Estimation of other coefficients of correlation from the phi coefficient

Formulas are developed for estimating a point-biserialr or a tetrachoricr from an obtained phi coefficient. The estimate of a tetrachoricr, which is calledr _φ, is shown to be equivalent to that obtained from first-order use of the tetrachoricr series. A tabulation is made of corrections needed to maker _φ equivalent numerically to the tetrachoricr. In spite of its greater generality than estimates of tetrachoricr by previous methods, there are limitations, which are pointed out.     

The Geometry of Enhancement in Multiple Regression

In linear multiple regression, “enhancement” is said to occur when R ²=b′r>r′r, where b is a p×1 vector of standardized regression coefficients and r is a p×1 vector of correlations between a criterion y and a set of standardized regressors, x. When p=1 then b≡r and enhancement cannot occur. When p=2, for all full-rank R _xx≠I, R _xx=E[xx′]=V Λ V′ (where V Λ V′ denotes the eigen decomposition of R _xx; λ ₁>λ ₂), the set B₁:={b_i:R²=b_i￠r_i=r_i￠r_i;0 < R² ￡ 1}\boldsymbol{B}_{1}:=\{\boldsymbol{b}_{i}:R^{2}=\boldsymbol{b}_{i}'\boldsymbol{r}_{i}=\boldsymbol{r}_{i}'\boldsymbol{r}_{i};0R² ￡ 1;R²l_p ￡ r_i￠r_i < R²}0p≥3 (and λ ₁>λ ₂>⋯>λ _p ), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B ₁ occurs at the intersection of two hyper-ellipsoids in ℝ ^p . Equations are provided for populating the sets B ₁ and B ₂ and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with λ _p (the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying geometry of enhancement in population, multiple-regression models. R code for simulating population regression models that exhibit enhancement of any degree and any number of predictors is included in Appendices A and B.     

Examination of the Relationship Between Perfectionism and Religiosity as Mediated by Psychological Inflexibility

A relationship between perfectionism and religiosity has been suggested in the literature, and this relationship is clarified further when the adaptive and maladaptive dimensions of both constructs are compared. Literature in both areas implicates the idea of a rigid and inflexible personality style that may explain why well meaning high standards can be associated with negative outcomes such as perfectionism. This investigation examined the relationship of perfectionism and religiosity, using adaptive and maladaptive dimensions, as mediated by psychological inflexibility. Validated measures of perfectionism, religiosity, and psychological inflexibility were given to 376 undergraduate college students in an anonymous online survey. Adaptive perfectionism (high standards) was found to be significantly correlated (r = .26, p < .01, two-tailed) with adaptive religiosity (intrinsic orientation). Maladaptive perfectionism (discrepancy) was found to be significantly correlated (r = .13, p < .05, two-tailed) with maladaptive religiosity (extrinsic orientation). Psychological inflexibility was found to be significantly correlated with the maladaptive dimensions of both perfectionism and religiosity. It was also shown to mediate the relationship between maladaptive (extrinsic) religiosity and maladaptive (discrepancy) perfectionism. Implications and future directions are discussed.     

Motivation for physical activity in young adults with physical disabilities during a rehabilitation stay: a longitudinal test of self‐determination theory

We tested a self‐determination theory (SDT) process model during a 3 week physical activity rehabilitation stay among young adults with a physical disability (N = 44, M_age = 24.7, SD = 5.1). As hypothesized, perceived autonomy support positively predicted needs satisfaction at the end of the stay (r = .38, p < .01). Further, needs satisfaction was positively linked to changes in autonomous motivation for physical activity (r = .47, p < .01). Both changes in autonomous motivation and self‐efficacy were associated with physical activity increases over the stay (r = .57, p < .01 and r = .47, p < .01, respectively). Bootstrapping results supported the SDT process model, indicating a support for a development toward more self‐determined motivation in rehabilitation.     

Happiness as Stable Extraversion: Internal Consistency Reliability and Construct Validity of the Oxford Happiness Questionnaire Among Undergraduate Students

The Oxford Happiness Questionnaire (OHQ) was developed by Hills and Argyle (2002) to provide a more accessible equivalent measure of the Oxford Happiness Inventory (OHI). The aim of the present study was to examine the internal consistency reliability, and construct validity of this new instrument alongside the Eysenckian dimensional model of personality. The Oxford Happiness Questionnaire was completed by a sample of 131 undergraduate students together with the abbreviated form of the Revised Eysenck Personality Questionnaire. The data demonstrated good internal consistency reliability (alpha = .92) and good construct validity in terms of positive association with extraversion (r = .38 p < .001) and negative association with neuroticism (r = −.57 p < .001). The kind of happiness measured by the OHQ is clearly associated with stable extraversion.     

