Properties of and Algorithms for Fitting Three-Way Component Models with Offset Terms

Prior to a three-way component analysis of a three-way data set, it is customary to preprocess the data by centering and/or rescaling them. Harshman and Lundy (1984) considered that three-way data actually consist of a three-way model part, which in fact pertains to ratio scale measurements, as well as additive “offset” terms that turn the ratio scale measurements into interval scale measurements. They mentioned that such offset terms might be estimated by incorporating additional components in the model, but discarded this idea in favor of an approach to remove such terms from the model by means of centering. Then estimates for the three-way component model parameters are obtained by analyzing the centered data. In the present paper, the possibility of actually estimating the offset terms is taken up again. First, it is mentioned in which cases such offset terms can be estimated uniquely. Next, procedures are offered for estimating model parameters and offset parameters simultaneously, as well as successively (i.e., providing offset term estimates after the three-way model parameters have been estimated in the traditional way on the basis of the centered data). These procedures are provided for both the CANDECOMP/PARAFAC model and the Tucker3 model extended with offset terms. The successive and the simultaneous approaches for estimating model and offset parameters have been compared on the basis of simulated data. It was found that both procedures perform well when the fitted model captures at least all offset terms actually underlying the data. The simultaneous procedures performed slightly better than the successive procedures. If fewer offset terms are fitted than there are underlying the model, the results are considerably poorer, but in these cases the successive procedures performed better than the simultaneous ones. All in all, it can be concluded that the traditional approach for estimating model parameters can hardly be improved upon, and that offset terms can sufficiently well be estimated by the proposed successive approach, which is a simple extension of the traditional approach. The author is obliged to Jos M.F. ten Berge and Marieke Timmerman for helpful comments on an earlier version of this paper. The author is obliged to Iven van Mechelen for making available the data set used in Section 6.     

Substance concepts and personal identity

According to one argument for Animalism about personal identity, animal, but not person, is a Wigginsian substance concept—a concept that tells us what we are essentially. Person supposedly fails to be a substance concept because it is a functional concept that answers the question “what do we do?” without telling us what we are. Since person is not a substance concept, it cannot provide the criteria for our coming into or going out of existence; animal, on the other hand, can provide such criteria. This argument has been defended by Eric Olson, among others. I argue that this line of reasoning fails to show Animalism to be superior to the Psychological Approach, for the following two reasons: (1) human animal, animal, and organism are all functional concepts, and (2) the distinction between what something is and what it does is illegitimate on the reading that the argument needs.     

One-Sided Arguments

When is an argument to be called one-sided? When is putting forward such an argument fallacious? How can we develop a model for critical discussion, such that a fallaciously one-sided argument corresponds to a violation of a discussion rule? These issues are dealt with within ‘the limits of the dialogue model of argument’ by specifying a type of persuasion dialogue in which an arguer can offer complex arguments to anticipate particular responses by a critic.     

The Mereological Foundation of Megethology

In Mathematics is megethology (Lewis (1993). Philosophia Mathematica, 1(1), 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification.     

Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case

Three-Mode Factor Analysis (3MFA) and PARAFAC are methods to describe three-way data. Both methods employ models with components for the three modes of a three-way array; the 3MFA model also uses a three-way core array for linking all components to each other. The use of the core array makes the 3MFA model more general than the PARAFAC model (thus allowing a better fit), but also more complicated. Moreover, in the 3MFA model the components are not uniquely determined, and it seems hard to choose among all possible solutions. A particularly interesting feature of the PARAFAC model is that it does give unique components. The present paper introduces a class of 3MFA models in between 3MFA and PARAFAC that share the good properties of the 3MFA model and the PARAFAC model: They fit (almost) as well as the 3MFA model, they are relatively simple and they have the same uniqueness properties as the PARAFAC model.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. Part of this research has been presented at the first conference on ThRee-way methods In Chemistry (TRIC), a meeting of Psychometrics and Chemometrics, Epe, The Netherlands, August 1993. The authors are obliged to Age Smilde for stimulating this research, and two anonymous reviewers for many helpful suggestions.     

