Noniterative estimation and the choice of the number of factors in exploratory factor analysis

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors, and discusses the properties of the noniterative estimation method of Ihara and Kano in exploratory factor analysis. The consistency of the Ihara and Kano estimator is shown to hold even for an overestimated number of factors, which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors. The comparative study of their estimator and that based on maximum likelihood is carried out by a Monte Carlo experiment.The author would like to express his thanks to Masashi Okamoto and Masamori Ihara for helpful comments and to the editor and referees for critically reading the earlier versions and making many valuable suggestions. He also thanks Shigeo Aki for his comments on physical random numbers.     

On the distinction between perception and cognition

To uphold the distinction between perception and cognition for certain classes of tasks or phenomena, it is proposed that three criteria must be met: (1) when perceptual and cognitive functions serve different biological purposes, (2) when stimulus information in dynamic events is necessary, but not sufficient for veridical perception, and (3) when the task emphasizes explicit retrieval, as opposed to implicit use of information. Conversely, when the three criteria have not been met, conditions for theoretical unification exist.     

Multiple factors of cognitive failure and their relationships with stress vulnerability

Use of the Cognitive Failures Questionnaire (CFQ) in clinical research assumes that the questionnaire measures a single factor. A factor analysis of the CFQ was performed, on a sample of 475 students, using accurate procedures for determining the number of factors. These procedures gave mutually inconsistent results: at least two alternative factor structures can be extracted from the CFQ. An interpretable seven factor solution was found, but the CFQ probably has insufficient items to measure more than two strongly defined factors. The capacity of CFQ multiple factors to predict measures related to stress vulnerability was tested in a further study (N=57). Correlations between CFQ total score and neuroticism and use of coping strategies appeared to depend mainly on a single CFQ multiple factor, related to failures of concentration. Some of the other CFQ factors predicted other criteria. Further research on multiple factors of cognitive failure might improve the validity of the CFQ as a predictor of stress vulnerability and of cognitive performance.     

Dimensionality of the Multiple Affect Adjective Check List-Revised: A comparison of factor analytic procedures

The purpose of the study was to determine the factor structure of the revised Multiple Affect Adjective Check List (MAACL-R). The data from 307 undergraduate students who completed the MAACL-R were factor analyzed using both principal-components and principal-axis techniques. Based upon research with the original MAACL, two- and five-factor solutions to the MAACL-R factor structure were examined. The principal-components and principal-axis techniques yielded similar item loadings for each solution and the results of both techniques indicated the superiority of the two-factor solution. The two identified factors could be best characterized as representing independent dimensions of negative and positive affect. These findings are interpreted as providing support for the use of the MAACL-R summary scores of Dysphoria and PASS (Positive Affect and Sensation Seeking) rather than for the use of the five MAACL-R subscales.     

Development and analysis of a community-based resource recovery program

Five studies were conducted over a 10-month period to determine the effectiveness of specific procedures in encouraging recycling among residential neighborhoods. Results indicated that: (a) initial levels of participation in neighborhoods were frequently related to housing values; (b) weekly recycling pick-ups that coincided with garbage collection days resulted in higher levels of participation than pick-ups that occurred at other times; (c) notifying homes about the recycling program through distributed door-to-door brochures was more effective than soliciting participation through newspaper ads; (d) distributing containers to help residents separate recyclable from nonrecyclable material proved to be an effective procedure, especially when combined with frequent prompting (prompting alone did not have much effect); and (e) procedures that facilitated the greatest levels of participation were not always cost-effective. The subsequent combination of these procedures into a package program resulted in high levels of neighborhood participation that were cost-effective and maintained over a 6-month period.     

Effects of lines of progress and semilogarithmic charts on ratings of charted data

The extent to which interrater agreement and ratings of significance on both changes in level and trend are affected by lines of progress and semilogarithmic charts was investigated. Thirteen graduate students rated four sets of charts, each set containing 19 phase changes. Set I data were plotted on equal interval charts. In Set II a line of progress was drawn through each phase on each chart. In Set III data points were replotted on semilogarithmic charts. In Set IV a line of progress was drawn through each phase of each Set III chart. A significant main effect on interrater agreement was found for lines of progress as well as a significant 2-way interaction between lines of progress and change type. Three main effects (chart type, lines of progress, and type of change) and a significant 3-way interaction were found for ratings of significance. Implications of these data for visual analysis of charted data are discussed.     

AN INSTITUTIONAL STAFF TRAINING AND SELF-MANAGEMENT PROGRAM FOR DEVELOPING MULTIPLE SELF-CARE SKILLS IN SEVERELY/PROFOUNDLY RETARDED INDIVIDUALS

Although considerable attention has been given to the development of institutional staff training and management programs, the generalized effects of such programs on staff and resident behavior have seldom been examined. This study evaluated a program for teaching institutional staff behavioral training and self-management skills during self-care teaching sessions with severely and profoundly retarded residents. Following baseline observations in three self-care situations (toothbrushing, haircombing, handwashing), four direct care staff were sequentially taught to use verbal instruction, physical guidance, and contingent reinforcement in the toothbrushing program. During maintenance, staff were simultaneously taught to record, graph, and evaluate resident and their own behavior in the toothbrushing sessions. Staff were taught use of the training and self-management skills through a sequence of written instructions, videotaped and live modeling, rehearsal, and videotaped feedback. Observer presence and experimenter supervision were gradually decreased during the maintenance condition. Results indicated that during training and maintenance staff: (a) learned to use the training skills appropriately and consistently in the example situation (toothbrushing); (b) applied the skills in the generalization situations (haircombing and handwashing); and thereafter (c) maintained consistent and appropriate use of the skills with infrequent supervision. In addition, important changes in retarded residents' independent self-care responding occurred as staff training skills developed. Results are discussed in terms of their implication for future research and continued development of effective staff training and management programs.     

More on EM for ML factor analysis

We address several issues that are raised by Bentler and Tanaka's [1983] discussion of Rubin and Thayer [1982]. Our conclusions are: standard methods do not completely monitor the possible existence of multiple local maxima; summarizing inferential precision by the standard output based on second derivatives of the log likelihood at a maximum can be inappropriate, even if there exists a unique local maximum; EM and LISREL can be viewed as complementary, albeit not entirely adequate, tools for factor analysis.This work was partially supported by the Program Statistics Research Project at Educational Testing Service.     

Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.     

A comparison of factor analysis programs in SPSS,BMDP, and SAS

Factor analysis programs in SAS, BMDP, and SPSS are discussed and compared in terms of documentation, methods and options available, internal logic, computational accuracy, and results provided. Some problems with respect to logic and output are described. Based on these comparisons, recommendations are offered which include a clear overall preference for SAS, and advice against general use of SPSS for factor analysis.