To what extent can communalities reduce rank?

The question is raised as to whether the null hypothesis concerning the number of common factors underlying a given set of correlations should be that this number is small. Psychological and algebraic evidence indicate that a more appropriate null hypothesis is that the number is relatively large, and that smallness should be but an alternative hypothesis. The question is also raised as to why approximation procedures should be aimed primarily at the observed correlation matrixR and not at, say,R ^–1. What may be best forR may be worst forR ^–1, and conversely, yetR ^–1 is directly involved in problems of multiple and partial regressions. It is shown that a widely accepted inequality for the possible rank to whichR can be reduced, when modified by communalities, is indeed false.This research was facilitated by a noncommitted grant-in-aid to the writer from the Ford Foundation.     

A linear conservative extension of Zermelo-Fraenkel set theory

In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF is a conservative extension of ZF^– i.e., the Zermelo-Fraenkel set theory without the axiom of regularity. We formulate LZF as a sequent calculus with abstraction terms and prove the partial cut-elimination theorem for it. The cut-elimination result ensures the subterm property for those formulas which contain only terms corresponding to sets in ZF^–. This implies that LZF is a conservative extension of ZF^– and therefore the former is consistent relative to the latter. Hiroakira Ono     

Memories of reward and nonreward regulate the extinction and reacquisition of both excitatory and inhibitory associations

The memories of the unconditioned stimulus (US) and its absence (No US), symbolized as S^R and S^N, respectively, may be retrieved on US or No US trials giving rise to four types of associations, S^R → US, S^R → No US, S^N → US, and S^N → No US. Here, following acquisition under partial reward (PRF), rats were shifted either to different schedules of PRF (Experiment 1) or extinction (Experiments 1 and 2). Inhibitory S^R → No US associations formed in acquisition survived extinction and shifts to one, but not another type of PRF schedule (Experiments 1 and 2). Excitatory S^R → US associations also survived extinction (Experiment 2). These findings, as well as the acquisition findings of Experiment 2, are consistent with the sequential model but not with the only other two theories said to be able to explain PRF findings, the frustration hypothesis of Amsel and the attention hypothesis of Mackintosh [see Haselgrove, M., Aydin, A., & Pearce, J. M. (2004). A partial reinforcement extinction effect despite equal rates of reinforcement during Pavlovian conditioning. Journal of Experimental Psychology: Animal Behavior Processes, 30, 240–250]. Also, the reacquisition findings obtained here are inconsistent with two views applied to several learning phenomena, the rule-learning view and the position-item view.     

Intermediate logics with the same disjunctionless fragment as intuitionistic logic

Given an intermediate prepositional logic L, denote by L ^–d its disjuctionless fragment. We introduce an infinite sequence {J _n}_n1 of propositional formulas, and prove:(1)For any L: L ^–d =I ^–d (I=intuitionistic logic) if and only if J _n L for every n 1.Since it turns out that L{J _{n} n}1 = Ø for any L having the disjunction property, we obtain as a corollary that L ^–d = I ^–d for every L with d.p. (cf. open problem 7.19 of [5]). Algebraic semantic is used in the proof of the if part of (1). In the last section of the paper we provide a characterization in Kripke's semantic for the logics J _n =I+ +J _n (n 1).     

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.     

Illness representations predict adherence in adolescents and young adults with type 1 diabetes

Objective: Most adolescents and young adults (AYAs) with type 1 diabetes struggle with diabetes self-management and exhibit suboptimal glycemic control. This study examined two models of association between illness representations, a modifiable predictor of suboptimal outcomes, and adherence and glycemic control in AYAs with type 1 diabetes.

Design and main outcome measures: Ninety-nine AYAs (ages 15–20?years) completed measures of illness representations and adherence at two visits. Blood glucose monitoring frequency and haemoglobin A1c were obtained via chart review. Relationships were examined using structural equation modelling.

