Oblique Rotaton in Canonical Correlation Analysis Reformulated as Maximizing the Generalized Coefficient of Determination

To facilitate the interpretation of canonical correlation analysis (CCA) solutions, procedures have been proposed in which CCA solutions are orthogonally rotated to a simple structure. In this paper, we consider oblique rotation for CCA to provide solutions that are much easier to interpret, though only orthogonal rotation is allowed in the existing formulations of CCA. Our task is thus to reformulate CCA so that its solutions have the freedom of oblique rotation. Such a task can be achieved using Yanai’s (Jpn. J. Behaviormetrics 1:46–54, 1974; J. Jpn. Stat. Soc. 11:43–53, 1981) generalized coefficient of determination for the objective function to be maximized in CCA. The resulting solutions are proved to include the existing orthogonal ones as special cases and to be rotated obliquely without affecting the objective function value, where ten Berge’s (Psychometrika 48:519–523, 1983) theorems on suborthonormal matrices are used. A real data example demonstrates that the proposed oblique rotation can provide simple, easily interpreted CCA solutions.     

Factor Analysis with EM Algorithm Never Gives Improper Solutions when Sample Covariance and Initial Parameter Matrices Are Proper

Rubin and Thayer (Psychometrika, 47:69–76, 1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one, when the covariance matrix to be analyzed and the initial matrices including unique variances and inter-factor correlations are positive definite. We further numerically demonstrate that the EM algorithm yields proper solutions for the data which lead the prevailing gradient algorithms for factor analysis to produce improper solutions. The numerical studies also show that, in real computations with limited numerical precision, Rubin and Thayer’s (Psychometrika, 47:69–76, 1982) original formulas for confirmatory factor analysis can make factor correlation matrices asymmetric, so that the EM algorithm fails to converge. However, this problem can be overcome by using an EM algorithm in which the original formulas are replaced by those guaranteeing the symmetry of factor correlation matrices, or by formulas used to prove the above fact.     

Patterns of Religious Coping among Bereaved College Students

Contemporary research has suggested that bereavement is a paramount issue in college populations, a group which has historically been underrepresented in grief research (Balk. in Death studies 25:67–84, 2001; Balk et al. in Death Studies 34:459–468, 2010). Indeed, there has been a call to generate new research on grief with specific populations and age groups (Center for the Advancement of Health. in Death Studies 28:568–575, 2004). Religion is often described as a primary way that individuals cope with bereavement in particular (Frantz et al. in Pastor Psychol 44(3):151–163, 1996) and has been shown to effect college student reactions to stress in general (Merrill et al. in Mental Health, Religion & Culture 12(5):501–511, 2009). The RCOPE (Pargament et al. in J Clin Psychol 56(4):519–543, 2000, J Health Psychol 9:713–730, 2004) is a frequently used measure of religious coping, but has not been evaluated with a bereaved undergraduate population. Given that emerging adulthood is a critical developmental phase of religious identity (Fowler. in New Directions for Child Development 3(52):27–45, 1991), the current study examined the factor structure of the RCOPE within a sample of bereaved college students. An exploratory factor analysis was performed, which approximated the factor structure proposed by Pargament et al. (J Clin Psychol 56(4):519–543, 2000). However, a high correlation between the positive and negative religious coping subscales (r = 0.71) detracted from the predictive utility of Pargament et al.′s (2000) two overarching subscales. Therefore, an exploratory factor analysis with an orthogonal rotation was used to identify two uncorrelated subscales (adaptive religious coping and maladaptive religious coping). This new two-factor, 39-item version of the RCOPE was found to demonstrate good internal consistency (α > 0.8) as well as convergent and discriminant validity. The interaction between religious coping strategies and core beliefs about the predictability of the world is explored, and directions for future research and clinical practice are suggested.     

Exploratory Bi-Factor Analysis

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger. The bi-factor model has a general factor and a number of group factors. The purpose of this paper is to introduce an exploratory form of bi-factor analysis. An advantage of using exploratory bi-factor analysis is that one need not provide a specific bi-factor model a priori. The result of an exploratory bi-factor analysis, however, can be used as an aid in defining a specific bi-factor model. Our exploratory bi-factor analysis is simply exploratory factor analysis using a bi-factor rotation criterion. This is a criterion designed to produce perfect cluster structure in all but the first column of a rotated loading matrix. Examples are given to show how exploratory bi-factor analysis can be used with ideal and real data. The relation of exploratory bi-factor analysis to the Schmid-Leiman method is discussed.     

