A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

The pursuit of Leonardo's constraint

Leonardo da Vinci (1452-1519) identified two stimulus situations that cannot be painted faithfully on a canvas: (a) when two objects are located in the same direction with respect to the painter's head, and (b) when parts of a surface are visible to one eye, but occluded from the other eye. He analysed these situations in terms of rays being emitted from the two eyes and, aside from the origin of the rays, the projective geometry he used was correct. His analyses showed that what can be seen from two vantage points cannot be represented on a canvas, because a 'correct' painting must be created from a single 'station point'. He was struck by the consequence of this fact that the depth seen on a canvas cannot match that of viewing the scene with two eyes. Subsequent visual scientists focused on Leonardo's observation about the lack of vivid depth in a picture. We argue that a complete understanding of what we see in the two stimulus situations requires consideration of visual direction in addition to visual depth. More specifically, we argue that the visual directions of the two objects, (a) above, and the visual direction of the monocular areas, (b) above, are dependent upon the constraint that two opaque objects cannot be represented in the same direction. Demonstrations that readers can perform, and that support this argument, are provided on the Perception website at http://www.perceptionweb.com/perc0102/ono.html.     

The Use of Multitrait–Multimethod Data for Detecting Nonlinear Relationships: The Case of Psychological Climate and Job Satisfaction

Previous monomethod research has found mixed support for nonlinear effects between certain job characteristics (e.g., job autonomy, job complexity) and outcome variables (e.g., job performance). We hypothesized that these weak nonlinear findings may be due to the prevalence of monomethod research that can lead to a lack of complete measurement and/or introduce common methods variance, either of which may mask the true shape of relationships. Using hierarchical regression analyses and a multitrait–multimethod (MTMM) research design, we found strikingly different results between monomethod and MTMM data when considering the relationships between three psychological climate variables and job satisfaction. While the monomethod results mirrored earlier inconclusive findings, the MTMM data indicated that nonlinear equations explained significantly more of the relationship between all three climate dimensions and job satisfaction. These results suggest that the use of MTMM data allows one to more effectively test for nonlinear effects. Furthermore, these nonlinear results suggest that the format of employee questionnaires should probably change from asking how much an employee has of certain constructs to asking does the employee want more or less of these constructs.     

Parenting and Family Stress Treatment Outcomes in Attention Deficit Hyperactivity Disorder (ADHD): An Empirical Analysis in the MTA Study

Parenting and family stress treatment outcomes in the MTA study were examined. Male and female (579), 7–9-year-old children with combined type Attention Deficit Hyperactivity Disorder (ADHD), were recruited at six sites around the United States and Canada, and randomly assigned to one of four groups: intensive, multi-faceted behavior therapy program alone (Beh); carefully titrated and monitored medication management strategy alone (MedMgt); a well-integrated combination of the two (Comb); or a community comparison group (CC). Treatment occurred over 14 months, and assessments were taken at baseline, 3, 9, and 14 months. Parenting behavior and family stress were assessed using parent-report and child-report inventories. Results showed that Beh alone, MedMgt alone, and Comb produced significantly greater decreases in a parent-rated measure of negative parenting, Negative/Ineffective Discipline, than did standard community treatment. The three MTA treatments did not differ significantly from each other on this domain. No differences were noted among the four groups on positive parenting or on family stress variables. Results are discussed in terms of the theoretical and empirically documented importance of negative parenting in the symptoms, comorbidities and long-term outcomes of ADHD.     

Neuromotor profiles: what are they and what can we learn from them?

Eye movements, alternating movements, rapid pointing movements, and various tremors were measured on patients with Parkinson's disease (n = 21), on Cree subjects exposed to methylmercury (n = 36), and on healthy control subjects (n = 30). Neuromotor profiles were created according to thirty characteristics extracted from test results of four subgroups matched for age and composed of six subjects each. Z scores were calculated with respect to the mean and standard deviation of the control group for each of the 30 characteristics. The subgroup with the lower methylmercury blood level had larger z scores than the control subgroup and with a few positive values above one standard deviation. The subgroup with the higher methylmercury blood level had several z scores above two standard deviations. Interestingly, the abnormal values for the subgroup with Parkinson's disease were mostly limited to static tremor recorded with no visual feedback and reached up to 5 standard deviations. These results indicate that neuromotor profiles can be used to summarize information extracted from different neuromotor tests and to differentiate neurological conditions.     

Reliability and validity of a self-efficacy instrument specific to sickle cell disease

The psychometric properties of a new, 9-item scale measuring disease-specific perceptions of self-efficacy were investigated in a community-based sample of adults (N = 83) with sickle cell disease (SCD). The Sickle Cell Self-Efficacy Scale (SCSES) was comprised of nine questions relating to participants' perceptions of their ability to function on a day-to-day basis and to manage SCD symptomatology (e.g. episodes of pain). The SCSES demonstrated good internal consistency, discriminant validity, and convergent and predictive validity, both with previously validated measures of related constructs as well as with reported SCD symptomatology. Overall, the instrument appears to be reliable and valid for assessing clients' self-efficacy for engaging successfully in day-to-day activities despite having SCD. Future investigators may wish to examine temporal and causal links between alterations in self-efficacy and changes in adjustment to sickle cell disease; the SCSES provides a psychometrically sound tool with which to investigate these phenomena.