Exploratory Bi-factor Analysis: The Oblique Case

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford (Psychometrika 47:41?C54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler (Psychometrika 76:537?C549, 2011) introduced an exploratory form of bi-factor analysis that does not require one to provide an explicit bi-factor structure a priori. They use exploratory factor analysis and a bifactor rotation criterion designed to produce a rotated loading matrix that has an approximate bi-factor structure. Among other things this can be used as an aid in finding an explicit bi-factor structure for use in a confirmatory bi-factor analysis. They considered only orthogonal rotation. The purpose of this paper is to consider oblique rotation and to compare it to orthogonal rotation. Because there are many more oblique rotations of an initial loading matrix than orthogonal rotations, one expects the oblique results to approximate a bi-factor structure better than orthogonal rotations and this is indeed the case. A surprising result arises when oblique bi-factor rotation methods are applied to ideal data.     

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.     

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.     

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.     

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     

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 Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions

The Graded Response Model (GRM; Samejima, Estimation of ability using a response pattern of graded scores, Psychometric Monograph No.?17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, ??, to underlie the ordinal item scores (Takane & de Leeuw in Psychometrika, 52:393?C408, 1987). Traditionally, a normal distribution is specified for Z implying homoscedastic error variances and a normally distributed ??. In this paper, we present the Heteroscedastic GRM with Skewed Latent Trait, which extends the traditional GRM by incorporation of heteroscedastic error variances and a skew-normal latent trait. An appealing property of the extended GRM is that it includes the traditional GRM as a special case. This enables specific tests on the normality assumption of Z. We show how violations of normality in Z can lead to asymmetrical category response functions. The ability to test this normality assumption is beneficial from both a statistical and substantive perspective. In a simulation study, we show the viability of the model and investigate the specificity of the effects. We apply the model to a dataset on affect and a dataset on alexithymia.     

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.     

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.     

Problems with EM algorithms for ML factor analysis

Rubin and Thayer recently presented equations to implement maximum likelihood (ML) estimation in factor analysis via the EM algorithm. They present an example to demonstrate the efficacy of the algorithm, and propose that their recovery of multiple local maxima of the ML function “certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.” It is shown here, in contrast, that these second derivatives verify that Rubin and Thayer did not find multiple local maxima as claimed. The only known maximum remains the one found by Jöreskog over a decade earlier. The standard errors obtained from the second derivatives and the Fisher information matrix thus remain appropriate where ML assumptions are met. The advantages of the EM algorithm over other algorithms for ML factor analysis remain to be demonstrated.     

The Spiritual Well-Being of Elderly People: A Study of a French Sample

The aim of our research was to identify predictors of the spiritual well-being of elderly people. More specifically, we postulated that subjective well-being and its components would be predictors of spiritual well-being, and more so than age and health status. We invited 133 people aged 60–95 to complete a questionnaire that included the French adaptation (Velasco and Rioux in Revue Canadienne des Sciences du Comportement 41(2):102–128, 2009) of Paloutzian and Ellison’s (Loneliness: A sourcebook of current theory, research and therapy, Wiley-Interscience, New York, 1982) Spiritual Well-Being Scale, Ryff and Essex’s (Psychol Aging 7:507–517, 1992) Psychological Well-Being Scale (translated by Lapierre and Desrochers 1997), Salamon and Conte’s (Meas Eval Guid 15(3):194–200, 1982) Life Satisfaction in the Elderly Scale (validated by Rousseau and Dubé in 1993), and the French version (Blais et al. in Can J Behav Sci 21:210–223, 1989) of Diener et al. (J Pers Assess 49:71–75, 1985) Satisfaction with Life Scale. The results only partially confirm our hypothesis, because only satisfaction with life as a whole and two items in “Life Satisfaction in the Elderly Scale” make it possible to predict the spiritual well-being of elderly people. Moreover, neither health status nor age was found to be a significant predictor of spiritual well-being. This research helps understand better the links between the concept of spiritual well-being and that of subjective well-being of elderly people and could contribute to the development of a tool that could take into account the spiritual well-being of elderly people, whether they be believers, agnostic, or atheist.     

