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.     

Bridging Ranking Theory and the Stability Theory of Belief

In this paper we compare Leitgeb’s stability theory of belief (Annals of Pure and Applied Logic, 164:1338-1389, 2013; The Philosophical Review, 123:131-171, [2014]) and Spohn’s ranking-theoretic account of belief (Spohn, 1988, 2012). We discuss the two theories as solutions to the lottery paradox. To compare the two theories, we introduce a novel translation between ranking (mass) functions and probability (mass) functions. We draw some crucial consequences from this translation, in particular a new probabilistic belief notion. Based on this, we explore the logical relation between the two belief theories, showing that models of Leitgeb’s theory correspond to certain models of Spohn’s theory. The reverse is not true (or holds only under special constraints on the parameter of the translation). Finally, we discuss how these results raise new questions in belief theory. In particular, we raise the question whether stability (a key ingredient of Leitgeb’s theory) is rightly thought of as a property pertaining to belief (rather than to knowledge).     

Consequences of Politicians’ Disrespectful Communication Depend on Social Judgment Dimensions and Voters’ Moral Identity

The present study investigates the consequences of respectful versus disrespectful communication in political debates on voters’ social judgments and voting decisions. Reconciling previously mixed results, we argue that the consequences of disrespect vary with the judgment dimension (communion vs. agency) and voters’ moral identity. An initial study (N = 197) finds that a political candidate's disrespect towards his or her opponent affects voting decision through voting intention. A second study (N = 327) shows that disrespect influences voting intention through communion but not through agency ratings. Qualifying the previous finding, a third study (N = 329) shows that both communion and agency judgments act as mediators, but in different ways depending on the level of moral identity. Overall, communion judgments played a more prominent part in explaining the consequences of disrespectful communication. Our findings thus present a nuanced picture of respect and disrespect in political communication and shed light on their ramifications.     

Reinterpreting Sellars in the Light of Brandom,McDowell, and A. D. Smith

Abstract: The intent of this paper is to indicate a development in Sellars' writings which points in another direction than the interpretations offered by Brandom, McDowell, and A. D. Smith. Brandom and McDowell have long claimed to preserve central insights of Sellars's theory of perception; however, they disagree over what exactly these insights are. A. D. Smith has launched a critique of Sellars in chapter 2 of his book The Problem of Perception which is so penetrating that it would tear Sellars' philosophy of perception apart if it were adequate. However, I try to show firstly that Brandom's and McDowell's interpretations are unsatisfying when Sellars' late writings are taking into consideration. And secondly that we can give another interpretation of Sellars that is not vulnerable to some of the problems of which Smith accuses Sellars.     

Direct brain communication: neuroelectric and metabolic approaches at Tübingen

The brain–computer interface (BCI) provides users with the possibility of sending messages and commands to the external world without using their muscles, thus enabling communication to occur independent of movement. Such a possibility is of utmost importance for paralyzed patients who may otherwise lose their ability to communicate. Enhanced methodology and the development of faster computers have substantially improved applications and offer new possibilities in this field. To date, there have been over 20 BCI research groups working on different approaches. In this paper, we review our studies of BCI based on electric and metabolic activity of the brain.     

Timing of multiple overlapping intervals: how many clocks do we have?

Humans perceive and reproduce short intervals of time (e.g. 1-60 s) relatively accurately, and are capable of timing multiple overlapping intervals if these intervals are presented in different modalities [e.g., Rousseau, L., & Rousseau, R. (1996). Stop-reaction time and the internal clock. Perception and Psychophysics, 58(3), 434-448]. Tracking multiple intervals can be explained either by assuming multiple internal clocks or by strategic arithmetic using a single clock. The underlying timescale (linear or nonlinear) qualitatively influences the predictions derived from these accounts, as assuming a nonlinear timescale introduces systematic errors in added or subtracted intervals. Here, we present two experiments that provide support for a single clock combined with a nonlinear underlying timescale. When two equal but partly overlapping time intervals had to be estimated, the second estimate was positively correlated with the stimulus onset asynchrony. This effect was also found in a second experiment with unequal intervals that showed evidence of subtraction of intervals. The findings were supported by computational models implemented in a previously validated account of interval timing [Taatgen, N. A., Van Rijn, H., & Anderson, J. R. (2007). An integrated theory of prospective time interval estimation: The role of cognition, attention and learning. Psychological Review, 114(3), 577-598].     

Delinquenzverläufe jugendlicher Sexualmörder

Sexual homicides by juvenile offenders are statistically rare and until now only a few studies explored this phenomenon. Studies on forensic psychiatric court reports and follow-up data from federal criminal records were used to investigate the delinquency of a sample of 19 juvenile sexual homicide perpetrators from their childhood up to the mean age of 45 years of age. More than the half (58%) committed or attempted sexual assaults prior to the sexual homicide. Seven from 13 who were released from custody (54%) committed sexual or violent reoffences. In a long-time analysis as much favourable as unfavourable developments were found. The results suggest that most of the persons who commit sexual homicides as juveniles already committed sexual offences before and have a high risk of sexual and violent reoffending even a long time after the homicide.     

The fallacy of the null hypothesis in soft psychology

In his classic article on the fallacy of the null hypothesis in soft psychology [J. Consult. Clin. Psychol. 46 (1978)], Paul Meehl claimed that, in nonexperimental settings, the probability of rejecting the null hypothesis of nil group differences in favor of a directional alternative was 0.50—a value that is an order of magnitude higher than the customary Type I error rate. In a series of real data simulations, using Minnesota Multiphasic Personality Inventory-Revised (MMPI-2) data collected from more than 80,000 individuals, I found strong support for Meehl’s claim.     

Ten Theses on the Future of Lutheran Theology Charisms, Contexts, and Challenges

Although Lutheran theology is a gift to the historic church, Martin Luther's own views are specifically formulated for their 16th century context. No universal or timeless theological system based upon Luther's authority should be appealed to. Then theses are here advanced that bridge the 16th and 21st centuries and challenge us to creative construction.