Further Evidence of the Reliability and Validity of the Multidimensional Anxiety

The psychometric properties of the Multidimensional Anxiety Scale for Children (MASC) were examined in adolescent psychiatric inpatient samples. In Study 1 (n = 287), confirmatory factor analyses provided satisfactory fit for the four-factor (comparative fit index; CFI = 0.856) and higher-order (CFI = 0.854) solutions. Using parcels as items, the fit of the four-factor model was improved substantially (CFI = 0.935). Next, in the bifactor analyses, support was attained for a model that included a general factor and four domain specific subfactors. In Study 2 (n = 195 inpatient youths), the MASC showed good scale reliability and concurrent validity. Results of the receiver operating characteristic curve and binary logistic regression analyses provided adequate evidence for discriminative validity. In Study 3 (n = 40), test–retest reliability of scores on the MASC-10 scale over a 3-week period was adequate (r _tt = 0.83, p < 0.001) for children ages 8 to 11 years.     

Assessment of tobacco craving by means of the affective image visualization paradigm

Smoking cues that increase craving are subjectively described by smokers as pleasant rather than unpleasant. However, it remains controversial whether the motivational nature of these smoking cues is consistent with an appetitive or aversion-relief model of tobacco craving. In the two studies presented here, the Bioinformational model of emotion proposed by Lang was used to address this issue. In study I, 40 smokers (10 males) assessed a set of tobacco-related pictures and a subset of standard pleasant, neutral, and unpleasant pictures in order to examine how craving relates to the three general dimensions of emotion: valence, arousal, and dominance. Results showed that the tobacco-related images were all assessed as appetitive, and craving was correlated positively with valence (r = .863, p < .0001) and arousal (r = .923, p < .0001) and negatively with dominance (r = −.504, p < .002). In study II, 24 female abstinent smokers were examined using Lang’s startle modulation paradigm in order to assess whether tobacco-related pictures, compared to standard pleasant and unpleasant ones, inhibited the startle response, consistent with an appetitive model of tobacco craving. Contrary to expectations, the startle response during visualization of tobacco-related pictures was more similar in magnitude to the response to unpleasant than to pleasant images, a finding inconsistent with an appetitive model of tobacco craving.     

Quantified coalition logic

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is nevertheless exponentially more succinct. The complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic, and satisfiability for QCL is shown to be no worse than satisfiability for Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents.     

On the relation between similarity and ratio estimates

Summary Data obtained in four sets of experiments involving pitch, heaviness, greyness, and circular area were re-analyzed. It was found (1) that similarity estimates S _ijare a power function of stimulus ratios S _ijwith the exponent n _s,(2) that ratio estimates q _ijare also a power function of stimulus ratios S _ijwith the exponent n _q(i.e., Stevens' power law), (3) that the exponent n of similarity estimates as power function of ratio estimates is equal to the ratio n _s/n _q,and (4) that, inversely, the exponent m of ratio estimates as power function of similarities is equal to the ratio n _q/n _s.The investigation was supported by a grant from the Swedish Council for Social Science Research.     

Temporal stability of behavioural intention as a moderator of intention–health behaviour relationships

Seven prospective studies of health behaviours containing eight prospective datasets testing the moderating role of intention stability on intention–behaviour and past behaviour–behaviour relationships were examined within the context of the Theory of Planned Behaviour. The measure of intention stability was based on lack of change in intentions between the two measurement time points. Across different behaviours, samples and time frames more stable intentions were associated with intentions at time 1 that were stronger predictors of behaviour at time 2. Intention stability did not consistently moderate the past behaviour–behaviour relationship. Across studies the frequency-weighted mean correlation between intentions and behaviour was substantially greater for stable (r ₊?=?0.60) compared to unstable (r ₊?=?0.27) intentions (Z _difference?=?6.65, p?<?0.001). The past behaviour–behaviour correlation was also stronger for stable (r ₊?=?0.50, p?<?0.001) compared to unstable (r₊ ?=?0.34, p?<?0.001) intentions (Z _difference?=?3.12, p?<?0.01). Perceived behavioural control was the variable most strongly related to stable intentions. Implications for understanding the role of health cognitions in the performance of health behaviour are discussed.     

