Application of the bootstrap methods in factor analysis

A Monte Carlo experiment is conducted to investigate the performance of the bootstrap methods in normal theory maximum likelihood factor analysis both when the distributional assumption is satisfied and unsatisfied. The parameters and their functions of interest include unrotated loadings, analytically rotated loadings, and unique variances. The results reveal that (a) bootstrap bias estimation performs sometimes poorly for factor loadings and nonstandardized unique variances; (b) bootstrap variance estimation performs well even when the distributional assumption is violated; (c) bootstrap confidence intervals based on the Studentized statistics are recommended; (d) if structural hypothesis about the population covariance matrix is taken into account then the bootstrap distribution of the normal theory likelihood ratio test statistic is close to the corresponding sampling distribution with slightly heavier right tail.This study was carried out in part under the ISM cooperative research program (91-ISM · CRP-85, 92-ISM · CRP-102). The authors would like to thank the editor and three reviewers for their helpful comments and suggestions which improved the quality of this paper considerably.     

Differential effects of cognitive behavior modification on seriously emotionally disturbed adolescents exhibiting internalizing or externalizing problems

This study examined the differential effects of a school-based cognitive behavior modification intervention on (a) the interpersonal/social skills and (b) the social competence and school adjustment of two groups of middle school students identified as seriously emotionally disturbed. One groups of students exhibited internalizing emotional problems and the other group exhibited externalizing emotional problems. The objective of the study was to investigate whether the effectiveness of a school-based cognitive behavior modification intervention was significantly related to the type of emotional disturbance a student exhibits (i.e. internalizing or externalizing emotional disturbance). The sample consisted of an experimental and a control group of middle school students identified as seriously emotionally disturbed. The intervention was implemented in 23 biweekly 42-minute sessions. The results indicated that teacher ratings of student social competence and school adjustment were sensitive to treatment effects, although students' social skills self-ratings were not significantly affected by the treatment. A differential treatment effect was established in that externalizing students were significantly more responsive than internalizing students.     

Factor structure of the basic personality inventory with incarcerated offenders

The item and scale factor structure of the Basic Personality Inventory (BPI) was examined in a sample of 486 offenders incarcerated for violent and sexual crimes. Separate principal-component analyses of the items for each of the 11 clinical scales, critical item scale, and social desirability scale indicated a one-dimensional factor solution for all scales except Depression and Persecutory Ideation. The Depression scale's two factors were Hopelessness and Depressive Affect and the Persecutory Ideation scale's two factors were General Paranoia and Perception of External Control. Although the factors for these two scales may assist in interpretation, the correlations between the factors and the total score of their respective scale were high. Confirmatory factor analysis of the 220 items from the 11 clinical scales supported the factorial logic of the scoring key. Analysis of the 11 clinical scales resulted in two factors: General Psychopathology/Adjustment and Antisocial Orientation. The results suggest that all but two scales can be viewed as unidimensional thereby allowing for a straightforward clinical interpretation. These analyses support the internal structure of the BPI and lend credence to external validity work with forensic populations.     

The effect of additional variables on factor indeterminacy in models with a single common factor

Determinate solutions for the indeterminate common factor ofp variables satisfying the single common factor model are not unique. Therefore an infinite sequence of additional variables that conform jointly with the originalp variables to the original single common factor model does not determine a unique solution for the indeterminate factor of thep variables (although the solution is unique for the factor of the infinite sequence). Other infinite sequences may be found to determine different solutions for the factor of the originalp variables. The paper discusses a number of theorems about the effects of additional variables on factor indeterminacy in a model with a single common factor and draws conclusions from them for factor theory in general.     

