An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data

Confirmatory factor analysis (CFA) is widely used for examining hypothesized relations among ordinal variables (e.g., Likert-type items). A theoretically appropriate method fits the CFA model to polychoric correlations using either weighted least squares (WLS) or robust WLS. Importantly, this approach assumes that a continuous, normal latent process determines each observed variable. The extent to which violations of this assumption undermine CFA estimation is not well-known. In this article, the authors empirically study this issue using a computer simulation study. The results suggest that estimation of polychoric correlations is robust to modest violations of underlying normality. Further, WLS performed adequately only at the largest sample size but led to substantial estimation difficulties with smaller samples. Finally, robust WLS performed well across all conditions.     

Natural anchoring at the neutral point of category rating scales

Contextual theories of judgment assume that the rating of any stimulus depends on its relationship to a context of similar stimuli. For example, any specific act of behavior would be rated less favorably when considered in the context of good behaviors then when considered in the context of bad ones. However, two experiments suggest an absolute anchoring of the natural neutral point, an exception to this generalization. In Experiment 1, morally indifferent acts remained “neutral,” regardless of context; and in Experiment 2 the break-even or zero-point in a simulated game of chance was always rated “neutral.” In both experiments, contextual manipulations had powerful effects upon ratings of other stimuli, though never shifting them across the neutral point. Furthermore, both experiments suggest that neutral-point anchoring also affects the use of the most extreme categories in a manner that is unique to this phenomena. In Experiment 2 for example, the introduction of extremely positive “wins” not only made other wins seem less favorable while leaving ratings of the zero-point unchanged, but also made the most negative losses seem more favorable. It is as if the introduction of an extremely positive “win” also introduces the possibility of an extremely negative “loss.” Taken together these findings contradict the basic adaptation-level premise that the entire scale is determined by the neutral point; they are also inconsistent with the assumption of range theories that the scale is anchored by the endpoints of the range of stimuli actually experienced.     

Relationships between two systems of factor analysis

Considering only population values, it is shown that the complete set of factors of a correlation matrix with units in the diagonal cells may be transformed into the factors derived by factoring these correlations with communalities in the diagonal cells. When the correlations are regarded as observed values, the common factors derived as a transformation of the complete set of factors of the correlation matrix with units in the diagonal cells satisfy Lawley's requirement for a maximum likelihood solution and are a first approximation to Rao's canonical factors.     

Relationships between job evaluation ratings and self-ratings of job characteristics

Self-ratings by 308 shop workers of their job variety, autonomy, task identity, and skill challenge correlate significantly with ratings by observers of the jobs' skill requirements. Self-ratings, however, are unrelated to observers' estimates of the physical demands of the jobs or to environmental conditions of the work. The self-ratings and observer measures provide complementary, not substitute, information. Self-ratings can signal person-job dysfunctions, and more objective job measures can identify possible sources of the dysfunctions. Modifications to job characteristics measures are discussed and suggestions are made to begin a new phase of programmatic job characteristics research.     

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.     

Confirmatory factor analysis and job burnout correlates of the Health Professions Stress Inventory

Previous research in 1994 by Gupchup and Wolfgang identified four factors from Wolfgang's Health Professions Stress Inventory (1988) that were common among a sample of practicing pharmacists. The factors were labeled Professional Recognition. Patient Care Responsibilities, Job Conflicts, and Professional Uncertainty, respectively. We used confirmatory factor analysis to assess whether this factor structure was generalizable to nurses. To examine concurrent validity, we correlated the factors with Maslach and Jackson's three dimensions of job burnout, i.e., Emotional Exhaustion, Depersonalization, and Personal Accomplishment. Data were collected through a questionnaire survey of a random sample of 9,380 nurses from across 43 public hospitals in Hong Kong, from which 2,267 (24.2%) responded. Analysis indicated statistically acceptable goodness of fit indices for the four-factor solution. Except for the factor Patient Care Responsibilities. all other factors had moderate correlations between .44 and .53 with Emotional Exhaustion and Depersonalization. Correlations between the factors of Stress Inventory and Personal Accomplishment were small but significant, ranging from -.25 to .13. Areas for further improving the psychometric properties of the inventory are discussed.     

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.     

Developing equivalent Chinese and English scale‐point labels for rating scales used in survey research

Rating scales are the most frequently‐used response tool in surveys, and the scale levels are commonly described with words [verbal scale‐point labels (VSPL)]. In this study, Chinese VSPL were identified which employ five‐point scales that are psychometrically equivalent to English VSPL. In several bilingual studies, a total of 61 Chinese and 44 English items addressing intensity, frequency, and agreement rating modalities were tested. For each VSPL, three aspects were measured: position between minimum and maximum, familiarity, and appeal. The correspondence between pertinent Chinese and English words was also assessed. Based on these findings, we recommend specific VSPL that are best‐suited for achieving equivalence between Chinese and English in rating scales.     

Format effects in two teacher rating scales of hyperactivity

The object of this study was to investigate the effect of differences in format on the precision of teacher ratings and thus on the reliability and validity of two teacher rating scales of children's hyperactive behavior. Teachers (N=242) rated a sample of children in their classrooms using rating scales assessing similar attributes with different formats. For a sub-sample the rating scales were readministered after 2 weeks. The results indicated that improvement can be made in the precision of teacher ratings that may be reflected in improved reliability and validity.This research was supported by grants from the Spencer Foundation and the National Institute of Mental Health (MH 29495). A somewhat different version of this paper was presented at the annual convention of the American Educational Research Association, Toronto, Canada, March 1978. The author thanks Nadine Lambert and Leonard Marascuilo for their assistance in the preparation of this paper.     

Meta-analysis of the brief psychiatric rating scale factor structure

A meta-analysis (N=17,620; k=26) of factor analyses of the Brief Psychiatric Rating Scale (BPRS) was conducted. Analysis of the 12 items from Overall et al.'s (J. E. Overall, L. E. Hollister, & P. Pichot, 1974) 4 subscales found support for his 4 subscales. Analysis of all 18 BPRS items found 4 components similar to those of Overall et al. In a 5-component solution, a 5th activation component emerged but was best supported among samples of schizophrenic patients. The first 4 components appear to form the core of the BPRS factor structure. Results of the meta-analysis suggest 5 subscales (with items in parentheses): Affect (anxiety, guilt, depression, somatic); Positive Symptoms (thought content, conceptual disorganization, hallucinatory behavior, grandiosity); Negative Symptoms (blunted affect, emotional withdrawal, motor retardation); Resistance (hostility, uncooperativeness, suspiciousness); and Activation (excitement, tension, mannerisms-posturing).