If Logic, Definitions and the Vicious Circle Principle

In a definition (∀x)((xєr)↔D[x]) of the set r, the definiens D[x] must not depend on the definiendum r. This implies that all quantifiers in D[x] are independent of r and of (∀x). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious Circle Principle was intended to bar such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if (bєa) or (b ⊆ a). Likewise, the truth of an ordinary first-order sentence with the G?del number of r is undefinable in Tarki’s sense because the quantifiers of the definiens depend unavoidably on r.     

On the size of refutation Kripke models for some linear modal and tense logics

LetL be any modal or tense logic with the finite model property. For eachm, definer _L (m) to be the smallest numberr such that for any formulaA withm modal operators,A is provable inL if and only ifA is valid in everyL-model with at mostr worlds. Thus, the functionr _L determines the size of refutation Kripke models forL. In this paper, we will give an estimation ofr _L (m) for some linear modal and tense logicsL.     

On Categorical Equivalences of Commutative BCK-algebras

A commutative BCK-algebra with the relative cancellation property is a commutative BCK-algebra (X;*,0) which satisfies the condition: if a ≤ x, a ≤ y and x * a = y * a, then x = y. Such BCK-algebras form a variety, and the category of these BCK-algebras is categorically equivalent to the category of Abelian ℓ-groups whose objects are pairs (G, G ₀), where G is an Abelian ℓ-group, G ₀ is a subset of the positive cone generating G ⁺ such that if u, v ∈ G ₀, then 0 ∨ (u - v) ∈ G ₀, and morphisms are ℓ-group homomorphisms h: (G, G ₀) → (G′,G′₀) with f(G ₀) ⫅ G′₀. Our methods in particular cases give known categorical equivalences of Cornish for conical BCK-algebras and of Mundici for bounded commutative BCK-algebras (= MV-algebras). This revised version was published online in June 2006 with corrections to the Cover Date.     

The Family Impact of Pain Scale: Preliminary Validation

A new questionnaire, the Family Impact of Pain Scale (FIPS), was designed in order to assess the effects of chronic pain on the significant other and family of the chronic pain patient. The FIPS is a 10-item self-report questionnaire examining the effect of pain on domestic duties, social functioning and communication within the family. It was administered to 177 chronic pain patients in two different samples to investigate its psychometric properties. Internal reliability (α = .94) and test–retest reliability (r = 0.79) were high. Exploratory factor analysis suggested a two-factor solution, relating to physical limitations and difficulties with communication. Construct validity was confirmed by significant Pearson correlations with pain intensity, pain distress, mood and the use of pain coping skills (r = −0.22–0.74, all at p < .05). Outcome data also showed that the measure is sensitive to the effects of a cognitive behavioural pain management intervention.     

An Infinitary Extension of Jankov’s Theorem

It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra B, A is embeddable into a quotient algebra of B, if and only if Jankov’s formula χ _A for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal number κ, we present Jankov’s theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible complete κ-Heyting algebras and κ-infinitary logic, where a κ-Heyting algebra is a Heyting algebra A with # ≥  κ and κ-infinitary logic is the infinitary logic such that for any set Θ of formulas with # Θ ≥  κ, ∨Θ and ∧Θ are well defined formulas.     

Health-related Internet habits and health anxiety in university students

Health-related Internet use has grown rapidly, yet little research has considered how health anxious individuals use the Internet for this purpose. Our aim was to examine the relationships between health anxiety and the extent of, reasons for, and consequences of health-related Internet usage in university students (n = 255). Responses on a purpose-made Internet use questionnaire were correlated with health anxiety scores; multiple regression analyses controlling for depression and anxiety were also conducted. Health anxiety positively correlated with (all ps < .01): frequency of health-related searching (r_s = .163), proportion of health-related information sought (r_s = .200), time spent online for health purposes (r_s = .166), and number of searches for both illness (r_s = .453) and wellness (r_s = .208) information. Health anxiety further positively correlated with advantages perceived in health-related Internet use (r_s = .183), heightened tension (r_s = .364) and relief (r_s = .174) post-search, and perceived doctor disadvantages (r_s = .306), yet a greater likelihood to visit a doctor post-search (r_s = .217). Health anxiety also correlated with six measures of possible addiction to using the Internet for health purposes (r_s range = .171 to .366, all ps < .01). Some (including several potentially dysfunctional) aspects of health-related Internet use correlate with health anxiety. Research evaluating the possible role of Internet use in the development and maintenance of health anxiety is warranted.     