The LMPCA program: A graphical user interface for fitting the linked-mode PARAFAC-PCA model to coupled real-valued data

In behavioral research, PARAFAC analysis, a three-mode generalization of standard principal component analysis (PCA), is often used to disclose the structure of three-way three-mode data. To get insight into the underlying mechanisms, one often wants to relate the component matrices resulting from such a PARAFAC analysis to external (two-way two-mode) information, regarding one of the modes of the three-way data. To this end, linked-mode PARAFAC-PCA analysis can be used, in which the three-way and the two-way data set, which have one mode in common, are simultaneously analyzed. More specifically, a PARAFAC and a PCA model are fitted to the three-way and the two-way data, respectively, restricting the component matrix for the common mode to be equal in both models. Until now, however, no software program has been publicly available to perform such an analysis. Therefore, in this article, the LMPCA program, a free and easy-to-use MATLAB graphical user interface, is presented to perform a linked-mode PARAFAC-PCA analysis. The LMPCA software can be obtained from the authors at http://ppw.kuleuven.be/okp/software/LMPCA. For users who do not have access to MATLAB, a stand-alone version is provided.     

Beyond cognitive myopia: a patchwork approach to the concept of neural function

In this paper, I argue that looking at the concept of neural function through the lens of cognition alone risks cognitive myopia: it leads neuroscientists to focus only on mechanisms with cognitive functions that process behaviorally relevant information when conceptualizing “neural function”. Cognitive myopia tempts researchers to neglect neural mechanisms with noncognitive functions which do not process behaviorally relevant information but maintain and repair neural and other systems of the body. Cognitive myopia similarly affects philosophy of neuroscience because scholars overlook noncognitive functions when analyzing issues surrounding e.g., functional decomposition or the multifunctionality of neural structures. I argue that we can overcome cognitive myopia by adopting a patchwork approach that articulates cognitive and noncognitive “patches” of the concept of neural function. Cognitive patches describe mechanisms with causally specific effects on cognition and behavior which are likely operative in transforming sensory or other inputs into motor outputs. Noncognitive patches describe mechanisms that lack such specific effects; these mechanisms are enabling conditions for cognitive functions to occur. I use these distinctions to characterize two noncognitive functions at the mesoscale of neural circuits: subsistence functions like breathing are implemented by central pattern generators and are necessary to maintain the life of the organism. Infrastructural functions like gain control are implemented by canonical microcircuits and prevent neural system damage while cognitive processing occurs. By adding conceptual patches that describe these functions, a patchwork approach can overcome cognitive myopia and help us explain how the brain’s capacities as an information processing device are constrained by its ability to maintain and repair itself as a physiological apparatus.     

Deontological evidentialism and <Emphasis Type="Italic">ought</Emphasis> implies <Emphasis Type="Italic">can</Emphasis>

Deontological evidentialism is the claim that S ought to form or maintain S’s beliefs in accordance with S’s evidence. A promising argument for this view turns on the premise that consideration c is a normative reason for S to form or maintain a belief that p only if c is evidence that p is true. In this paper, I discuss the surprising relation between a recently influential argument for this key premise and the principle that ought implies can. I argue that anyone who antecedently accepts or rejects this principle already has a reason to resist either this argument’s premises or its role in support of deontological evidentialism.     

Higher-order theories of consciousness and what-it-is-like-ness

Ambitious higher-order theories of consciousness aim to account for conscious states when these are understood in terms of what-it-is-like-ness. This paper considers two arguments concerning this aim, and concludes that ambitious theories fail. The misrepresentation argument against HO theories aims to show that the possibility of radical misrepresentation—there being a HO state about a state the subject is not in—leads to a contradiction. In contrast, the awareness argument aims to bolster HO theories by showing that subjects are aware of all their conscious states. Both arguments hinge on how we understand two related notions which are ubiquitous in discussions of consciousness: those of what-it-is-like-ness and there being something it is like for a subject to be in a mental state. This paper examines how HO theorists must understand the two crucial notions if they are to reject the misrepresentation argument but assert the awareness argument. It shows that HO theorists can and do adopt an understanding—the HO reading—which seems to give them what they want. But adopting the HO reading changes the two arguments. On this reading, the awareness argument tells us nothing about those states there is something it is like to be in, and so offers no support to ambitious HO theories. And to respond to the misrepresentation understood according to the HO reading is to simply ignore the argument presented, and so to give no response at all. As things stand, we should deny that HO theories can account for what-it-is-like-ness.     