Rumination, Inhibition and Stress: The Construction of A New Scale for Assessing Emotional Style

Emotional rumination and inhibition were identified in the Emotion Control Questionnaire (ECQ—Roger and Nesshoever 1987; Roger and Najarian 1989) as two relatively independent dimensions of emotional style, and the two measures have subsequently been shown to be important moderator variables in a range of health and forensic settings. Two other dimensions that emerged in the ECQ, labelled aggression control and benign control, have been shown to form part of the extraversion constellation, and the present paper describes the construction and validation of a new scale focusing exclusively on rumination and inhibition. Revised and expanded item pools for the scales were subjected to exploratory and confirmatory factor analyses, which endorsed the two-factor structure. The new scales were validated concurrently against related scales in different samples, and were shown to be systematically related to two independent indices of health status.     

A Multicomponent Latent Trait Model for Diagnosis

This paper presents a noncompensatory latent trait model, the multicomponent latent trait model for diagnosis (MLTM-D), for cognitive diagnosis. In MLTM-D, a hierarchical relationship between components and attributes is specified to be applicable to permit diagnosis at two levels. MLTM-D is a generalization of the multicomponent latent trait model (MLTM; Whitely in Psychometrika, 45:479–494, 1980; Embretson in Psychometrika, 49:175–186, 1984) to be applicable to measures of broad traits, such as achievement tests, in which component structure varies between items. Conditions for model identification are described and marginal maximum likelihood estimators are presented, along with simulation data to demonstrate parameter recovery. To illustrate how MLTM-D can be used for diagnosis, an application to a large-scale test of mathematics achievement is presented. An advantage of MLTM-D for diagnosis is that it may be more applicable to large-scale assessments with more heterogeneous items than are latent class models.     

The Adolescent Religious Coping Questionnaire. Translation and Cultural Adaptation of Pargament’s RCOPE Scale for Polish Adolescents

The paper presents the process of translation and cultural adaptation of the Religious Coping Questionnaire (the RCOPE) by Pargament et al. (2000) for Polish adolescents. The work was driven by the necessity to obtain a structural and measurement equivalence between the American and Polish versions of the instrument. The Polish version was created at the Department of Clinical Psychology of Children and Adolescents at The John Paul II Catholic University of Lublin, Poland. The exploratory factor analysis with the Oblimin oblique rotation was carried out. The principal components method was used as an extraction method of common factors. The results provided input for constructing the scales. The Adolescent Religious Coping Questionnaire consists of 105 items, grouped in 16 scales, which reflects positive and negative religious coping strategies.     

A Study of the Psychometric Properties of the Social Support Scale for Children

The Social Support Scale for Children (SSSC; Harter, 1985a) is one of the most commonly used measures of perceived social support and positive regard from others in children and young adolescents. Research on the validity of the SSSC, however, is limited. The current study examined the test-retest reliability, internal validity intersubscale correlations, and convergent validity of the SSSC. A confirmatory factor analysis was performed using structural equation modeling. The participants included 279 youth between the ages of 6 to 15 from three metropolitan areas in the Midwest. The results supported the reliability and validity of the SSSC. The results supported the four factor solution reported by Harter (1985a). Rewording or removal of two items is suggested.     

Importing Logics

The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and exogenous enrichment.     

Multidimensional CAT Item Selection Methods for Domain Scores and Composite Scores: Theory and Applications

Multidimensional computer adaptive testing (MCAT) can provide higher precision and reliability or reduce test length when compared with unidimensional CAT or with the paper-and-pencil test. This study compared five item selection procedures in the MCAT framework for both domain scores and overall scores through simulation by varying the structure of item pools, the population distribution of the simulees, the number of items selected, and the content area. The existing procedures such as Volume (Segall in Psychometrika, 61:331?C354, 1996), Kullback?CLeibler information (Veldkamp & van?der Linden in Psychometrika 67:575?C588, 2002), Minimize the error variance of the linear combination (van?der Linden in J. Educ. Behav. Stat. 24:398?C412, 1999), and Minimum Angle (Reckase in Multidimensional item response theory, Springer, New York, 2009) are compared to a new procedure, Minimize the error variance of the composite score with the optimized weight, proposed for the first time in this study. The intent is to find an item selection procedure that yields higher precisions for both the domain and composite abilities and a higher percentage of selected items from the item pool. The comparison is performed by examining the absolute bias, correlation, test reliability, time used, and item usage. Three sets of item pools are used with the item parameters estimated from real live CAT data. Results show that Volume and Minimum Angle performed similarly, balancing information for all content areas, while the other three procedures performed similarly, with a high precision for both domain and overall scores when selecting items with the required number of items for each domain. The new item selection procedure has the highest percentage of item usage. Moreover, for the overall score, it produces similar or even better results compared to those from the method that selects items favoring the general dimension using the general model (Segall in Psychometrika 66:79?C97, 2001); the general dimension method has low precision for the domain scores. In addition to the simulation study, the mathematical theories for certain procedures are derived. The theories are confirmed by the simulation applications.     

