Factor analysis and personality theory

This article deals with the factor analytic approach to personality. More specifically, it deals with problems in factor analyses of personality questionnaires which contribute to factorial confusion. It is stated that in fact the factorial results make better sense than is usually admitted. The apparent disparity of results can be accounted for by technical defects in the chosen factor analytic method. Furthermore, it is shown that another source of disagreement lies in the interpretation of what are essentially the same factors.     

A generalization of stimulus sampling theory

A modification of stimulus sampling theory is presented. The restriction that each stimulus element is conditioned to one and only one response is replaced with the notion of a scale of conditioning for each element. This variation provides a context in which such variables as reward magnitude and motivation can be viewed as determiners of behavior. Some experimental results on multiple response problems also have a natural interpretation in terms of these ideas.     

Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis

One of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries. We show in this paper that the set of matrices, which can be reduced to rankr, has positive (Lebesgue) measure if and only ifr is greater or equal to the Ledermann bound. In other words the Ledermann bound is shown to bealmost surely the greatest lower bound to a reduced rank of the sample covariance matrix. Afterwards an asymptotic sampling theory of so-called minimum trace factor analysis (MTFA) is proposed. The theory is based on continuous and differential properties of functions involved in the MTFA. Convex analysis techniques are utilized to obtain conditions for differentiability of these functions.     

On the sampling theory roundations of item response theory models

Item response theory (IT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the stochastic subject versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating versus estimating -predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.A presidential address can serve many different functions. This one is a report of investigations I started at least ten years ago to understand what IRT was all about. It is a decidedly one-sided view, but I hope it stimulates controversy and further research. I have profited from discussions of this material with many people including: Brian Junker, Charles Lewis, Nicholas Longford, Robert Mislevy, Ivo Molenaar, Donald Rock, Donald Rubin, Lynne Steinberg, Martha Stocking, William Stout, Dorothy Thayer, David Thissen, Wim van der Linden, Howard Wainer, and Marilyn Wingersky. Of course, none of them is responsible for any errors or misstatements in this paper. The research was supported in part by the Cognitive Science Program, Office of Naval Research under Contract No. Nooo14-87-K-0730 and by the Program Statistics Research Project of Educational Testing Service.     

Factor analysis and Psychometrika: Major developments

Papers on factor analysis appearing inPsychometrika reflect the initial efforts of the Thurstonians to reformulate psychology as a quantitative science. The Thurstonians' emphasis on the development of factor analysis as an exploratory methodology was not new with them but was taken from British statisticians and psychologists who preceded them, whose literature the Thurstonians otherwise tended to ignore. The Thurstonians' rejection of general factors and focus on rotation to simple structure reflected an attempt to avoid statistical artifact and to identify factors with psychological substance. Much of the literature on factor analysis inPsychometrika concerned solving technical problems in the exploratory factor analysis method. Factor analysis took a major shift in direction in the 1970's with the development of confirmatory methodologies, many of which now receive greater attention than the method of exploratory factor analysis, most of the problems of which are now resolved.     

Chinese affect circumplex: I. Structure of recalled momentary affect

The structure of momentary affect among Cantonese-speaking Chinese was explored by developing questionnaire scales in four response formats. Scales can be scored for dimensions defined by Feldman Barrett and Russell; Thayer; Larsen and Diener; and Watson and Tellegen. In a study of recalled affect ( N  = 487), the newly translated scales were found to support all but Watson and Tellegen's structural model originating from English. Results cross-validated well in a second sample ( N  = 402). Affect dimensions were interrelated as found with English-speaking Canadians and they could be integrated into a two-dimensional bipolar space.     

Antecedents of everyday positive emotions: An experience sampling analysis

The focus of this study is on everyday positive emotions and their relations to critical appraisal antecedents. Following from classical appraisal theory and Pekrun’s (2006) control-value theory of achievement emotions, two research questions were addressed, namely whether cognitive appraisals of control and value were related to discrete positive emotions in everyday situations and whether control and value antecedents interact in predicting these emotions. We further investigated whether control/value and positive emotion relations changed as a function of situational factors (achievement vs. non-achievement settings). 50 university freshmen (78% female) were assessed by use of the experience sampling method for a period of 1 week, with intraindividual analyses conducted using a multilevel, idiographic approach. Consistent with our hypotheses, the emotions of enjoyment, pride, and contentment were positively related to control and value appraisals. Further, control and value interacted to predict these positive emotions. The strength of appraisal/positive emotion relations was equivalent across achievement vs. non-achievement settings. Implications for future research are discussed.     