Discovering Argumentative Patterns in Energy Polylogues: A Macroscope for Argument Mining

A macroscope is proposed and tested here for the discovery of the unique argumentative footprint that characterizes how a collective (e.g., group, online community) manages differences and pursues disagreement through argument in a polylogue. The macroscope addresses broader analytic problems posed by various conceptualizations of large-scale argument, such as fields, spheres, communities, and institutions. The design incorporates a two-tier methodology for detecting argument patterns of the arguments performed in arguing by an interactive collective that produces views, or topographies, of the ways that issues are generated in the making and defending of standpoints. The design premises for the macroscope build on insights about argument patterns from pragma-dialectical theory by incorporating research and theory on disagreement management and the Argumentum Model of Topics. The design reconceptualizes prototypical and stereotypical argument patterns for characterizing large-scale argumentation. A prototype of the macroscope is tested on data drawn from six threads about oil-drilling and fracking from the subreddit Changemyview. The implementation suggests the efficacy of the macroscope’s design and potential for identifying what communities make controversial and how the disagreement space in a polylogue is managed through stereotypical argument patterns in terms of claims/premises, inferential relations, and presentational devices.     

Logically Incorrect Arguments

What do we learn when we find out that an argument is logically incorrect? If logically incorrect means the same as not logically correct, which in turn means not having a valid logical form, it seems that we do not learn anything too useful—an argument which is logically incorrect can still be conclusive. Thus, it seems that it makes sense to fix a stronger interpretation of the term under which a logically incorrect argument is guaranteed to be wrong (and is such for purely logical reasons). In this paper, we show that pinpointing this stronger sense is much trickier than one would expect; but eventually we reach an explication of the notion of (strong) logical incorrectness which we find non-trivial and viable.     

A Preliminary Study of MV-Algebras with Two Quantifiers Which Commute

In this paper we investigate the class of MV-algebras equipped with two quantifiers which commute as a natural generalization of diagonal-free two-dimensional cylindric algebras (see Henkin et al., in Cylindric algebras, 1985). In the 40s, Tarski first introduced cylindric algebras in order to provide an algebraic apparatus for the study of classical predicate calculus. The diagonal–free two-dimensional cylindric algebras are special cylindric algebras. The treatment here of MV-algebras is done in terms of implication and negation. This allows us to simplify some results due to Di Nola and Grigolia (Ann Pure Appl Logic 128(1-3):125–139, 2004) related to the characterization of a quantifier in terms of some special sub-algebra associated to it. On the other hand, we present a topological duality for this class of algebras and we apply it to characterize the congruences of one algebra via certain closed sets. Finally, we study the subvariety of this class generated by a chain of length n + 1 (n <  ω). We prove that the subvariety is semisimple and we characterize their simple algebras. Using a special functional algebra, we determine all the simple finite algebras of this subvariety.     

Estimating psychological networks and their accuracy: A tutorial paper

The usage of psychological networks that conceptualize behavior as a complex interplay of psychological and other components has gained increasing popularity in various research fields. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.     

“Other selves”: moral and legal proposals regarding the personhood of cryopreserved human embryos

This essay has two purposes. The first is to argue that our moral duties towards human embryos should be assessed in light of the Golden Rule by asking the normative question, “how would I want to be treated if I were an embryo?” Some reject the proposition “I was an embryo” on the basis that embryos should not be recognized as persons. This essay replies to five common arguments denying the personhood of human embryos: (1) that early human embryos lack ontological individuation; (2) that they are members of the species Homo sapiens but not yet human persons; (3) that the argument for personhood commits the “heap argument” fallacy; (4) that since human procreation in nature is inefficient, human embryos cannot be persons; and (5) the “burning building” scenario proves that all arguments for personhood are irrational or inconsistent. The second purpose is to set forth and criticize in light of the normative judgement defended in part one the present legal situation of cryo-preserved embryos in the U.S. The essay ends by proposing legislative reforms to protect ex utero human embryos.     

Eine Welt ohne Individuelle EntitÄten?

A world without individual entities? An advice to not to extract immediate ontological consequences from quantum theory. Should we assume a world without individual entities? I pledge not to extract immediate ontological consequences from quantum theory. My intention is to focus on the complexity of ontological concepts commonly associated with quantum theory. Using as an example the compatibility of EPR correlations with the existence of individual entities, it is shown that an absolute rejection of an ontological category, based on some aspects of the formalism of quantum theory, does not seem reasonable. A consequence of this argument is that the common sense view – the world is composed of individual entities – can be maintained, despite of the particularities of quantum mechanics.     

