biases and other asymptotic values are discussed.The author is indebted to the editor and anonymous reviewers for their comments, corrections, and suggestions on this paper, and to Yutaka Kano for discussion on biases.     

Examining Interindividual Differences in Cyclicity of Pleasant and Unpleasant Affects Using Spectral Analysis and Item Response Modeling

Weekly cycles in emotion were examined by combining item response modeling and spectral analysis approaches in an analysis of 179 college students' reports of daily emotions experienced over 7 weeks. We addressed the measurement of emotion using an item response model. Spectral analysis and multilevel sinusoidal models were used to identify interindividual differences in intraindividual cyclic change. Simulations and incomplete data designs were used to examine how well this combination of analysis techniques might work when applied to other practical data problems. Empirically, we found systematic individual differences in the extent to which individuals' emotions follow a weekly cycle, and in how such cycles are exhibited. Weekly cycles accounted for very little variance in day to day emotions at the individual level. Analytically, we illustrate how measurement, change, and interindividual difference models from different traditions may be combined in a practical manner to describe some of the complexities of human behavior. The authors gratefully acknowledge the support provided by grant T32 AG20500 from the National Institute on Aging in the preparation of this article. Special thanks to those at the Institute for Developmental and Health Research Methodology at the University of Virginia and to Paul De Boeck and the reviewers for helpful comments on earlier versions of this work.     

Prior distributions on symmetric groups

Fully and partially ranked data arise in a variety of contexts. From a Bayesian perspective, attention has focused on distance-based models; in particular, the Mallows model and extensions thereof. In this paper, a class of prior distributions, the Binary Tree, is developed on the symmetric group. The attractive features of the class are: it provides a closed-form solution to the posterior distribution; and a simple way to interpret the parameters of the prior distribution. The advantages of the proposed method are illustrated by comparing it to metric-based models using data analyzed by other researchers in this context.This revised article was published online in August 2005 with the PDF paginated correctly.     

Probabilistic Subset Conjunction

The authors introduce subset conjunction as a classification rule by which an acceptable alternative must satisfy some minimum number of criteria. The rule subsumes conjunctive and disjunctive decision strategies as special cases. Subset conjunction can be represented in a binary-response model, for example, in a logistic regression, using only main effects or only interaction effects. This results in a confounding of the main and interaction effects when there is little or no response error. With greater response error, a logistic regression, even if it gives a good fit to data, can produce parameter estimates that do not reflect the underlying decision process. The authors propose a model in which the binary classification of alternatives into acceptable/unacceptable categories is based on a probabilistic implementation of a subset-conjunctive process. The satisfaction of decision criteria biases the odds toward one outcome or the other. The authors then describe a two-stage choice model in which a (possibly large) set of alternatives is first reduced using a subset-conjunctive rule, after which an alternative is selected from this reduced set of items. They describe methods for estimating the unobserved consideration probabilities from classification and choice data, and illustrate the use of the models for cancer diagnosis and consumer choice. They report the results of simulations investigating estimation accuracy, incidence of local optima, and model fit. The authors thank the Editor, the Associate Editor, and three anonymous reviewers for their constructive suggestions, and also thank Asim Ansari and Raghuram Iyengar for their helpful comments. They also thank Sawtooth Software, McKinsey and Company, and Intelliquest for providing the PC choice data, and the University of Wisconsin for making the breast-cancer data available at the machine learning archives.     

Visual field differences in spatial frequency discrimination

Subjects discriminated between sine-wave gratings that differed by either +/-0.125 octaves (small difference) or +/-1.0 octaves (large difference). Baseline stimuli consisted of either 1.0 or 4.0 cycles per degree gratings. A left visual field advantage was obtained for the small difference in frequency, with no visual field advantages for the large difference in frequency. Similarly, moderate support for right versus left visual field advantages in processing high versus low spatial frequencies was found, although these interactions were not statistically significant. The results are discussed in light of Kosslyn's (1987) categorical and coordinate framework.     

Self-Constitution in the Ethics of Plato and Kant

Plato and Kant advance a constitutional model of the soul, in which reason and appetite or passion have different structural and functional roles in the generation of motivation, as opposed to the familiar Combat Model in which they are portrayed as independent sources of motivation struggling for control. In terms of the constitutional model we may explain what makes an action different from an event. What makes an action attributable to a person, and therefore what makes it an action, is that it issues from the person's constitution, and therefore from the person as a whole, rather than from some force working on or in the person. This in turn implies an account of what makes an action good: what makes an action good is that it is deliberated upon and chosen in a way that unifies the person into a constitutional system. Through deliberative action we constitute ourselves as unified agents. Platonic justice and Kant's categorical imperative are shown to be normative standards for action because they are principles of self-constitution.     

What comes out of the consulting-room? The reporting of clinical material

The author addresses the difficulties inherent in reporting clinical material. These fall into two main categories, the ethical problem of upholding confidentiality, and the technical problems which include the definition of analytical data, and the numerous ways in which truth can be distorted in the analytic context. It is advocated that consent be obtained from patients before publishing their material. It is also suggested that clinical reports should contain enough detail of the analytic interaction, including the analyst's thoughts and feelings, to convey the analytic process, and to enable the listener/reader to consider the evidence for himself and to draw his own conclusions. It is concluded that an analyst's anxiety about exposing a patient might obscure an anxiety about exposing himself.