Validating a selection test,a predictive probability approach

The problem of inferring the validity of a selection test (x) as a predictor of some criterion (y) when completexy data are not available is investigated. The basic approach is to construct the predictive probability distribution of the unobservedy scores and then derive interval estimates of the least squares regression weights, the difference in averagey scores for selected and unselected cases, and the residual variance in predictingy fromx. Further, an approximation to the predictive distribution of the squared correlation betweenx andy in a future group is derived.     

Grounds and limits: Reichenbach and foundationalist epistemology

From 1929 onwards, C. I. Lewis defended the foundationalist claim that judgements of the form ‘x is probable’ only make sense if one assumes there to be a ground y that is certain (where x and y may be beliefs, propositions, or events). Without this assumption, Lewis argues, the probability of x could not be anything other than zero. Hans Reichenbach repeatedly contested Lewis’s idea, calling it “a remnant of rationalism”. The last move in this debate was a challenge by Lewis, defying Reichenbach to produce a regress of probability values that yields a number other than zero. Reichenbach never took up the challenge, but we will meet it on his behalf, as it were. By presenting a series converging to a limit, we demonstrate that x can have a definite and computable probability, even if its justification consists of an infinite number of steps. Next we show the invalidity of a recent riposte of foundationalists that this limit of the series can be the ground of justification. Finally we discuss the question where justification can come from if not from a ground.     

Conditional Direction Dependence Analysis: Evaluating the Causal Direction of Effects in Linear Models with Interaction Terms

Abstract

Direction dependence analysis (DDA) makes use of higher than second moment information of variables (x and y) to detect potential confounding and to probe the causal direction of linear variable relations (i.e., whether x?→?y or y?→?x better approximates the underlying causal mechanism). The “true” predictor is assumed to be a continuous nonnormal exogenous variable. Existing methods compatible with DDA, however, are of limited use when the relation of a focal predictor and an outcome is affected by a moderator. This study presents a conditional direction dependence analysis (CDDA) framework which enables researchers to evaluate the causal direction of conditional regression effects. Monte–Carlo simulations were used to evaluate two different moderation scenarios: Study 1 evaluates the performance of CDDA tests when a moderator affects the strength of the causal effect x?→?y. Study 2 evaluates cases in which the causal direction itself (x?→?y vs y?→?x) depends on moderator values. Study 3 evaluates the robustness of DDA tests in the presence of functional model misspecifications. Results suggest that significance tests compatible with CDDA are suitable in both moderation scenarios, i.e., CDDA allows one to discern regions of a moderator in which the causal direction is uniquely identifiable. An empirical example is provided to illustrate the approach.     

A maximum likelihood approach to test validation with missing and censored dependent variables

A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censoredy scores present in the data set. The missing data are due to selection on a latent variable (y _s ) which may be conditionally related toy givenx. Thus, the missing data may not be missing random. The censoring process in due to the presence of a floor or ceiling effect. The maximum likelihood estimates are constructed using the EM algorithm. The entire analysis is demonstrated in terms of hypothetical data sets.     

Characterizing linguistic structure with mutual information

We explore mutual information (MI) as a means of characterizing linguistic statistical structure. The MI between two linguistic tokens x and y is the degree to which seeing x helps us anticipate the occurrence of y. We computed MI between words in 595 samples of written text in 25 languages. Our analyses indicate that MI dependencies do not extend beyond a range of five words. Moreover, the similarity between MI profiles of different languages was used to cluster the languages. These results are discussed in terms of a putative link between short‐term memory and linguistic structure and the further utility of MI in terms of characterizing the latter.     