Direction dependence analysis: A framework to test the direction of effects in linear models with an implementation in SPSS

In nonexperimental data, at least three possible explanations exist for the association of two variables x and y: (1) x is the cause of y, (2) y is the cause of x, or (3) an unmeasured confounder is present. Statistical tests that identify which of the three explanatory models fits best would be a useful adjunct to the use of theory alone. The present article introduces one such statistical method, direction dependence analysis (DDA), which assesses the relative plausibility of the three explanatory models on the basis of higher-moment information about the variables (i.e., skewness and kurtosis). DDA involves the evaluation of three properties of the data: (1) the observed distributions of the variables, (2) the residual distributions of the competing models, and (3) the independence properties of the predictors and residuals of the competing models. When the observed variables are nonnormally distributed, we show that DDA components can be used to uniquely identify each explanatory model. Statistical inference methods for model selection are presented, and macros to implement DDA in SPSS are provided. An empirical example is given to illustrate the approach. Conceptual and empirical considerations are discussed for best-practice applications in psychological data, and sample size recommendations based on previous simulation studies are provided.     

Distinct neuronal patterns of positive and negative moral processing in psychopathy

Psychopathy is a disorder characterized by severe and frequent moral violations in multiple domains of life. Numerous studies have shown psychopathy-related limbic brain abnormalities during moral processing; however, these studies only examined negatively valenced moral stimuli. Here, we aimed to replicate prior psychopathy research on negative moral judgments and to extend this work by examining psychopathy-related abnormalities in the processing of controversial moral stimuli and positive moral processing. Incarcerated adult males (N = 245) completed a functional magnetic resonance imaging protocol on a mobile imaging system stationed at the prison. Psychopathy was assessed using the Hare Psychopathy Checklist–Revised (PCL-R). Participants were then shown words describing three types of moral stimuli: wrong (e.g., stealing), not wrong (e.g., charity), and controversial (e.g., euthanasia). Participants rated each stimulus as either wrong or not wrong. PCL-R total scores were correlated with not wrong behavioral responses to wrong moral stimuli, and were inversely related to hemodynamic activity in the anterior cingulate cortex in the contrast of wrong > not wrong. In the controversial > noncontroversial comparison, psychopathy was inversely associated with activity in the temporal parietal junction and dorsolateral prefrontal cortex. These results indicate that psychopathy-related abnormalities are observed during the processing of complex, negative, and positive moral stimuli.     

Characterizing belief bias in syllogistic reasoning: A hierarchical Bayesian meta-analysis of ROC data

The belief-bias effect is one of the most-studied biases in reasoning. A recent study of the phenomenon using the signal detection theory (SDT) model called into question all theoretical accounts of belief bias by demonstrating that belief-based differences in the ability to discriminate between valid and invalid syllogisms may be an artifact stemming from the use of inappropriate linear measurement models such as analysis of variance (Dube et al., Psychological Review, 117(3), 831–863, 2010). The discrepancy between Dube et al.’s, Psychological Review, 117(3), 831–863 (2010) results and the previous three decades of work, together with former’s methodological criticisms suggests the need to revisit earlier results, this time collecting confidence-rating responses. Using a hierarchical Bayesian meta-analysis, we reanalyzed a corpus of 22 confidence-rating studies (N =?993). The results indicated that extensive replications using confidence-rating data are unnecessary as the observed receiver operating characteristic functions are not systematically asymmetric. These results were subsequently corroborated by a novel experimental design based on SDT’s generalized area theorem. Although the meta-analysis confirms that believability does not influence discriminability unconditionally, it also confirmed previous results that factors such as individual differences mediate the effect. The main point is that data from previous and future studies can be safely analyzed using appropriate hierarchical methods that do not require confidence ratings. More generally, our results set a new standard for analyzing data and evaluating theories in reasoning. Important methodological and theoretical considerations for future work on belief bias and related domains are discussed.     

How high the sky? Rumfitt on the (putative) indeterminacy of the set-theoretic universe

This comment focuses on Chapter 9 of The Boundary Stones of Thought and the argument, due to William Tait, that Ian Rumfitt there sustains for the indeterminacy of set. I argue that Michael Dummett’s argument, based on the notion of indefinite extensibility and set aside by Rumfitt, provides a more powerful basis for the same conclusion. In addition, I outline two difficulties for the way Rumfitt attempts to save classical logic from acknowledged failures of the principle of bivalence, one specifically for his treatment of the set-theoretic case, the other of more general bearing but especially germane to the case of vagueness.