Disrupting the Coloniality of Being: Toward De-colonial Ontologies in Philosophy of Education

This essay works to bridge conversations in philosophy of education with decolonial theory. The author considers Margonis?? (1999, 2011a, b) use of Rousseau (1979) and Heidegger (1962) in developing an ontological attitude that counters social hierarchies and promotes anti-colonial relations. While affirming this effort, the essay outlines a coloniality of being at work in Rousseau and Heidegger through thier reliance on the colonial conceptualization of African Americans and Native Americans as savage and primitive. The essay turns to decolonial theory and the work of Maldenado-Torres (Cult Stud 21(2?C3):240?C270, 2007, 2009) to highlight how a decolonial attitude complicates, yet enriches Margonis?? philosophical framework.     

Margaret R. Miles’ Augustine and the Fundamentalist’s Daughter: An Eriksonian Perspective

My perspective on Margaret R. Miles’s Augustine and the Fundamentalist’s Daughter is informed by Erik H. Erikson’s life cycle model (Erikson 1950, 1959, 1963, 1964, 1968a, b, 1982; Erikson and Erikson 1997) and, more specifically, by my relocation of his life stages and their accompanying human strengths (Erikson 1964) according to decades (Capps 2008). I interpret Miles’s account of her life from birth to age forty as revealing the selves that comprise the composite Self (Erikson 1968a) that come into their own during the first four decades of the life cycle, i.e., the hopeful, willing, purposeful, and competent selves     

Rational intuition and understanding

Rational intuitions involve a particular form of understanding that gives them a special epistemic status. This form of understanding and its epistemic efficacy are not explained by several current theories of rational intuition, including Phenomenal Conservatism (Huemer, Skepticism and the veil of perception, 2001; Ethical intuitionism, 2005; Philos Phenomenol Res 74:30–55, 2007), Proper Functionalism (Plantinga, Warrant and proper function, 1993), the Competency Theory (Bealer Pac Philos Q 81:1–30, 2000; Sosa, A virtue epistemology, 2007) and the Direct Awareness View (Conee, Philos Phenomenol Res 4:847–857, 1998; Bonjour, In defense of pure reason, 1998). Some overlook it; others try to account for it but fail. We can account for the role of understanding in rational intuition by returning to the view of some of the early Rationalists, e.g. Descartes and Leibniz. While that view carries a prohibitive cost, it does contain an insight that may help us solve the problem of giving understanding its due.     

An Introduction to Issues of Gender in Stalking Research

Stalking research has increased substantially in the past 20?years. This special issue is intended to contribute to this literature by using gender as a focus point in 1) applying new theoretical perspectives that incorporate the role of gender to the study of stalking perpetration (Davis et al. 2010; Duntley and Buss 2010), 2) addressing divergent findings regarding gender in experiences of victims (Sheridan and Lyndon 2010) and perpetrators (Thompson et al. 2010), and 3) furthering the study of how gender influences perceptions of stalking (Cass and Rosay 2011; Dunlap et al. 2011; Sinclair 2010; Yanowitz and Yanowitz 2010). To place this special issue in context of the current state of knowledge on gender and stalking, we review the state of the existing research as it relates to the domains covered by articles present in this issue.     

Tempo and Temperament: A Music Lesson on the Significance of Time for the Art of Pastoral Care

This article will focus on the relationship between tempo and temperament and the power of music to facilitate healing, especially for individuals who struggle with temperament or mood disorders, by examining briefly how individuals diagnosed with depression may be helped by listening to or performing music as a form of treatment. Current research into the “science” of music is providing concrete evidence for the reality that musicians and music therapists have long intuited to be true–music does have the capacity to facilitate healing by influencing brain activity and altering moods (Cambell and Doman 2011; Levitin 2007, 2008; Mannes 2011; Powell 2010; Pruyser 1983; Rose 2004). Insofar as music is an integral part of most worship traditions, it provides a common ground for conversation that may seem more natural and less formidable to ministers and lay people alike than the structures of conventional counseling or care-giving relationships, especially for those who have a tendency to be suspicious of all things psychological.     