On the dynamics of institutional agreements

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form A_G:x j{\rm A}_{G:x} \varphi reading ‘if the agents in the set of agents G identify themselves with institution x then they together accept that j{\varphi} ’. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x!y{x!\psi}, meaning that the agents learn that y{\psi} is the case in context x. Formulae of the form [x!y]j{[x!\psi]\varphi} mean that j{\varphi} is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all \lnoty{\lnot\psi} -worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form G:x-y{G:x\uparrow\psi}. The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called ‘doctrinal paradox’ or ‘discursive dilemma’ (Pettit, Philosophical Issues 11:268–299, 2001; Kornhauser and Sager, Yale Law Journal 96:82–117, 1986).     

Tolerant, Classical, Strict

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.     

Polger on the Illusion of Contingent Identity

Abstract

Thomas Polger has argued in favour of the mind–brain type‐identity theory, the view that mental states or processes are type‐identical to states of the central nervous system. Acknowledging that the type‐materialist must respond to Kripke’s modal anti‐materialist argument, Polger insists that Kripke’s argument rests on dubious assumptions concerning the identity conditions of brain states. In brief, Polger claims that one knows that x and y are non‐identical when one knows the identity conditions for both x and y. Replace x and y with ‘brain states’ and ‘sensations’ and it follows that one can know that brain states and sensations are non‐identical only if one knows the identity conditions for brain states. But according to Polger, we do not know the identity conditions for brain states. Hence, we should not be so confident that brain states and sensations are non‐identical after all. But Polger’s account is terribly flawed. Ironically, if Polger’s scepticism is warranted, then Polger himself has no good reasons to be a type‐materialist. But more importantly, Polger’s scepticism regarding the identity conditions of brain states is deeply defective. We do, I submit, understand the identity conditions of brain states. In the end, I submit, Kripke is safe from Polger.     

The bi‐dimensional rejection taxonomy: Organizing responses to interpersonal rejection along antisocial–prosocial and engaged–disengaged dimensions

Responses to interpersonal rejection vary widely in form and function. Existing theories of interpersonal rejection have exclusively focused on organizing these responses on a single antisocial–prosocial dimension. Accumulating evidence suggests a gap in this approach: Variability in social responses to rejection cannot solely be explained by the antisocial–prosocial dimension alone. To fill this gap, we propose the bi‐dimensional rejection taxonomy, consisting of the antisocial–prosocial x‐axis and engaged–disengaged y‐axis, a novel contribution to the literature. We demonstrate that both the x‐ and y‐axes are necessary for understanding interpersonal responses to rejection and avoiding erroneous conclusions. We also show how this new framework allows researchers to generate more nuanced and accurate hypotheses about how people respond when rejected. We further demonstrate how existing research about individual differences and situational factors that predict responses to rejection can be viewed in a new light within the bi‐dimensional rejection taxonomy. We conclude by suggesting how the taxonomy inspires innovative questions for future research, including understanding spontaneous responses and neurophysiological markers. The preprint of this paper is available at https://psyarxiv.com/56ptx/     

Affine representations in psychophysics and the near-miss to Weber’s law

A theoretical account for the near-miss to Weber’s law in the form of a power function, with a special emphasis on the interpretation of the exponent, was proposed by Falmagne [Falmagne, J.-C. (1985). Elements of psychophysical theory. New York: Oxford University Press] within the framework of a subtractive representation, P(x,y)=F(u(x)−g(y)). In this paper, we examine a more general affine representation, P(x,y)=F(u(x)h(y)+g(y)). We first obtain a uniqueness theorem for the affine representation. We then study the conditions that force an affine representation to degenerate to a subtractive one. Part of that study involves the case for which two different affine representations co-exist for the same data. We also show that the balance condition P(x,y)+P(y,x)=1 constrains an affine representation to be a special kind of subtractive representation, a Fechnerian one. We further show that Falmagne’s power law takes on a special form for a so-called weakly balanced system of probabilities, in which case the affine representation is Fechnerian. Finally, following Iverson [Iverson, G.J. (2006a). Analytical methods in the theory of psychophysical discrimination I: Inequalities, convexity and integration of just noticeable differences. Journal of Mathematical Psychology, 50, 271-282], we generalize the Fechner method to construct the sensory scales in a weakly balanced affine representation by integrating (derivatives of) just noticeable differences.     