Results: Illness representations accounted for a significant proportion of the variance in blood glucose monitoring frequency (ΔR^2?=?.23, p?<?.01) and adherence to emergency precautions at Time 1 (ΔR^2?=?.07, p?=?.03). Illness representations also accounted for significant variance in blood glucose monitoring frequency (ΔR^2?=?.08, p?=?.01), adherence to recommendations for insulin and food (ΔR²?=?.08, p?=?.02) and exercise (ΔR^2?=?.10, p?<?.01), and adherence to emergency precautions (ΔR^2?=?.16, p?<?.01) at Time 2.

Conclusion: Illness representations are salient predictors of adherence in this population. Interventions targeting adherence promotion and glycemic control in AYAs with type 1 diabetes may be enhanced by efforts to modify illness representations.     

Narcissism, vanity, personality and mating effort

The current study examined the relationship between narcissism and vanity, and the degree these are predicted by the ‘Big Five’ personality traits and mating effort (ME) using a sample of 103 females recruited from a large beauty salon. Narcissism correlated with vanity at 0.72 (P < 0.001), and was associated positively with extraversion (E), ME and the subscales of vanity; narcissism was associated negatively with neuroticism (N) and agreeableness (A). Vanity correlated positively with E, conscientiousness, both subscales of narcissism, and ME, and negatively with N and A. A composite narcissism–vanity score was produced using principal components analysis, and used along with scores from the NEO-FFI-R to predict mating effort. The narcissism–vanity composite, low A and E significantly and independently predicted mating effort (adjusted R² = 0.28, F(9.96) = 7.74, P < 0.001). These results show that mating effort is additionally predicted by narcissism as well as self-reported personality.     

Rosser orderings and free variables

It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R ^–. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts oneself to usual proof predicates.     

Locating the Extrema of Fungible Regression Weights

In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of “fungible weights” (Waller, Psychometrica, in press) that yields identical SSE (sum of squared errors) and R ² values. When the R ² using the alternate weights is a fixed value, fungible weights (a _i ) that yield the maximum or minimum cosine with an OLS weight vector (b) are called “fungible extrema.” We describe two methods for locating fungible extrema and we report R code (R Development Core Team, 2007) for one of the methods. We then describe a new approach for populating a class of fungible weights that is derived from the geometry of alternate regression weights. Finally, we illustrate how fungible weights can be profitably used to gauge parameter sensitivity in linear models by locating the fungible extrema of a regression model of executive compensation (Horton & Guerard, Commun. Stat. Simul. Comput. 14:441–448, 1985).     

Hypothetico-Deductivism: Incomplete But Not Hopeless

Alleged counter-examples deployed in Park (2004) [Erkenntnis 60: 229–240] against the account of selective hypothetico-deductive confirmation offered in Gemes (1998) [Erkenntnis 49: 1–20] are shown to be ineffective. Furthermore, the reservations expressed in Gemes (1998) [ibid] and (1993) [Philosophy of Science 62: 477–487] about hypothetico-deductivism (H-D) are retracted and replaced with the conclusion that H-D is a viable account of confirmation that captures much of the practice of working scientists. However, because it cannot capture cases of inference to the best explanation and cases of the observational confirmation of statistical hypotheses, it is concluded that H-D cannot supply a complete theory of confirmation.     

The evaluation of linear forms

This presentation deals with the evaluation and transformation of linear forms. Especial emphasis is given to implicit methods in which it is not necessary to find the explicit values,x _i . The relation of the Aitken triple product matrixCA ^–1 B to the result of a linear transformation of linear forms is noted, and the numerical computation of this triple product matrix is indicated with the use of the simple Abbreviated Doolittle solution. Application is also made to the evaluation ofA ^–1 and ofA ^–1 C.     

