Intuitive prediction: ecological validity versus representativeness

Insufficiently regressive intuitive predictions have been attributed to mistaken reliance on the representativeness heuristic. In contrast, we suggest that intuitive predictions stem from a conceptualization of ‘goodness of prediction’ that differs from the accepted statistical definition in terms of error minimization, namely, ecological validity—that is, representation of the substantive characteristics of the predicted variable Y and its distribution as well as of the relationship between Y and the predictor X—rather than minimization of prediction errors. Simultaneous satisfaction of the above representation requirements is achieved by multivalued prediction: The prediction of different Y′ values for the same X value, resulting in conditional distributions Y′|X for at least some X values. Empirical results supporting this hypothesis are presented and discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

The conjunction fallacy: a misunderstanding about conjunction?

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners’ interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems.     

Is there a phenomenological argument for higher-order representationalism?

In his 2009 article “Self-Representationalism and Phenomenology,” Uriah Kriegel argues for self-representationalism about phenomenal consciousness primarily on phenomenological grounds. Kriegel’s argument can naturally be cast more broadly as an argument for higher-order representationalism. I examine this broadened version of Kriegel’s argument in detail and show that it is unsuccessful for two reasons. First, Kriegel’s argument (in its strongest form) relies on an inference to the best explanation from the claim that all experiences of normal adult human beings are accompanied by peripheral awareness of those very experiences to the claim that all experiences are accompanied by peripheral awareness of those very experiences. This inference is inadequately defended, for the explanandum may also be given a straightforward evolutionary explanation. Second, contra Kriegel, I argue that phenomenological investigation does not support the thesis that we are always peripherally aware of our experiences. Instead, it delivers no verdict on this thesis. Kriegel’s phenomenological mistake may be explained via a highly diluted version of the famous transparency thesis about experience.     

Depicting and seeing-in. The <Emphasis Type="Italic">‘Sujet’</Emphasis> in Husserl’s phenomenology of images

In this paper I investigate an underappreciated element of Husserl’s phenomenology of images: the consciousness of the depicted subject (Sujet or Bildsujet), which Husserl calls the Sujetintention, e.g. the awareness of the sitter of a portrait. Husserl claims that when a consciousness regards a figurative image, it is absorbed in the awareness of the depicted subject and yet this subject some how withholds its presence in the midst of its appearance in the image-object (Bildobjekt). Image-consciousness is an intuitive (anschaulich) consciousness that intends a being that is both ‘in’ and ‘beyond’ the image: the depicted subject haunts the image. Borrowing Richard Wollheim’s language, the aim of this study is to determine what it means for a consciousness to see a depicted-subject in an image-depiction, which happens on the basis of seeing an image-object in a material image-thing, like paint, canvas, ink, paper etc. Restricting myself to figurative images, I will argue against the view that the relation to the depicted subject is symbolic or signitive. I argue that the consciousness of the Sujet is quasi-perceptual, which allows for a better account of the depicted subject’s sense of absence. I develop this view on the basis of Husserl’s claims that the depicted subject is the bearer of norms inherent to intuitive appearances, which concern how the profiles and movements of an object ought to unfold, though they fail to do so for image-consciousness. This failure is not a mere privation for the image as a perceptual appearance but is inherent to its status as a mediated and artificial presence.     

Prediction with single event versus aggregate data

The impact of statistical information on predictive judgment was studied in a cue probability learning (CPL) task. Two kinds of aggregate information about criterion events were used: the conditional mean (Z_M) and the conditional interquartile range (Z_R). The single event information was the exact criterion value for one randomly selected past case (Z_O). Results showed that Z_Mand Z_R increased prediction consistency and accuracy and reduced bias while Z_O led to more appropriate cue weighting but lower consistency and accuracy. When Z_M, Z_R, and Z_O were all provided, the unique benefits of single-event and aggregate data were combined. This was true even for subjects without any prior task experience. When able to select only one of Z_M, Z_R, and Z_O, judges most often chose aggregate information, particularly Z_R. However, the statistical information was underutilized. Recommendations for aiding predictive judgment are made.     

The Sequential Dominance Argument for the Independence Axiom of Expected Utility Theory

Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions.     

Verification of algebra step problems: A chronometric study of human problem solving

A class of simple problem solving tasks requiring fast accurate solutions is introduced. In an experiment subjects memorized a mapping rule represented by lists of words labeled by cue words and made true/false decisions about conjunctions of propositions of the form “Y is in the list labeled by X”, written “X → Y”. Response times are analyzed using a “stage modeling” technique where problem solving algorithms are composed using a small set of psychological operations that have real time characteristics specified parametrically. The theoretical analysis shows that response time performance is adequately described in terms of the sequential application of elementary psychological operations. Unexpectedly, it was found that the proposition “X → YandX → Z” was verified as quickly as the apparently simpler “X → Y”. A case is presented for the modeling technique as applied to memory and problem solving tasks in terms of theoretical parsimony, statistical simplicity, and flexibility in investigative empirical research. Suggestions are made as to possible theoretical relations among fast problem solving, more complex and slower problem solving, and research in fundamental memory processes.     

