A comparative evaluation of several prominent methods of oblique factor transformation

The oblimax, promax, maxplane, and Harris-Kaiser techniques are compared. For five data sets, of varying reliability and factorial complexity, each having a graphic oblique solution (used as criterion), solutions obtained using the four methods are evaluated on (1) hyperplane-counts, (2) agreement of obtained with graphic within-method primary factor correlations and angular separations, (3) angular separations between obtained and corresponding graphic primary axes. The methods are discussed and ranked (descending order): Harris-Kaiser, promax, oblimax, maxplane. The Harris-Kaiser procedure—independent cluster version for factorially simple data,P'P proportional to , with equamax rotations, for complex—is recommended.This paper is based upon part of the author's doctoral dissertation [Hakstian, 1969] completed at the University of Colorado. The author is greatly indebted to Dr. Gene V Glass, who, as thesis advisor, generously contributed his time, erudition, and encouragement.     

A comparison of four methods of constructing factor scores

Four least-squares methods for constructing factor scores have been described in the literature. The formal properties of these scores are developed, and they are compared in terms of four generally desirable properties of constructed factor scores. In particular, it is shown that two of the methods yield scores that are conditionally unbiassed, and univocal in the sense of Guilford and Michael, though not orthogonal, while one of the other methods yields orthogonal scores.It is shown that constructed factor scores cannot be simultaneously univocal and orthogonal, unless we choose the special basis in factor space given by Canonical Factor Analysis.The general problem of choosing between the methods is discussed, on the basis of the theoretical relations obtained.EDITOR'S NOTE: The reader will quickly discover that this article develops several of the generalizations given in the second part of the preceding article, On Factors and Factor Scores. Independent development of the same generalizations is, of course, not a new phenomenon. Because the Presidential Address automatically is accepted for publication and given space in the December issue, it was decided that the only fair thing to do was to print this article in the same issue.     

On the least-squares orthogonalization of an oblique transformation

After proving a special case of a theorem stated by Eckart and Young, namely, that an oblique transformationG is the product of two different orthogonal transformations and an intervening diagonal, this note shows that the best fitting orthogonal approximation toG is obtained simply by replacing the intervening diagonal by the identity matrix. This result is shown to be identical with two earlier orthogonalizing procedures whenG is of full rank. A multiplicity of solutions is shown for the case of a singularG.I am grateful to J. J. Mellinger for pointing out a flaw in a previous version of this paper.Opinions expressed herein are those of the author, not necessarily those of the Army.     

A comparison of factor scores under conditions of factor obliquity

Six different methods of computing factor scores were investigated in a simulation study. Population scores created from oblique factor patterns selected from the psychological literature served as the bases for the simulations, and the stability of the different methods was assessed through cross-validation in a subject-sampling model. Results from 5 evaluative criteria indicated that a simplified, unit-weighting procedure based on the factor score coefficients was generally superior to several unit-weighting procedures based on the pattern or structure coefficients. This simplified method of computing factor scores also compared favorably with an exact-weighting scheme based on the full factor score coefficient matrix. Results are discussed with regard to their potential impact on current practice, and several recommendations are offered.     

A note on identification in the oblique and orthogonal factor analysis models

Conditions for removing the indeterminancy due to rotation are given for both the oblique and orthogonal factor analysis models. The conditions indicate why published counterexamples to conditions discussed by Jöreskog are not identifiable.The author would like to thank Gordon Bechtel and the reviewers for their comments and suggestions.     

A comparison of five methods of illusion measurement

The relative efficiency of five techniques of illusion measurement were tested on parametric variations of the Mueller-Lyer and Ebbinghaus figures. The methods of average error, reproduction, and selection from a graded series all showed significant effects of configurational variations. The subjective scaling techniques each failed to measure adequately changes in illusion magnitude for one illusion configuration. The suitability of the tested measures for group administration is also discussed.     

A comparison of preference‐assessment methods

In Study 1, we evaluated preference stability across 4 preference‐assessment methods for 6 individuals, 5 of whom had autism spectrum disorder and 1 of whom had traumatic brain injury. We also measured participants’ problem behavior as a corollary measure during all assessment methods. The highest mean correlation coefficients and Kendall rank coefficients of concordance across administrations were observed for the paired‐stimulus and multiple‐stimulus‐without‐replacement methods. Lower correspondence across administrations was observed for the free‐operant and response‐restriction methods. Although differentially higher levels of problem behavior did not occur with a single method, lower levels were consistently observed with the free‐operant method. During Study 2, we evaluated the implications of lower coefficients on reinforcer efficacy by comparing an initially identified and an immediately identified high‐preference stimulus in a reinforcer assessment. Initially identified and immediately identified high‐preference stimuli were equally effective reinforcers, suggesting that fluctuations in preference do not necessarily affect reinforcer efficacy in practice.     

A comparison of parent-education methods in maternity wards

This study investigated the effect of three parent-education methods for use with mothers in maternity wards. The three methods were videotapes and a handbook, videotapes only, and handbook only. The two groups who received the videotapes performed better on a posttest than two no-treatment control groups. No differences were evident between the videotapes and handbook group and the videotapes-only group. The handbook-only condition was better than only one of the control groups. Usefulness of the program, problems encountered, and future research needs are discussed.     

A comparison of two psychophysical methods using animals

A discrimination box containing two levers with a light above each was used to train eight rats to press beneath the brighter light for a milk reinforcer. The brighter light was held constant and the comparison light was varied to produce 12 brightness differences. The animals were run under two experimental methods: the block method in which each brightness level comparison was presented for a block of 11 contiguous trials, and the staircase method in which the sequence of brightness comparisons was determined by the correctness of the response on the preceding comparison. The block method produced a smaller differential brightness threshold and a larger change in discrimination performance for stimulus magnitude changes than did the staircase method.     