On modal logic with an intuitionistic base

A definition of the concept of Intuitionist Modal Analogue is presented and motivated through the existence of a theorem preserving translation fromMIPC (see [2]) to a bimodalS ⁴–S⁵ calculus.Allatum est die 9 Septembris 1975     

Motor assessment of preschool aged children: A preliminary investigation of the validity of the Bruininks–Oseretsky test of motor proficiency – Short form

The aim of this study was to examine the validity of the Bruininks–Oseretsky test of motor proficiency – short form (BOTMP-SF) [Bruininks, R. (1978). Bruininks–Oseretsky test of motor proficiency: Examiners manual. Circle Pines, MN] for the assessment of preschool aged children. Three-hundred and eighteen children 48–71 months old (M = 58.97 months, SD = 6.73) participated in the study. For the data analysis both an ANOVA and a MANOVA were applied with the total battery score and the 14 item scores being the dependent variables, respectively. Age was found to have a significant effect on both children’s total battery score (F(3, 314) = 110.65, p < .001, η² = .68) and 13 item scores (minimum F(3, 314) = 8.75, p < .001, minimum η² = .145). Although the aforementioned results represent an evidence for the validity of the BOTMP-SF, a closer study on the score of each item revealed a high percentage of zero scores on four items. Task difficulty has caused a floor effect, constituting a threat to the validity of the preschoolers’ motor assessment with the above battery. A modification of the battery items is suggested, so that the BOTMP-SF will give valid results for children 4–6 years old.     

Are There Algorithms That Discover Causal Structure?

There have been many efforts to infer causation from association byusing statistical models. Algorithms for automating this processare a more recent innovation. In Humphreys and Freedman[(1996) British Journal for the Philosophy of Science 47, 113–123] we showed that one such approach, by Spirtes et al., was fatally flawed. Here we put our arguments in a broader context and reply to Korb and Wallace [(1997) British Journal for thePhilosophy of Science 48, 543–553] and to Spirtes et al.[(1997) British Journal for the Philosophy of Science 48, 555–568]. Their arguments leave our position unchanged: claims to have developed a rigorous engine for inferring causation from association are premature at best, the theorems have no implications for samples of any realistic size, and the examples used to illustrate the algorithms are indicative of failure rather than success. The gap between association and causation has yet to be bridged.     

Correlation Weights in Multiple Regression

A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights. We then derive the least squares weights (for any set of predictors) that yield the largest drop in R ² (the coefficient of determination) when switching to correlation weights. Our findings suggest that two characteristics of a model/data combination are especially important in determining the effectiveness of correlation weights: (1) the condition number of the predictor correlation matrix, R _xx , and (2) the orientation of the correlation weights to the latent vectors of R _xx .     

Investigating the Performance of Alternate Regression Weights by Studying All Possible Criteria in Regression Models with a Fixed Set of Predictors

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n×1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a full-rank predictor correlation matrix, R _xx, of order n, and for regression models with constant R ² (coefficient of determination), the OLS weight vectors for all possible criteria terminate on the surface of an n-dimensional ellipsoid. The population performance of alternate regression weights—such as equal weights, correlation weights, or rounded weights—can be modeled as a function of the Cartesian coordinates of the ellipsoid. These geometrical notions can be easily extended to assess the sampling performance of alternate regression weights in models with either fixed or random predictors and for models with any value of R ². To illustrate these ideas, we describe algorithms and R (R Development Core Team, 2009) code for: (1) generating points that are uniformly distributed on the surface of an n-dimensional ellipsoid, (2) populating the set of regression (weight) vectors that define an elliptical arc in ℝ ⁿ , and (3) populating the set of regression vectors that have constant cosine with a target vector in ℝ ⁿ . Each algorithm is illustrated with real data. The examples demonstrate the usefulness of studying all possible criteria when evaluating alternate regression weights in regression models with a fixed set of predictors.     