Pseudocontingencies derived from categorically organized memory representations

Pseudocontingencies (PCs) allow for inferences about the contingency between two variables X and Y when the conditions for genuine contingency assessment are not met. Even when joint observations X _i and Y _i about the same reference objects i are not available or are detached in time or space, the correlation r(X _i ,Y _i ) is readily inferred from base rates. Inferred correlations are positive (negative) if X and Y base rates are skewed in the same (different) directions. Such PC inferences afford useful proxies for actually existing contingencies. While previous studies have focused on PCs due to environmental base rates, the present research highlights memory organization as a natural source of PC effects. When information about two attributes X and Y is represented in a hierarchically organized categorical memory code, as category-wise base rates p(X) and p(Y), the reconstruction of item-level information from category base rates will naturally produce PC effects. Three experiments support this contention. When the yes base rates of two respondents in four questionnaire subscales (categories) were correlated, recalled and predicted item-level responses were correlated in the same direction, even when the original responses to specific items within categories were correlated in the opposite direction.     

Do people reason rationally about causally related events? Markov violations,weak inferences,and failures of explaining away

Making judgments by relying on beliefs about the causal relationships between events is a fundamental capacity of everyday cognition. In the last decade, Causal Bayesian Networks have been proposed as a framework for modeling causal reasoning. Two experiments were conducted to provide comprehensive data sets with which to evaluate a variety of different types of judgments in comparison to the standard Bayesian networks calculations. Participants were introduced to a fictional system of three events and observed a set of learning trials that instantiated the multivariate distribution relating the three variables. We tested inferences on chains X₁ → Y → X₂, common cause structures X₁ ← Y → X₂, and common effect structures X₁ → Y ← X₂, on binary and numerical variables, and with high and intermediate causal strengths. We tested transitive inferences, inferences when one variable is irrelevant because it is blocked by an intervening variable (Markov Assumption), inferences from two variables to a middle variable, and inferences about the presence of one cause when the alternative cause was known to have occurred (the normative “explaining away” pattern). Compared to the normative account, in general, when the judgments should change, they change in the normative direction. However, we also discuss a few persistent violations of the standard normative model. In addition, we evaluate the relative success of 12 theoretical explanations for these deviations.     

A constrained optimization model of risky decisions

A decision model is formulated for individual choices between gambles whose probabilities and payoffs are explicitly stated. The decision situation is characterized as R_N = (X, P, Z, T, α) where X is a payoff matrix, P is the objective probability distribution over the states of nature, Z is a class of objective functions, T is tolerable regret and 1 ? α is the maximum probability for accepting regrets greater than T. Given R_N, the problem of selecting a strategy is the solution of a chance constrained optimization problem. The solutions for choice situations having two alternatives and n states of nature are developed in a series of theorems. Some implications for experimentation and possible applications are discussed.     

Lexicographic additive differences

Several authors have identified sets of axioms for a preference relation ? on a two-factor set A × X which imply that ? can be represented by specific types of numerical structures. Perhaps the two best-known of these are the additive representation, for which there are real valued functions f_A on A and f_X on X such that (a, x) ? (b, y) if and only if f_A(a) + f_X(x) > f_A(b) + f_X(y), and the lexicographic representation which, with A as the dominant factor, has (a, x) ? (b, y) if and only if f_A(a) > f_A(b) or {f_A(a) = f_A(b) and f_X(x) > f_X(y)}. Recently, Duncan Luce has combined the additive and lexicographic notions in a model for which A is the dominant factor if the difference between a and b is sufficiently large but which adheres to the additive representation when the difference between a and b lies within what might be referred to as a lexicographic threshold. The present paper specifies axioms for ? which lead to a numerical model which also has a lexicographic component but whose local tradeoff structure is governed by the additive-difference model instead of the additive model. Although the additive-difference model includes the additive model as a special case, the new lexicographic additive-difference model is not more general than Luce's model since the former has a “constant” lexicographic threshold whereas Luce's model has a “variable” lexicographic threshold. Realizations of the new model range from the completely lexicographic representation to the regular additive-difference model with no genuine lexicographic component. Axioms for the latter model are obtained from the general axioms with one slight modification.     

Weight for Stephen Finlay

According to Stephen Finlay, ‘A ought to X’ means that X-ing is more conducive to contextually salient ends than relevant alternatives. This in turn is analysed in terms of probability. I show why this theory of ‘ought’ is hard to square with a theory of a reason’s weight which could explain why ‘A ought to X’ logically entails that the balance of reasons favours that A X-es. I develop two theories of weight to illustrate my point. I first look at the prospects of a theory of weight based on expected utility theory. I then suggest a simpler theory. Although neither allows that ‘A ought to X’ logically entails that the balance of reasons favours that A X-es, this price may be accepted. For there remains a strong pragmatic relation between these claims.     

