Ordinal Information Research Articles

Alternative ways to use and evaluate Kohler's ordinal scale to assess aquatic macrophyte abundance

To assess numerical information on the aquatic vegetation of running water bodies, the ‘Kohler method’, a five-level descriptor scale estimating the relative abundance of species in river sections as survey units has been frequently used. Although this scale is ordinal without any information on differences between the states, data are often evaluated by arithmetic operations as if they were on the ratio scale. Metrizing ordinal information may facilitate correct data evaluation; however, the outcome highly depends on mathematical procedures applied to the data set.This paper demonstrates that if ordinal data are analyzed by ordination methods suited to this scale type, then results primarily reflect presence/absences. To the contrary, additional information was added to Kohler's scale when the applied analyses used values on ratio scales; therefore they provided inappropriate data evaluation.Four different conversion methods (the use of 1–5 values, the third power, the mean values of Braun-Blanquet cover classes and the replacement of ordinal states by ranks) were applied to reveal how the conversion procedures determine the intervals between the substituting metric values and the level of importance given to species frequency and abundance. When ordinal scale was substituted by numbers 1–5 and ranks, frequency of species was taken greatly into account. After cubic conversion the large values became considerably overemphasized, therefore species occurring in a few (or very few) survey units with high abundance values were considered more dominant than less abundant but frequently present ones. The mean values of Braun-Blanquet's cover classes gave large ordinal scores and the frequent species to have substantive representation.The results demonstrate that conscious choice of intervals between the scores is inevitable; otherwise one generates unknown or misleading differences in species abundance. Although every researcher assessing aquatic macrophytes by Kohler's method surely has an idea on the differences between the applied scores, the use of identical, widely accepted scale substitution is prerequisite for reliable comparison.

Dominance Measuring Method Performance under Incomplete Information about Weights

ABSTRACTIn multi‐attribute utility theory, it is often not easy to elicit precise values for the scaling weights representing the relative importance of criteria. A very widespread approach is to gather incomplete information. A recent approach for dealing with such situations is to use information about each alternative's intensity of dominance, known as dominance measuring methods. Different dominance measuring methods have been proposed, and simulation studies have been carried out to compare these methods with each other and with other approaches but only when ordinal information about weights is available. In this paper, we use Monte Carlo simulation techniques to analyse the performance of and adapt such methods to deal with weight intervals, weights fitting independent normal probability distributions or weights represented by fuzzy numbers. Moreover, dominance measuring method performance is also compared with a widely used methodology dealing with incomplete information on weights, the stochastic multicriteria acceptability analysis (SMAA). SMAA is based on exploring the weight space to describe the evaluations that would make each alternative the preferred one. Copyright © 2012 John Wiley & Sons, Ltd.

Comparison of decision rules to mediate negotiations with incomplete information

Decisions in society resulting from negotiation among two parties are often inefficient (in terms of Pareto efficiency) as the parties fail to identify an agreement that would make both better off. A third party mediating the negotiation can increase the chances of reaching a Pareto efficient alternative. However, in most practical situations the mediator does not have a precise model of the parties’ preferences, and therefore cannot identify which alternatives are efficient. This paper assesses the performance of decision rules that a mediator can apply in multi-issue bilateral negotiation analysis given ordinal information about the importance of the issues and the value of the potential alternatives in each issue. We assume the preferences of the parties can be modelled by an additive multiattribute value function, but without assuming the precise parameters of this model are known. We study three mediation criteria: maximising the sum of the values, maximising the product of the excesses, or maximising the minimal proportion of potential. Monte-Carlo simulation is used to assess how good the alternative chosen by each decision rule is, and to provide guidelines about the use of these rules in a context of selecting a subset of promising alternatives.