New Directions for Research on the Role of Parents and Teachers in the Development of Gender-Related Math Attitudes: Response to Commentaries

We frame our response to the commentaries by Cheryan (2011), Lane (2011), and Shapiro and Williams (2011), in terms of two broad points made by Lane (2011). First, we agree that the various constructs that we termed “math attitudes”—including math-gender stereotypes, math anxiety, math self-concepts, and achievement motivation in math—are in fact distinct (Gunderson et al. 2011b). Nevertheless, we argue that investigating common mechanisms underlying the transmission of these constructs from adults to children is a productive approach because it can lead to general interventions to boost children’s performance and dispositions toward math. Second, we argue that research on the development of gender-related math attitudes exists at the intersection of multiple research areas, including research on attitudes (broadly defined), math, gender, social learning, and child development, and that drawing on well-developed theories in these areas can lead to novel research questions and predictions. The three excellent commentaries broaden the scope of our article on gender-related math attitudes to include the transmission of implicit attitudes from adults to children, stereotype threat, and gender roles in math-related careers (Cheryan 2011; Gunderson et al. 2011b; Lane 2011; Shapiro and Williams 2011).     

Exemplification as molecular function

Since the publication of Universals and Scientific Realism (Armstrong 1978a, b) until Sketch for a Systematic Metaphysics (Armstrong 2010), via Universals: An Opinionated Introduction (Armstrong 1989), a World of States of Affairs (Armstrong 1997), and Truth and Truthmakers (Armstrong 2004), David Armstrong has developed one of the most influential theories of instantiation in contemporary analytic metaphysics (see, for example, Lewis, in Aust J Phil 61(4), 343–377, 1983; Baxter in Aust J Phil, 79, 449–464, 2001; Forrest, in Aust J Phil, 83, 213–228, 2006). Instantiation has been advocated by Armstrong to give a solution to what he has called the “pressing problem” of “the multiple location of property universals” (Armstrong, in Universals: An opinionated introduction. University Press, Cambridge, 1989, pp. 89–90). Here I argue that Armstrong’s theory of instantiation fails to solve the problem because it involves two kinds of instantiation to account for particulars “having” and “sharing” universals. As a viable alternative to Armstrong’s theory, I propose a theory of instantiation capable of accounting for both phenomena in a univocal way.     

How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis

We investigate the performance of three statistics, R ₁, R ₂ (Glas in Psychometrika 53:525–546, 1988), and M ₂ (Maydeu-Olivares & Joe in J. Am. Stat. Assoc. 100:1009–1020, 2005, Psychometrika 71:713–732, 2006) to assess the overall fit of a one-parameter logistic model (1PL) estimated by (marginal) maximum likelihood (ML). R ₁ and R ₂ were specifically designed to target specific assumptions of Rasch models, whereas M ₂ is a general purpose test statistic. We report asymptotic power rates under some interesting violations of model assumptions (different item discrimination, presence of guessing, and multidimensionality) as well as empirical rejection rates for correctly specified models and some misspecified models. All three statistics were found to be more powerful than Pearson’s X ² against two- and three-parameter logistic alternatives (2PL and 3PL), and against multidimensional 1PL models. The results suggest that there is no clear advantage in using goodness-of-fit statistics specifically designed for Rasch-type models to test these models when marginal ML estimation is used.     

Pereboom’s Frankfurt case and derivative culpability

Pereboom has formulated a Frankfurt-style counterexample in which an agent is alleged to be responsible despite the fact that there are only non-robust alternatives present (Pereboom, Moral responsibility and alternative possibilities: essays on the importance of alternative possibilities, 2003; Phil Explor 12(2):109–118, 2009). I support Widerker’s objection to Pereboom’s Tax Evasion 2 example (Widerker, J Phil 103(4):163–187, 2006) (which rests on the worry that the agent in this example is derivatively culpable as opposed to directly responsible) against Pereboom’s recent counterarguments to this objection (Pereboom 2009). Building on work by Moya (J Phil 104:475–486, 2007; Critica 43(128):3–26, 2011) and Widerker (Widerker 2006), I argue that there is good reason to measure the robustness of alternatives in terms of comparative, rather than non-comparative likelihood of exemption, where the important factor for blame is whether the agent is “doing her reasonable best” to avoid blameworthy behaviour. I maintain that an agent only ever appears responsible when alternatives are robust in this sense. In Pereboom’s examples, both Tax Evasion 2, and his more recent version, Tax Evasion 3 (Pereboom 2009), I maintain the robustness of the alternatives, so understood, is unclear. We can clear up any ambiguity by sharpening the examples, and the result is that the agent appears responsible when the alternatives are made clearly robust, and does not appear responsible when alternatives appear clearly non-robust. The comparative nature of our judgements about blame, I maintain helps to explain the continuing appeal of the “leeway-incompatibilist” viewpoint.