Norms for two types of manipulability (graspability and functional usage), familiarity,and age of acquisition for 320 photographs of objects

There is increasing interest in the role that manipulability plays in processing objects. To date, Magnié, Besson, Poncet, and Dolisi’s (2003) manipulability ratings, based on the degree to which objects can be uniquely pantomimed, have been the reference point for many studies. However, these ratings do not fully capture some relevant dimensions of manipulability, including whether an object is graspable and the extent to which functional motor associations above and beyond graspability are present. To address this, we collected ratings of these dimensions, in addition to ratings of familiarity and age of acquisition (AoA), for a set of 320 black-and-white photographs of objects. Familiarity and AoA ratings were highly correlated with previously reported ratings of the same dimensions (r =.853, p<.001, and r=.771, p<.001, respectively), validating the present norms. Grasping and functional use ratings, in contrast, were more moderately correlated with Magnié et al.’s pantomime manipulability ratings (r=.507, p<.001). These results were taken as evidence that the new manipulability ratings collected in this research capture distinct aspects of object manipulability. The complete stimuli and norms from this study may be downloaded from http://brm.psychonomic-journals.org/content/supplemental.     

Examining Youth Anxiety Symptoms and Suicidal Ideation in the Context of the Tripartite Model of Emotion

This study sought to clarify the relation of anxiety symptoms and suicidal ideation in children and adolescents by examining these variables in the context of depression and negative affect. As outlined in the tripartite model of anxiety and depression, negative affectivity is common to both emotional constructs; therefore negative affectivity may best explain the relation of each to suicidal ideation. Self report measures of generalized anxiety, depression, negative affectivity, and suicidal ideation were assessed in a primarily externalizing sample of children ages 7–18. Results suggested that the relation between anxiety and suicidal ideation was best accounted for by depression, not negative affectivity. Results also suggested that negative affectivity was associated with suicidal ideation but did not account for the relations among anxiety, depression, and suicidal ideation. Further, depression, negative affect, and anxiety all significantly contributed to the prediction of suicidal ideation scores (r ²  = .307, p < .01).     

A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model

An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model which assumes both common and specific dimensions is described and contrasted with the standard (Two-Way) MDS model. In this Extended Two-Way Euclidean model then stimuli (or other objects) are assumed to be characterized by coordinates onR common dimensions. In addition each stimulus is assumed to have a dimension (or dimensions) specific to it alone. The overall distance between objecti and objectj then is defined as the square root of the ordinary squared Euclidean distance plus terms denoting the specificity of each object. The specificity,s _j , can be thought of as the sum of squares of coordinates on those dimensions specific to objecti, all of which have nonzero coordinatesonly for objecti. (In practice, we may think of there being just one such specific dimension for each object, as this situation is mathematically indistinguishable from the case in which there are more than one.)We further assume that _ij =F(d _ij ) +e _ij where _ij is the proximity value (e.g., similarity or dissimilarity) of objectsi andj,d _ij is the extended Euclidean distance defined above, whilee _ij is an error term assumed i.i.d.N(0, ²).F is assumed either a linear function (in the metric case) or a monotone spline of specified form (in the quasi-nonmetric case). A numerical procedure alternating a modified Newton-Raphson algorithm with an algorithm for fitting an optimal monotone spline (or linear function) is used to secure maximum likelihood estimates of the paramstatistics) can be used to test hypotheses about the number of common dimensions, and/or the existence of specific (in addition toR common) dimensions.This approach is illustrated with applications to both artificial data and real data on judged similarity of nations.     

A comment on Birnbaum's three-parameter logistic model in the latent trait theory

Birnbaum's three-parameter logistic model for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. It is clarified that with models of knowledge or random guessing nature, which include the three-parameter logistic model, the unique maximum condition is not satisfied for the correct answer, and the item response information function is negative for the interval (− ∞,θ _g ). It is suggested that we should useθ _g as a criterion in selecting optimal items for a specified group of examinees, so that we can practically avoid the possibility of non-unique maxima of the likelihood function on the response pattern given by an examinee in the group. The work described in this paper was partially done while the author was at University of New Brunswick, Canada, in 1968–1970, supported by NRC Grant APA-345 from National Research Council of Canada.