The nature of spatial coding of ordinal information in working memory

Event Abstract Back to Event The nature of spatial coding of ordinal information in working memory Veronique Ginsburg1*, Jean-Philippe Van Dijck2, Paola Previtali3, Wim Fias2 and Wim Gevers1 1 Université Libre de Bruxelles, Faculté des Sciences psychologiques et de l'éducation, Belgium 2 Universiteit Gent, Department of Experimental Psychology, Belgium 3 Department of Psychology, Italy Generally, subjects respond faster to relatively small numbers with the left hand side and to relatively large numbers with the right hand side. This observation is called the SNARC effect. Recent data indicate that numbers are not automatically related to space but rather that numbers-space associations are created during task execution. This suggests a determinant implication of working memory. In a recent study of Van Dijck and Fias (2011), participants had to memorise a sequence of serially presented numbers. In a second phase they had to perform a parity judgment task only on numbers belonging to the working memory load. An association was observed between the ordinal position and response side, called the ordinal position effect (i.e. early position in the memorized sequence was responded faster with the left hand side and late position with the right hand side). Interestingly, no SNARC effect occurred: Numbers are coded for their ordinal position in working memory rather than for their magnitude. In the present study, we adapted the procedure of Van Dijck and Fias (2011) to investigate whether the passive (items just maintained in working memory) vs. active (items maintained and processed) state of numbers in working memory influences the SNARC effect and the ordinal position effect. As expected, if numbers are actively maintained in working memory, lateralized responses are linked to the ordinal position of numbers (i.e., the ordinal position effect) and not to magnitude information. On the contrary, the ordinal position effect disappears and we observe a SNARC effect if the memorized sequence is in a passive state. Additionally, these results are observed regardless of whether magnitude information is relevant to the task (i.e., magnitude comparison vs. parity judgment). Acknowledgements FNRS References van Dijck, J.-P., & Fias, W. (2011). A working memory account for spatial numerical associations. Cognition, 119, 114–119. Keywords: numbers, space, working memory, SNARC effect, ordinal position Conference: Belgian Brain Council, Liège, Belgium, 27 Oct - 27 Oct, 2012. Presentation Type: Poster Presentation Topic: Higher Brain Functions in health and disease: cognition and memory Citation: Ginsburg V, Van Dijck J, Previtali P, Fias W and Gevers W (2012). The nature of spatial coding of ordinal information in working memory. Conference Abstract: Belgian Brain Council. doi: 10.3389/conf.fnhum.2012.210.00031 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 10 Sep 2012; Published Online: 12 Sep 2012. * Correspondence: Miss. Veronique Ginsburg, Université Libre de Bruxelles, Faculté des Sciences psychologiques et de l'éducation, Brussels, Belgium, veginsbu@ulb.ac.be Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Veronique Ginsburg Jean-Philippe Van Dijck Paola Previtali Wim Fias Wim Gevers Google Veronique Ginsburg Jean-Philippe Van Dijck Paola Previtali Wim Fias Wim Gevers Google Scholar Veronique Ginsburg Jean-Philippe Van Dijck Paola Previtali Wim Fias Wim Gevers PubMed Veronique Ginsburg Jean-Philippe Van Dijck Paola Previtali Wim Fias Wim Gevers Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

ON THE CARDINAL MEASUREMENT OF HEALTH INEQUALITY WHEN ONLY ORDINAL INFORMATION IS AVAILABLE ON INDIVIDUAL HEALTH STATUS

This paper suggests new indices of health inequality which may be used when only ordinal information is available on individual health status. We borrow ideas from the literature on the measurement of occupational or residential segregation and show that indices of ordinal segregation which have been recently proposed may be also applied to the measurement of health inequality. We also prove that these indices satisfy four axioms introduced to measure inequality with ordered response health data so that the new indices presented in this paper are consistent with the inequality ordering proposed by Allison and Foster. We also suggest an extension of the family of indices proposed by Abul Naga and Yalcin.

Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made “ordered” or “non-ordered” judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

Pay for Percentile

We propose an incentive pay scheme for educators that links educator compensation to the ranks of their students within appropriately defined comparison sets, and we show that under certain conditions our scheme induces teachers to allocate socially optimal levels of effort to all students. Because this scheme employs only ordinal information, our scheme allows education authorities to employ completely new assessments at each testing date without ever having to equate various assessment forms. This approach removes incentives for teachers to teach to a particular assessment form and eliminates opportunities to influence reward pay by corrupting the equating process or the scales used to report assessment results. Our system links compensation to the outcomes of properly seeded contests rather than cardinal measures of achievement growth. Thus, education authorities can employ our incentive scheme for educators while employing a separate system for measuring growth in student achievement that involves no stakes for educators. This approach does not create direct incentives for educators to take actions that contaminate the measurement of student progress.

Cultural Characteristics Dissociate Magnitude and Ordinal Information Processing

The SNARC effect reflects an association between the processing of quantity information and the side of response. A close relationship has been demonstrated between the direction of this association (SNARC effect) and reading direction habit. In the present study, the authors investigated the relationship between processing of magnitude and ordinal information processing. In the first experiment, bilingual Hebrew-English participants judged the ordinal position of letters in both the English (left-to-right) and the Hebrew (right-to-left) alphabet. The observed direction of the SNARC effect was congruent with the direction of reading in both languages. The second experiment explored the same task, but now the instructions emphasized the magnitude meaning of Hebrew letters (e.g., classify the letter as smaller or larger than 5). Contrary to Experiment 1, a regular left-to-right SNARC effect was observed. Finally, in Experiment 3, we demonstrate that this left-to-right-oriented SNARC effect is robustly observed in Hebrew participants if magnitude information is relevant to the task. Relevant interpretations regarding the observed dissociation between magnitude and ordinal processing are discussed.

Hierarchical Partition Approach with Application on Enterprise Credit Assessment

A new SVM (Support Vector Machine) classifier-combination model, based on Hierarchical Partition approach, for enterprise credit assessment is proposed in this paper. Enterprise credit assessment is essentially an ordinal classification (or ranking), and the popular multi-classification technique does not deal with the ordinal information in the sample data. Hierarchical Partition approach makes use of the ordinal characteristics to simplify the structure of classifiers, as well as to decrease the training and testing time. It can also be used to solve the problems where the imbalance sample distribution and different loss-costs among different ranks present. Experimental results show that the generalization ability of the new model using Hierarchical Partition approach are better than that of neural network model and traditional 1-vs-1 combined SVM model.

Integration of temporal and ordinal information during serial interception sequence learning.

The expression of expert motor skills typically involves learning to perform a precisely timed sequence of movements. Research examining incidental sequence learning has relied on a perceptually cued task that gives participants exposure to repeating motor sequences but does not require timing of responses for accuracy. In the 1st experiment, a novel perceptual-motor sequence learning task was used, and learning a precisely timed cued sequence of motor actions was shown to occur without explicit instruction. Participants learned a repeating sequence through practice and showed sequence-specific knowledge via a performance decrement when switched to an unfamiliar sequence. In the 2nd experiment, the integration of representation of action order and timing sequence knowledge was examined. When either action order or timing sequence information was selectively disrupted, performance was reduced to levels similar to completely novel sequences. Unlike prior sequence-learning research that has found timing information to be secondary to learning action sequences, when the task demands require accurate action and timing information, an integrated representation of these types of information is acquired. These results provide the first evidence for incidental learning of fully integrated action and timing sequence information in the absence of an independent representation of action order and suggest that this integrative mechanism may play a material role in the acquisition of complex motor skills.