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.     

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.     

Luck,propositional perception,and the Entailment Thesis

Looking out the window, I see that it’s raining outside. Do I know that it’s raining outside? According to proponents of the Entailment Thesis, I do. If I see that p, I know that p. In general, the Entailment Thesis is the thesis that if S perceives that p, S knows that p. But recently, some philosophers (McDowell, in Smith (ed.) Reading McDowell on mind and world, 2002; Turri, Theoria 76(3):197–206, 2010; Pritchard, Philos Issues (Supplement to Nous) 21:434–455, 2011; Pritchard, Epistemological disjunctivism, 2012) have argued that the Entailment Thesis is false. On their view, we can see p and not know that p. In this paper, I argue that their arguments are unsuccessful.     

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.     

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.     

Hierarchical Diagnostic Classification Models Morphing into Unidimensional ‘Diagnostic’ Classification Models—A Commentary

This commentary addresses the modeling and final analytical path taken, as well as the terminology used, in the paper “Hierarchical diagnostic classification models: a family of models for estimating and testing attribute hierarchies” by Templin and Bradshaw (Psychometrika, doi:10.1007/s11336-013-9362-0, 2013). It raises several issues concerning use of cognitive diagnostic models that either assume attribute hierarchies or assume a certain form of attribute interactions. The issues raised are illustrated with examples, and references are provided for further examination.     

25 years of research on the use of geometry in spatial reorientation: a current theoretical perspective

The purpose of this article is to review and evaluate the range of theories proposed to explain findings on the use of geometry in reorientation. We consider five key approaches and models associated with them and, in the course of reviewing each approach, five key issues. First, we take up modularity theory itself, as recently revised by Lee and Spelke (Cognitive Psychology, 61, 152–176, 2010a; Experimental Brain Research, 206, 179–188, 2010b). In this context, we discuss issues concerning the basic distinction between geometry and features. Second, we review the view-matching approach (Stürzl, Cheung, Cheng, & Zeil, Journal of Experimental Psychology: Animal Behavior Processes, 34, 1–14, 2008). In this context, we highlight the possibility of cross-species differences, as well as commonalities. Third, we review an associative theory (Miller & Shettleworth, Journal of Experimental Psychology: Animal Behavior Processes, 33, 191–212, 2007; Journal of Experimental Psychology: Animal Behavior Processes, 34, 419–422, 2008). In this context, we focus on phenomena of cue competition. Fourth, we take up adaptive combination theory (Newcombe & Huttenlocher, 2006). In this context, we focus on discussing development and the effects of experience. Fifth, we examine various neurally based approaches, including frameworks proposed by Doeller and Burgess (Proceedings of the National Academy of Sciences of the United States of America, 105, 5909–5914, 2008; Doeller, King, & Burgess, Proceedings of the National Academy of Sciences of the United States of America, 105, 5915–5920, 2008) and by Sheynikhovich, Chavarriaga, Strösslin, Arleo, and Gerstner (Psychological Review, 116, 540–566, 2009). In this context, we examine the issue of the neural substrates of spatial navigation. We conclude that none of these approaches can account for all of the known phenomena concerning the use of geometry in reorientation and clarify what the challenges are for each approach.     

Defending the Possibility of Knowledge

In this paper, I propose a solution to Fitch’s paradox that draws on ideas from Edgington (Mind 94:557–568, 1985), Rabinowicz and Segerberg (1994) and Kvanvig (Noûs 29:481–500, 1995). After examining the solution strategies of these authors, I will defend the view, initially proposed by Kvanvig, according to which the derivation of the paradox violates a crucial constraint on quantifier instantiation. The constraint states that non-rigid expressions cannot be substituted into modal positions. We will introduce a slightly modified syntax and semantics that will help underline this point. Furthermore, we will prove results about the consistency of verificationism and the principle of non-omniscience by model-theoretical means. Namely, we prove there exists a model of these principles, and delineate certain constraints they pose on a structure in which they are true.