Sequential sampling designs for the two-parameter item response theory model

In optimal design research, designs are optimized with respect to some statistical criterion under a certain model for the data. The ideas from optimal design research have spread into various fields of research, and recently have been adopted in test theory and applied to item response theory (IRT) models. In this paper a generalized variance criterion is used for sequential sampling in the two-parameter IRT model. Some general principles are offered to enable a researcher to select the best sampling design for the efficient estimation of item parameters.     

Retrospective spiritual narratives: exploring recalled childhood and adolescent spiritual experiences

This paper draws on a collection of retrospective narratives of childhood and adolescent spiritual experiences to explore the qualities and characteristics of the spirituality of the young. They recall a range of spiritual experiences that touch on death, mortality, visions, and perceptions and connections beyond the self. Their experiences include varying intensities of emotion and invoke a range of responses in them and others. The paper considers the social, emotional and familial context of these early life experiences and their impact on spiritual experience and the possibility/impossibility and freedom/lack of freedom to express, and integrate spirituality.     

Factor analysis and AIC

The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation. It was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis. The use of the AIC criterion in the factor analysis is particularly interesting when it is viewed as the choice of a Bayesian model. This observation shows that the area of application of AIC can be much wider than the conventional i.i.d. type models on which the original derivation of the criterion was based. The observation of the Bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings.The author would like to express his thanks to Jim Ramsay, Yoshio Takane, Donald Ramirez and Hamparsum Bozdogan for helpful comments on the original version of the paper. Thanks are also due to Emiko Arahata for her help in computing.     

Factor analysis of ipsative data: a simulation study

This paper introduces a summary on how to proceed to conduct a factor analysis when the input data are ipsative. The classical factor analysis procedures cannot be used because the covariance matrix is singular. Additionally, previous research on the optimal conditions to conduct factor analysis for ipsatized data is reviewed, and the results of a simulation study are presented. The study includes conditions of sample size, model complexity, and model specification (correct vs. incorrect). The results suggest that researchers should be careful when factor analyzing ipsatized data, particularly if they suspect that the model is incorrectly specified and includes a smaller number of factors.     

Application of a large sampling criterion to some sampling problems in factor analysis

A technique is presented to test the completeness of factor solutions and also to test the significance of common-component loadings. The chisquare test involved is based upon the asymptotic normal properties of the residuals.The research work on which the results presented are based was conducted under the supervision of Prof. P. S. Dwyer, Mathematics Department, University of Michigan. The complete results of this research were presented in a Ph. D. thesis, June, 1951.     

Quantified statements are recalled as generics: evidence from preschool children and adults

Generics are sentences such as "ravens are black" and "tigers are striped", which express generalizations concerning kinds. Quantified statements such as "all tigers are striped" or "most ravens are black" also express generalizations, but unlike generics, they specify how many members of the kind have the property in question. Recently, some theorists have proposed that generics express cognitively fundamental/default generalizations, and that quantified statements in contrast express cognitively more sophisticated generalizations (Gelman, 2010; Leslie, 2008). If this hypothesis is correct, then quantified statements may be remembered as generics. This paper presents four studies with 136 preschool children and 118 adults, demonstrating that adults and preschoolers alike tend to recall quantified statements as generics, thus supporting the hypothesis that generics express cognitively default generalizations.     

Factor analysis and physical types

Physical measurements, obtained from several different age-groups and national groups, have been correlated and factorized. The largest of the investigations was based on 2,400 British airmen in the R.A.F., and the most recent included as many as 17 traits. The methods of factorization employed were those worked out in early investigations of mental and scholastic tests, and differed in minor respects from those more recently used by Thurstone in his re-analysis of some of our data. The factor patterns reveal a remarkable constancy from age to age and from one national group to another. The general factor accounts for about the same proportion of the variance as the general factor in cognitive tests. The largest of the bipolar factors classifies traits into longitudinal and transverse, thus in some measure confirming the traditional classification of body-types.