Asymmetric dominance and phantom decoy effects in games

In individual choices between alternatives x and y, the availability of a third alternative z, judged inferior to x but not to y, tends to increase preferences for x. Two experiments investigated corresponding strategic asymmetric dominance effects in games. In Experiment 1, 72 players chose strategies in six symmetric 3 × 3 games, each having one strategy dominating just one other, or in reduced 2 × 2 games constructed by deleting the dominated strategies. Asymmetrically dominated strategies, even when unavailable (phantom decoy), increased choices of the strategies that dominated them and bolstered decision confidence. In Experiment 2, 81 participants played 12 similar but asymmetric games with or without dominated strategies, and similar asymmetric dominance, phantom decoy, and confidence effects were found.     

Value Incomparability and Indeterminacy

Two competing accounts of value incomparability have been put forward in the recent literature. According to the standard account, developed most famously by Joseph Raz, ‘incomparability’ means determinate failure of the three classic value relations (better than, worse than, and equally good): two value-bearers are incomparable with respect to a value V if and only if (i) it is false that x is better than y with respect to V, (ii) it is false that x is worse than y with respect to V and (iii) it is false that x and y are equally good with respect to V. Most philosophers have followed Raz in adopting this account of incomparability. Recently, however, John Broome has advocated an alternative view, on which value incomparability is explained in terms of vagueness or indeterminacy. In this paper I aim to further Broome’s view in two ways. Firstly, I want to supply independent reasons for thinking that the phenomenon of value incomparability is indeed a matter of the indeterminacy inherent in our comparative predicates. Secondly, I attempt to defend Broome’s account by warding off several objections that worry him, due mainly to Erik Carlson and Ruth Chang.     

The Distance Function in Commutative ℓ-semigroups and the Equivalence in Łukasiewicz Logic

The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.     

Similarity of rectangles

Krantz and Tversky found that neither (log-) height (y) and width (x), nor area (x + y) and shape (x ? y) qualify as “subjective dimensions of rectangles” because both pairs violate the decomposability condition for their dissimilarity data. However, the data suggest a nonlinear transformation of x, y into a pair of subjective dimensions u(x, y), v(x, y) for which decomposability should be approximately satisfied. An explicit statement of this mapping is given.     

WHAT ARE DESIRES GOOD FOR? TOWARDS A COHERENT ENDORSEMENT THEORY

Desire‐based theories of well‐being are often said to accept (G), x is good for a person just in case he wants it, and (B), x is better for a person than y just in case he prefers x to y. I shall argue that (G) and (B) are inconsistent, and this inconsistency resists any plausible refinement of these principles. The inconsistency is brought out by cases in which our wants and preferences for certain life‐options are contingent on which life‐option we realize. My argument can be generalized to endorsement theories that define a person’s good as the right combination of some kind of objective desirability and subjective endorsement, and allow preferences to be tie‐breakers when the compared objects are equally desirable (or incommensurable). My conclusions will not just be negative. I shall argue that if the choice is between (G) and (B), the most attractive option is to keep (G), slightly refined, and drop (B). 1     

MouseTracker: Software for studying real-time mental processing using a computer mouse-tracking method

In the present article, we present a software package, MouseTracker, that allows researchers to use a computer mouse-tracking method for assessing real-time processing in psychological tasks. By recording the streaming x-, y-coordinates of the computer mouse while participants move the mouse into one of multiple response alternatives, motor dynamics of the hand can reveal the time course of mental processes. MouseTracker provides researchers with fine-grained information about the real-time evolution of participant responses by sampling 60–75 times/sec the online competition between multiple response alternatives. MouseTracker allows researchers to develop and run experiments and subsequently analyze mouse trajectories in a user-interactive, graphics-based environment. Experiments may incorporate images, letter strings, and sounds. Mouse trajectories can be processed, averaged, visualized, and explored, and measures of spatial attraction/curvature, complexity, velocity, and acceleration can be computed. We describe the software and the method, and we provide details on mouse trajectory analysis. We validate the software by demonstrating the accuracy and reliability of its trajectory and reaction time data. The latest version of MouseTracker is freely available at http://mousetracker.jbfreeman.net.     

