Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels and better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.     

Lifespan normative data (18–89 years) for Raven's Advanced Progressive Matrices Set I

Raven's Advanced Progressive Matrices (APM) Set I is a validated and brief test of fluid intelligence, ideal for use in busy clinical settings. However, there is a dearth of normative data allowing an accurate interpretation of APM scores. To address this, we present normative data from across the adult lifespan (18–89 years) for the APM Set I. Data are presented in five age cohorts (total N = 352), including two older adult cohorts (65–79 years and 80–89 years), which allows age-standardized assessment. We also present data from a validated measure of premorbid intellectual ability, which was absent from previous standardizations of longer forms of the APM. In line with previous findings, a striking age-related decline was noted, beginning relatively early in adulthood and most marked amongst lower-scoring individuals. Older adults did not demonstrate difficulty with specific test items or make an increased proportion of specific errors. Sex was not a significant predictor of performance. The data set is of particular use in the neuropsychological assessment of older adults, given the known susceptibility of fluid intelligence to both the effects of normal ageing and acquired brain injury in older age. The results are discussed in light of theories of neurological ageing.     

A generalized family of coefficients of relational agreement for numerical scales

A family of coefficients of relational agreement for numerical scales is proposed. The theory is a generalization to multiple judges of the Zegers and ten Berge theory of association coefficients for two variables and is based on the premise that the choice of a coefficient depends on the scale type of the variables, defined by the class of admissible transformations. Coefficients of relational agreement that denote agreement with respect to empirically meaningful relationships are derived for absolute, ratio, interval, and additive scales. The proposed theory is compared to intraclass correlation, and it is shown that the coefficient of additivity is identical to one measure of intraclass correlation.The author thanks the Editor and anonymous reviewers for helpful suggestions.     

Some properties of estimated scale invariant covariance structures

Scale invariance is a property shared by many covariance structure models employed in practice. An example is provided by the well-known LISREL model subject only to classical normalizations and zero constraints on the parameters. It is shown that scale invariance implies that the estimated covariannce matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. In this context, the paper considers two classes of fitting functions: weighted least squares and the class of functions proposed by Swain.Constructive comments by the referees are greatly appreciated. The author gratefully acknowledges Michael Browne's interest in his work.     

Separability of item and person parameters in response time models

This paper discusses two forms of separability of item and person parameters in the context of response time (RT) models. The first is separate sufficiency: the existence of sufficient statistics for the item (person) parameters that do not depend on the person (item) parameters. The second is ranking independence: the likelihood of the item (person) ranking with respect to RTs does not depend on the person (item) parameters. For each form a theorem stating sufficient conditions, is proved. The two forms of separability are shown to include several (special cases of) models from psychometric and biometric literature. Ranking independence imposes no restrictions on the general distribution form, but on its parametrization. An estimation procedure based upon ranks and pseudolikelihood theory is discussed, as well as the relation of ranking independence to the concept of double monotonicity.I am indebted to Wim van der Linden for bringing Thissen's (1983) paper to my notice, and to Martijn Berger, Frans Tan, and the anonymous reviewers for their constructive comments on earlier drafts of this paper.     

Two Books for Teachers

Murphy, Nancey and Ellis, George F. R. On the Moral Nature of the Universe: Theology, Cosmology, and Ethics
Haught, John F. Science and Religion: From Conflict to Conversation     

An advocacy intervention program for women with abusive partners: Six-month follow-up

Presented the 6-month follow-up findings of an experimental intervention designed to provide postshelter advocacy services to women with abusive partners. The intervention involved randomly assigning half the research participants to receive the free services of an advocate, 4 to 6 hours per week, for the first 10 weeks postshelter. One hundred forty-one battered women were interviewed about their experiences immediately upon their exit from a domestic violence shelter: 95% of the sample were interviewed 10 weeks thereafter (postintervention), and 93% were successfully tracked and interviewed 6 months later. At the 6-month follow-up, participants in both groups reported increased social support, increased quality of life, less depression, less emotional attachment to their assailants, and an increased sense of personal power. Although women in both groups reported some decrease in physical abuse over time, there were no statistically significant differences between those with and those without advocates, and abuse continued to be a problem for many women. Those who were still involved with their assailants continued to experience higher levels of abuse and had been more economically dependent upon the men prior to entering the shelter. Women who had worked with advocates continued to report being more satisfied with their overall quality of life than did the women in the control group. The authors thank the Editor and anonymous reviewers for their helpful comments. Thanks also to all present and past staff of the Community Advocacy Project, who helped in data collection and analyses. This work was supported by National Institute of Mental Health Grant 1R01 MH 44849.     

The Revised Conners' Parent Rating Scale (CPRS-R): Factor Structure, Reliability, and Criterion Validity

The Conners' Parent Rating Scale (CPRS) is a popular research and clinical tool for obtaining parental reports of childhood behavior problems. The present study introduces a revised CPRS (CPRS-R) which has norms derived from a large, representative sample of North American children, uses confirmatory factor analysis to develop a definitive factor structure, and has an updated item content to reflect recent knowledge and developments concerning childhood behavior problems. Exploratory and confirmatory factor-analytic results revealed a seven-factor model including the following factors: Cognitive Problems, Oppositional, Hyperactivity-Impulsivity, Anxious-Shy, Perfectionism, Social Problems, and Psychosomatic. The psychometric properties of the revised scale appear adequate as demonstrated by good internal reliability coefficients, high test-retest reliability, and effective discriminatory power. Advantages of the CPRS-R include a corresponding factor structure with the Conners' Teacher Rating Scale—Revised and comprehensive symptom coverage for attention deficit hyperactivity disorder (ADHD) and related disorders. Factor congruence with the original CPRS as well as similarities with other parent rating scales are discussed.     

An Ecological Approach to Enhancing Parenting Skills in Family Therapy

To increase the effectiveness of parent education interventions, family therapists can address those factors that shape the way in which parents interact with their children. This article presents ecological theory as a framework that can help clinicians expand the range of their parent training efforts. In order to assess the utility of ecological theory for clinical practice, the present study empirically explored the ways in which selected characteristics of parents, children, and the family context related to mothers' parenting behavior. Specific recommendations for family therapists who employ parent training techniques are offered.     

Aggression Observation Scale for Group Psychotherapy

An observational scale to record aggressive behaviors, defenses, and interventions that occur during a psychotherapy group has been developed. Content and process items were included. The content items focus on the spoken material and are on a continuum of increasing group members' awareness of and responsibility for their anger. The process items are directed to underlying psychodynamic issues on a continuum from avoiding anger, to indirect and then expression of anger. Leader interventions (responses) are also included. The development of the scale, the Aggression Observation Scale for Group Psychotherapy (AOSGP), is described including pilot testing and reliability and validity findings.