A comparison of presentation methods of video identification parades

Researchers have demonstrated that sequential lineup presentation reduces false identifications from perpetrator absent lineups. In England and Wales police identification parades are shown on video in a sequential manner. However, police sequential presentation varies from the strict sequential presentation advocated by researchers. In addition, after police have shown the sequential presentation they also have the option to show witnesses a matrix of the parade where witnesses can see all members of the parade simultaneously. The research reported investigated the effect of strict sequential presentation, police sequential presentation and police sequential presentation plus matrix on mock witnesses' performance on perpetrator present and absent video identification parades. Strict sequential presentation led to fewer correct identifications of the perpetrator than police sequential and police sequential plus matrix, with no difference in performance between either of the police conditions. For perpetrator absent lineups there was no effect of lineup presentation condition on lineup performance. Copyright © 2010 John Wiley & Sons, Ltd.     

Dimensions of perfectionism and goal commitment: A further comparison of two perfectionism measures

Research on perfectionism has suggested that a strong association exists between the setting and striving for excessively high standards. However, the motivational aspects of perfectionism have yet to be empirically identified. The purpose of the present study was to evaluate the usefulness and psychometric properties of a new goal commitment scale by assessing commitment to perfection in seven content areas. In addition to identifying individual differences in perfectionism goal commitment, the current research also investigated the association between commitment to perfectionism and trait indices of perfectionism. A sample of 261 students rated degree of commitment to perfectionistic goals and completed two multidimensional perfectionism scales that assess the personal and social aspects of perfectionism. Analyses confirmed the presence of individual differences in perfectionism goal commitment. Correlational tests revealed that the trait perfectionism dimensions were correlated with the goal commitment measure, but the findings varied as a function of the specific perfectionism goal. Overall, the current data are consistent with the view that the perfectionism construct has a salient motivational component. Our findings suggest that the assessment of goal commitment is a useful means of examining specific facets of the perfectionism construct.     

A comparison of analysis methods to estimate contingency strength

To date, several data analysis methods have been used to estimate contingency strength, yet few studies have compared these methods directly. To compare the relative precision and sensitivity of four analysis methods (i.e., exhaustive event‐based, nonexhaustive event‐based, concurrent interval, concurrent+lag interval), we applied all methods to a simulated data set in which several response‐dependent and response‐independent schedules of reinforcement were programmed. We evaluated the degree to which contingency strength estimates produced from each method (a) corresponded with expected values for response‐dependent schedules and (b) showed sensitivity to parametric manipulations of response‐independent reinforcement. Results indicated both event‐based methods produced contingency strength estimates that aligned with expected values for response‐dependent schedules, but differed in sensitivity to response‐independent reinforcement. The precision of interval‐based methods varied by analysis method (concurrent vs. concurrent+lag) and schedule type (continuous vs. partial), and showed similar sensitivities to response‐independent reinforcement. Recommendations and considerations for measuring contingencies are identified.     

A comparison of three methods for scoring figure drawings

Figure drawings obtained from 758 white male medical students were scored using three different methods. Method I involved 16 different physical size measurements; Method II involved six separate sophistication of body concept ratings; and Method III involved 42 separate aspects of the drawings weighted in direct proportion to their relative frequency of occurrence in the sample studied (conventionality scoring). Separate factor analyses of the scores derived from each method revealed that Methods I and II each reflect only a single underlying factor, and that these factors are uncorrelated in the population studied. Method III yielded eight meaningful factors, each of which may be construed as an independent area of conventionality/deviancy. An overall conventionality/deviancy score was also derived. It is believed that these three methods of scoring capture most of the variance inherent in existing figure drawing scoring systems, but that use of all three is necessary for a comprehensive analysis.     

A comparison of methods for calculating a severe discrepancy

Given the substantial rise in the number of students identified as learning-disabled, increasing attention has centered on methods for determining a severe discrepancy between ability and achievement. Using scores from 86 learning disabilities referrals, we compared four such methods (a z-score discrepancy, an estimated true score discrepancy, an unadjusted regression procedure, and an adjusted regression procedure). Each student was evaluated with the WISC-R, PIAT, and K-ABC. A high degree of agreement was found between z-score and estimated true score difference approaches. Less agreement was found between the unadjusted regression procedure and the other methods. It was concluded that the four methods cannot be used interchangeably in the calculation of severe discrepancies. Of the four methods that were analyzed, the unadjusted regression procedure selected the smallest percentage of students.     

A further investigation of the filled-duration illusion with a comparison between children and adults

This study investigated the filled duration illusion in children in comparison to adults, using a temporal bisection task with two ranges of anchor durations (1 vs. 4s and 2 vs. 8s). The results revealed a marked filled duration effect when filled and empty durations were presented in the same session (within-subjects condition), with the filled durations being judged to be longer than the empty durations in all age groups. However, the magnitude of this effect appeared to be larger in the children than in the adults. Furthermore, the filled duration effect decreased with the longest duration stimuli, and apparent reversals of this effect were observed with the empty durations being judged longer. In the between-subjects experiment, the filled duration effect disappeared in all age groups. However, in the children, the variability in the temporal judgment appeared to be greater for the empty than for the filled durations, thus indicating a lower sensitivity to empty durations.     

Maximally correlated orthogonal composites and oblique factor analytic solutions

Kaiser presented a method for finding a set of derived orthogonal variables which correlate maximally with a set of original variables. A simpler, more complete derivation of Kaiser's result is given and compared to related types of transformations. The transformation derived here suggests a direct method for finding the orthogonal factor solution which is maximally similar to a given oblique solution.