The Influence of Sex,Gender, Self-Discrepancies,and Self-Awareness on Anger and Verbal Aggressiveness Among U.S. College Students

Abstract

Among a sample of 445 U.S. college students, the authors examined the extent to which individual differences (e.g., sex, gender, self-discrepancies, self-awareness) explained anger tendencies and verbal aggressiveness. Regression analyses showed that (a) the tendency to repress anger (anger-in) was explained by masculinity, desire to be masculine, and public self-awareness, R ² = .19, F(11, 433) = 8.44, p < .001; (b) the tendency to express anger (anger-out) was explained by sex, masculinity, and public self-awareness, R ² = .17, F(11, 433) = 7.38, p < .001; and (c) willingness to be verbally aggressive was explained by sex, femininity, and private self-awareness, R ² = .32, F(11, 433) = 16.94, p < .001. In addition, different types of individual difference variables accounted for anger tendencies and verbal aggressiveness across sex and gender categories, suggesting that anger and verbal aggressiveness may be driven by different psychological processes across types of participants.     

Houston Conference: Need for More Fundamental Knowledge in Neuropsychology

Two training models in neuropsychology have been recently proposed (Guidelines of the INS-Division 40 Task Force on Education, Accreditation, and Credentialing, Clin. Neuropsychol. 1: 29–34, 1987; Hannay, H. J. et al., Arch. Clin. Neuropsychol. 13: 157–250, 1998). When comparing both educational models, similarities but also differences are found. According to the Houston Conference model—but not to the former model—neuropsychology represents a specialty of psychology. In the Houston Conference training model, applied knowledge is overtly emphasized, whereas fundamental or basic knowledge in neuropsychology appears weak. The proposed program does not seem to provide sufficient emphasis and background knowledge in (1) History of neuropsychology, (2) Neuropsychological syndromes, and (3) Neuropsychology theory.     

Study of Sexual Concordance in Men and Women with Different Typologies of Adherence to the Sexual Double Standard

Background/ObjectiveSexual concordance (i.e., relationship between genital response and subjective sexual arousal) is higher in men than in women. Among the factors that could explain this difference would be the sexual double standard (SDS). Sexual concordance is examined by SDS typologies of adherence (egalitarian, man-favorable, and woman-favorable).MethodDuring exposure to a film with sexual content, genital response (penile circumference/vaginal pulse amplitude) and self-reported sexual arousal were recorded in 104 young adults (42 men and 62 women), distributed into SDS typologies of adherence on the basis of their scores on the Sexual Double Standard Scale.ResultsSexual concordance was obtained in men and women with egalitarian and man-favorable typology. Subjective sexual arousal explained a significant percentage of the variance in genital response in the egalitarian typology (men: R² = .32, p < .01; women: R² = .19, p < .05) and man-favorable typology (men: R² = .21, p < .05; women: R² = .23, p < .05).ConclusionsAgreement between genital responsiveness and subjective sexual arousal depends on DES adherence typology.     

Asymmetrical stimulus generalization following differential fear conditioning

Rodent ultrasonic vocalizations (USVs) are ethologically critical social signals. Rats emit 22 kHz USVs and 50 kHz USVs, respectively, in conjunction with negative and positive affective states. Little is known about what controls emotional reactivity to these social signals. Using male Sprague–Dawley rats, we examined unconditional and conditional freezing behavior in response to the following auditory stimuli: three 22 kHz USVs, a discontinuous tone whose frequency and on–off pattern matched one of the USVs, a continuous tone with the same or lower frequencies, a 4 kHz discontinuous tone with an on–off pattern matched to one of the USVs, and a 50 kHz USV. There were no differences among these stimuli in terms of the unconditional elicitation of freezing behavior. Thus, the stimuli were equally neutral before conditioning. During differential fear conditioning, one of these stimuli (the CS⁺) always co-terminated with a footshock unconditional stimulus (US) and another stimulus (the CS⁻) was explicitly unpaired with the US. There were no significant differences among these cues in CS⁺-elicited freezing behavior. Thus, the stimuli were equally salient or effective as cues in supporting fear conditioning. When the CS⁺ was a 22 kHz USV or a similar stimulus, rats discriminated based on the principal frequency and/or the temporal pattern of the stimulus. However, when these same stimuli served as the CS⁻, discrimination failed due to generalization from the CS⁺. Thus, the stimuli differed markedly in the specificity of conditioning. This strikingly asymmetrical stimulus generalization is a novel bias in discrimination.