The circumplex: A slightly stronger than ordinal approach

For some proximity matrices, multidimensional scaling yields a roughly circular configuration of the stimuli. Being not symmetric, a row-conditional matrix is not fit for such an analysis. However, suppose its proximities are all different within rows. Calling {{x,y},{x,z}} a conjoint pair of unordered pairs of stimuli, let {x,y}→{x,z} mean that row x shows a stronger proximity for {x,y} than for {x,z}. We have a cyclic permutation π of the set of stimuli characterize a subset of the conjoint pairs. If the arcs {x,y}→{x,z} between the pairs thus characterized are in a specific sense monotone with π, the matrix determines π uniquely, and is, in that sense, a circumplex with π as underlying cycle. In the strongest of the 3 circumplexes thus obtained, → has circular paths. We give examples of analyses of, in particular, conditional proximities by these concepts, and implications for the analysis of presumably circumplical proximities. Circumplexes whose underlying permutation is multi-cyclic are touched.     

Split identity: intransitive judgments of the identity of objects

Identity is a transitive relation, according to all standard accounts. Necessarily, if x = y and y = z, then x = z. However, people sometimes say that two objects, x and z, are the same as a third, y, even when x and z have different properties (thus, x = y and y = z, but x ≠ z). In the present experiments, participants read stories about an iceberg that breaks into two icebergs, one to the east and the other to the west. Many participants (32–54%, in baseline conditions across experiments) decided that both successors were the original iceberg, despite the different spatial locations of the successors. Experiment 1 shows that this tendency is not due to participants failing to understand both to mean both are simultaneously the original. Similarly, Experiment 2 demonstrates that the tendency is not solely due to their interpreting the question to be about properties of the icebergs rather than about the icebergs themselves. Experiments 3 and 4 suggest, instead, that participants may understand Which is the original? to mean Which, in its own right, is entitled to be the original? Emphasizing entitlement increases the number of seemingly intransitive responses, whereas emphasizing the formal properties of identity decreases them.     

Moral supervenience

Abstract

It is widely held, even among nonnaturalists, that the moral supervenes on the natural. This is to say that for any two metaphysically possible worlds w and w′, and for any entities x in w and y in w′, any isomorphism between x and y that preserves the natural properties preserves the moral properties. In this paper, I put forward a conceivability argument against moral supervenience, assuming non-naturalism. First, I argue that though utilitarianism may be true, and the trolley driver is permitted to kill the one to save the five, there is a conceivable scenario that is just like our world in all natural respects, yet at which deontology is true, and the trolly driver is not permitted to kill the one to save the five. I then argue that in the special case of morality, it is possible to infer from the conceivability of such a scenario to its possibility. It follows that supervenience is false.     

Testing for selectivity in the dependence of random variables on external factors

Random variables A and B, whose joint distribution depends on factors (x,y), are selectively influenced by x and y, respectively, if A and B can be represented as functions of, respectively, (x,S_A,C) and (y,S_B,C), where S_A,S_B,C are stochastically independent and do not depend on (x,y). Selective influence implies selective dependence of marginal distributions on the respective factors: thus no parameter of A may depend on y. But parameters characterizing stochastic interdependence of A and B, such as their mixed moments, are generally functions of both x and y. We derive two simple necessary conditions for selective dependence of (A,B) on (x,y), which can be used to conduct a potential infinity of selectiveness tests. One condition is that, for any factor values x,x^′ and y,y^′,

s_xy≤s_xy^′+s_x^′y^′+s_x^′y,