Interdependent preferences on finite sets

The degree of interdependence of a preference relation ? on a finite subset X of a product set X₁ × X₂ × … × X_n is defined in terms of the highest order of preference interaction among the X_i that must be taken into account in a real-valued, interdependent additive representation for ?. The degree is zero when indifference holds throughout X, and zero or one in the additive conjoint measurement case. A degree of n signifies complete preference interdependence among the X_i.     

The effects of response-reinforcer contingency on time allocation in the open field

The present experiment explores the effects of the response (1-sec occupancy of a target area in an open field)—reinforcer (intracranial stimulation) contingency on time allocation in the open field in rats. The probability of reinforcement given a response (X) and the probability of reinforcement given the absence of a response (Y) were varied randomly across sessions within a subject. The following (X, Y) values were utilized: (.05, 0), (.15, 0), (.25, 0), (.15, .05), and (.15, .15). The results of this experiment indicate that rate of acquisition of time allocation preference is uniformly rapid during all contingency treatments wherein Y = 0 and is negatively related to the value of Y when X = .15. The relationship between the asymptote of the time allocation acquisition function and the value of X (when Y = 0) is positively sloped and negatively accelerated, while the relationship between asymptote and the value of Y (when X = .15) is negatively sloped with zero acceleration. Proposed contingency metrics are evaluated.     

Husserl’s hyletic data and phenomenal consciousness

In the Logical Investigations, Ideas I and many other texts, Husserl maintains that perceptual consciousness involves the intentional “animation” or interpretation of sensory data or hyle, e.g., “color-data,” “tone-data,” and algedonic data. These data are not intrinsically representational nor are they normally themselves objects of representation, though we can attend to them in reflection. These data are “immanent” in consciousness; they survive the phenomenological reduction. They partly ground the intuitive or “in-the-flesh” aspect of perception, and they have a determinacy of character that we do not create but can only discover. This determinate, non-representational stratum of perceptual consciousness also serves as a bridge between consciousness and the world beyond it. I articulate and defend this conception of perceptual consciousness. I locate the view in the space of contemporary positions on phenomenal character and argue for its superiority. I close by briefly arguing that the Husserlian account is perfectly compatible with physicalism (this involves disarming the Grain Problem).     

Exploring Longitudinal Mechanisms of Irritability in Children: Implications for Cognitive-Behavioral Intervention

Severe irritability is a common and clinically important problem longitudinally associated with internalizing and externalizing problems in children. To better understand these mechanisms and to inform treatment research, we tested cognitive-behavioral processes as candidate mediators in the paths from irritability to later problems. Methods: A school sample (N = 238, 48% female, ages 8–10) was assessed at ~6-month intervals in fall (T1) and spring (T2) of third to fourth grade, and again the following fall (T3). Measures assessed irritability (T1/predictor); anger and sadness coping, intolerance of uncertainty, and rumination; (T1–T2/mediators); and anxiety, depressive symptoms, reactive aggression, and oppositionality (T1–T3/outcomes). Focused cross-lagged panel models, controlling for gender and grade, were specified to examine full (X_T1 ➔ M_T2 ➔ Y_T3) and half (X_T1 ➔ M_T2; M_T1 ➔ Y_T2) longitudinal mediation. Across one or more intervals, irritability predicted higher depressive symptoms, anxiety, reactive aggression, oppositionality, intolerance of uncertainty, and poor emotion coping. From T1 irritability to T2/T3 outcomes, mediation was found for poor sadness coping leading to reactive aggression and oppositionality; poor anger coping to anxiety, depressive symptoms, and oppositionality; and intolerance of uncertainty to anxiety. Results offer further evidence for internalizing and externalizing outcomes of youth irritability and new evidence suggesting underlying mechanisms. Irritability may confer risk for externalizing problems via poor sadness/anger coping, and for internalizing problems via poor anger coping and intolerance of uncertainty. Theoretical models and psychosocial treatment should consider addressing regulation of various unpleasant emotions as well as psychological flexibility and tolerating uncertainty.     

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.     

The generalized Logit-Linear Item Response Model for Binary-Designed Items

This paper introduces the generalized logit-linear item response model (GLLIRM), which represents the item-solving process as a series of dichotomous operations or steps. The GLLIRM assumes that the probability function of the item response is a logistic function of a linear composite of basic parameters which describe the operations, and the coefficients depend on three design matrices X, Y and Z. The GLLIRM provides a tool for testing hypotheses on the item-solving process and generalizes existing models. An empirical application is included, in which the model is applied to evaluate sources of difficulty and pairwise item interactions in a logical analysis test. This research was supported by the Comunidad de Madrid grant CCG06-UAM/ESP-0043.