Dissociating between cardinal and ordinal and between the value and size magnitudes of coins

In mathematics, the ordinal (relative) magnitude of a numerical object conveys a separate meaning from its cardinal (absolute) magnitude, whereas its physical size bears no inherent relationship to its magnitude. In numerical cognition, the ordinal-cardinal distinction has been scarcely addressed, whereas the size-magnitude distinction has been studied extensively, with the surprising demonstration of an interaction between semantic magnitude and physical size (Besner & Coltheart, 1979). The present work used coins to study the intricate relations between these meanings. In two experiments, Israeli observers (Experiment 1) and American observers (Experiment 2) performed numerical and physical comparative judgments of coins. Consensual markers of magnitude activation (e.g., the size congruity effect and the distance effect) were obtained. The results of the two experiments converged on the same conclusions. Comparisons of value were governed by ordinal magnitude. Magnitude interfered with comparisons of size, but size did not affect value. The results provided a set of clear dissociations between cardinal and ordinal magnitude and between value and size of coins. They highlight the important role played by ordinal information in magnitude processing.

Simple procedures of choice in multicriteria problems without precise information about the alternatives’ values

The additive model of multiattribute value theory is widely used in multicriteria choice problems. But often it is not easy to obtain precise values for the scaling weights or the alternatives’ value in each function. Several decision rules which require weaker information, such as ordinal information, have been proposed to select an alternative under these circumstances. We propose new decision rules and test them using Monte-Carlo simulation, considering that there is ordinal information both on the scaling weights and on the alternatives’ values. Results show the new rules constitute a good approximation. We provide guidelines about how to use these rules in a context of selecting a subset of the most promising alternatives, considering the contradictory objectives of keeping a low number of alternatives yet not excluding the best one.

Second-order motion alone does not convey ordinal depth information

Second-order motion alone does not convey ordinal depth information

Supply side risk assessment: an application of Yager's methodology based on fuzzy sets

This paper discusses the potential application of fuzzy set theory in the area of supply side risk assessment using linguistic variables/values. The application has been illustrated through its use in a process industry. Yager's methodology for ordinal multi-objective decisions based on fuzzy sets has been chosen since the model only demands ordinal information of expert's preferences and the importance of each individual factor. It allows supply chain risk evaluation, ranking and prioritisation based on expert's knowledge, experiences and opinions. Moreover, this model can be used by the practicing managers who may not be having in-depth knowledge on fuzzy mathematics. Typical supply related risks in a process industry have been used in this application.

Online Reranking via Ordinal Informative Concepts for Context Fusion in Concept Detection and Video Search

To exploit the co-occurrence patterns of semantic concepts while keeping the simplicity of context fusion, a novel reranking approach is proposed in this paper. The approach, called ordinal reranking, adjusts the ranking of an initial search (or detection) list based on the co-occurrence patterns obtained by using ranking functions such as ListNet. Ranking functions are by nature more effective than classification-based reranking methods in mining ordinal relationships. In addition, the ordinal reranking is free of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> thresholding for noisy binary labels and requires no extra offline learning or training data. To select informative concepts for reranking, we also propose a new concept selection measurement, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wc-tf-idf</i> , which considers the underlying ordinal information of ranking lists and is thus more effective than the feature selection algorithms for classification. Being largely unsupervised, the reranking approach to context fusion can be applied equally well to concept detection and video search. While being extremely efficient, ordinal reranking outperforms existing methods by up to 40% in mean average precision (MAP) for the baseline text-based search and 12% for the baseline concept detection over TRECVID 2005 video search and concept detection benchmark.

Sequence Learning in 4‐Month‐Old Infants: Do Infants Represent Ordinal Information?

This study investigated how 4-month-old infants represent sequences: Do they track the statistical relations among specific sequence elements (e.g., AB, BC) or do they encode abstract ordinal positions (i.e., B is second)? Infants were habituated to sequences of 4 moving and sounding elements-3 of the elements varied in their ordinal position while the position of 1 target element remained invariant (e.g., ABCD, CBDA)-and then were tested for the detection of changes in the target's position. Infants detected an ordinal change only when it disrupted the statistical co-occurrence of elements but not when statistical information was controlled. It is concluded that 4-month-olds learn the order of sequence elements by tracking their statistical associations but not their invariant ordinal position.