An alternative to the methodology for analysis of covariance

A general statistical model for simultaneous analysis of data from several groups is described. The model is primarily designed to be used for the analysis of covariance. The model can handle any number of covariates and criterion variables, and any number of treatment groups. Treatment effects may be assessed when the treatment groups are not randomized. In addition, the model allows for measurement errors in the criterion variables as well as in the covariates. A wide variety of hypotheses concerning the parameters of the model can be tested by means of a large sample likelihood ratio test. In particular, the usual assumptions of ANCOVA may be tested.Research reported in this paper has been partly supported by the Swedish Council for Social Science Research under project Statistical methods for analysis of longitudinal data, project director Karl G. Jöreskog, and partly by the Bank of Sweden Tercentenary Foundation under project Structural Equation Models in the Social Sciences, project director Karl G. Jöreskog.     

A note on sufficient conditions that a common factor will be determinate in an infinite domain of variables

It is proved for the common factor model withr common factors that under certain condition s which maintain the distinctiveness of each common factor a given common factor will be determinate if there exists an unlimited number of variables in the model each having an absolute correlation with the factor greater than some arbitrarily small positive quantity.The author is indebted to R. P. McDonald for suggesting the proof of Guttman's determinantal equation for the squared multiple correlation in predicting a factor from the observed variables used in the parenthetical note.     

The microanalysis of fixed-interval responding

The fixed-interval schedule of reinforcement is one of the more widely studied schedules in the experimental analysis of behavior and is also a common baseline for behavior pharmacology. Despite many intensive studies, the controlling variables and the pattern of behavior engendered are not well understood. The present study examined the microstructure and superstructure of the behavior engendered by a fixed-interval 5- and a fixed-interval 15-minute schedule of food reinforcement in the pigeon. Analysis of performance typical of fixed-interval responding indicated that the scalloped pattern does not result from smooth acceleration in responding, but, rather, from renewed pausing early in the interval. Individual interresponse-time (IRT) analyses provided no evidence of acceleration. There was a strong indication of alternation in shorter-longer IRTs, but these shorter-longer IRTs did not occur at random, reflecting instead a sequential dependency in successive IRTs. Furthermore, early in the interval there was a high relative frequency of short IRTs. Such a pattern of early pauses and short IRTs does not suggest behavior typical of reinforced responding as exemplified by the pattern found near the end of the interval. Thus, behavior from clearly scalloped performance can be classified into three states: postreinforcement pause, interim behavior, and terminal behavior.     

ENFORCEMENT OR INCENTIVES? PROMOTING SAFETY BELT USE AMONG MILITARY PERSONNEL IN THE NETHERLANDS

During a nationwide campaign to promote safety belt use among military personnel, a field study was conducted at 12 different military bases in the Netherlands. Amount of enforcement, type of publicity, and incentive strategies were varied among military bases. Observations of safety belt use among servicemen in their personal vehicles were conducted before the campaign, immediately following the campaign, and 3 months later. Safety belt use increased from 65% during baseline to 73% directly after the campaign and to 76% 3 months later. An overall 28.6% increase in safety belt use (from 63% to 81%) was observed at seven bases, whereas no changes were found at five bases (68% on all occasions). To a large degree the effects were due to a 37.7% increase among young drivers. These results confirmed that enforcement, as well as incentives, can be effective in promoting safety belt use. However, treatment effects were not systematic, thereby complicating the interpretation of the results. Implications of these varied outcomes are discussed.     

Minimum rank and minimum trace of covariance matrices

This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.     

The Headache Symptom Questionnaire: Discriminant classificatory ability and headache syndromes suggested by a factor analysis

A brief Headache Symptom Questionnaire was administered to 129 chronic headache Sufferers. The questionnaire accurately classified 68.42% of headache subjects in their proper diagnostic category, comparable to, but statistically less accurate than, the 86.4% agreement between expert headache diagnosticians using clinical interviews. Results of a factor analysis of the Headache Symptom Questionnaire lend support for their being two commonly accepted global headache categories—vascular/migraine and muscle contraction—and one headache dimension concerned with duration of headache pain. Combined migraine-muscle contraction headache was found to be related more to migraine than to muscle contraction headache, and cluster headaches emerged as a separate clinical entity, not loading positively on any factor and loading negatively on all three.This research was supported in part by Grant NS-15235 from the National Institute of Neurological and Communicative Disorders and Stroke.