Order and Magnitude Share a Common Representation in Parietal Cortex

The role of the intraparietal sulcus (IPS) in the representation of numerical magnitude is well established. Recently, there has also been speculation that the IPS is involved in the representation of ordinal information as well. These claims, however, overlook the fact that all neuroimaging paradigms in which participants make judgments about either magnitude and/or order result in a behavioral distance effect (i.e., the comparison is easier when the stimuli span a greater distance). This leaves open two possibilities: It may be that activation of the IPS is due to the mechanism that yields distance effects, or it may be that the IPS is involved in the representation of information about both magnitude and order. The current study used fMRI to compare a magnitude task in which participants show distance effects to an order-judgment task that yields reverse-distance effects. The results reveal activation of the IPS for both the magnitude and order tasks that is based on participants' strategies as opposed to the actual distance between the numbers. This leads to the conclusion that the IPS represents a mental number line, and that accessing this line can lead to distance effects when participants compare magnitudes and to reverse-distance effects when participants check for order.

An approach to aggregation of ordinal information in multi-criteria multi-person decision making using Choquet integral of Fubini type

An algorithm for the selection among n alternatives based on the evaluation of n (distinct) groups of persons according to the same m criteria is described. The evaluation of each person for each criterion is represented by a proportional ordinal 2-tuple and the overall opinion is aggregated by a pair of quantifier-guided ordered weighted averaging (OWA) aggregation and (floating) anchoring value-based ordered weighted averaging (AV-OWA) aggregation operators. An example is provided to illustrate the algorithm. The decision function of the algorithm is shown to be a Choquet integral of the associated function of two variables (corresponding to the two aggregation processes in the algorithm) which can be accomplished alternatively by a Choquet integral of Fubini type.

Beyond quantity: Individual differences in working memory and the ordinal understanding of numerical symbols

In two different contexts, we examined the hypothesis that individual differences in working memory (WM) capacity are related to the tendency to infer complex, ordinal relationships between numerical symbols. In Experiment 1, we assessed whether this tendency arises in a learning context that involves mapping novel symbols to quantities by training adult participants to associate dot-quantities with novel symbols, the overall relative order of which had to be inferred. Performance was best for participants who were higher in WM capacity (HWMs). HWMs also learned ordinal information about the symbols that lower WM individuals (LWMs) did not. In Experiment 2, we examined whether WM relates to performance when participants are explicitly instructed to make numerical order judgments about highly enculturated numerical symbols by having participants indicate whether sets of three Arabic numerals were in increasing order. All participants responded faster when sequential sets (3–4–5) were in order than when they were not. However, only HWMs responded faster when non-sequential, patterned sets (1–3–5) were in order, suggesting they were accessing ordinal associations that LWMs were not. Taken together, these experiments indicate that WM capacity plays a key role in extending symbolic number representations beyond their quantity referents to include symbol–symbol ordinal associations, both in a learning context and in terms of explicitly accessing ordinal relationships in highly enculturated stimuli.

Multiattribute Choice With Ordinal Information: A Comparison of Different Decision Rules

In the context of additive multiattribute aggregation, we address problems with ordinal information, i.e., considering a ranking of the weights (the scaling coefficients). Several rules for ranking alternatives in these situations have been proposed and compared, such as the rank-order-centroid weight, minimum value, central value, and maximum regret rules. This paper compares these rules, together with two rules that had never been studied (quasi-dominance and quasi-optimality) that use a tolerance parameter to extend the concepts of dominance and optimality. Another contribution of this paper is the study of the behavior of these rules in the context of selecting a subset of the most promising alternatives. This study intends to provide guidelines about which rules to choose and how to use them (e.g., how many alternatives to retain and what tolerance to use), considering the contradictory goals of keeping a low number of alternatives yet not excluding the best one. The comparisons are grounded on Monte Carlo simulations.