A statistical test of the equality of latent orders

Kalish, Michael L.; Dunn, John C.; Burdakov, Oleg; Sysoev, Oleg

doi:10.1016/j.jmp.2015.10.004

Cited by 34 publications

(70 citation statements)

References 17 publications

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“…Rips found that valid-unbelievable arguments received higher deduction endorsements than invalid-believable arguments, but this pattern was reversed for induction judgments. However, applied statetrace analysis to these data (see Dunn & Kalish, 2018), which involved plotting induction endorsement rates against deduction endorsement rates, and examining the fit of a model that assumes a single latent variable and thus a monotonic relationship (using an appropriate conjoint monotonic regression [CMR] procedure; Kalish, Dunn, Burdakov, & Sysoev, 2016).…”

Section: Tests Of the Simplest Single-process Model Using State-tracementioning

confidence: 99%

A test of two processes: The effect of training on deductive and inductive reasoning

et al. 2020

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Dual-process theories posit that separate kinds of intuitive (Type 1) and reflective (Type 2) processes contribute to reasoning. Under this view, inductive judgments are more heavily influenced by Type 1 processing, and deductive judgments are more strongly influenced by Type 2 processing. Alternatively, single-process theories propose that both types of judgments are based on a common form of assessment. The competing accounts were respectively instantiated as two-dimensional and one-dimensional signal detection models, and their predictions were tested against specifically targeted novel data using signed difference analysis. In two experiments, participants evaluated valid and invalid arguments, under induction or deduction instructions. Arguments varied in believability and type of conditional argument structure. Additionally, we used logic training to strengthen Type 2 processing in deduction (Experiments 1 & 2) and belief training to strengthen Type 1 processing in induction (Experiment 2). The logic training successfully improved validity-discrimination, and differential effects on induction and deduction judgments were evident in Experiment 2. While such effects are consistent with popular dual-process accounts, crucially, a one-dimensional model successfully accounted for the results. We also demonstrate that the one-dimensional model is psychologically interpretable, with the model parameters varying sensibly across conditions. We argue that single-process accounts have been prematurely discounted, and formal modeling approaches are important for theoretical progress in the reasoning field.

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Section: Tests Of the Simplest Single-process Model Using State-tracementioning

confidence: 99%

A test of two processes: The effect of training on deductive and inductive reasoning

et al. 2020

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“…This, like in the PAV algorithm, assumes merging the corresponding adjacent blocks, which explains why we call our algorithm SPAV (smoothed pool-adjacent-violators). The merging is associated with updating the coefficients that define the linear system (7). The corresponding number of arithmetic operations is proportional to the number of new active constraints.…”

Section: Smoothed Pool-adjacent-violators Algorithmmentioning

confidence: 99%

“…In order not to separately consider k = 0 as a special case, we introduce artificial μ 0 = 0 and constant-valued function y 0 (y k ). This does not change the relations established by (7). The equations of this linear system that correspond to j ∈ [k + 1, k − 1] can be represented in the form of the following recursive relation…”

Section: Lemma 42mentioning

confidence: 99%

“…The enormous amount of publications related to the MR, as well as a growing variety of its application areas, testifies to its exceptional importance. Examples are found in such areas as operations research [3], genetics [4], environmental science [5], meteorology [6], psychology [7], and many others. One can find very large-scale MR problems, e.g., in machine learning [8][9][10] and computer simulations [11].…”

Section: Introductionmentioning

confidence: 99%

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A Dual Active-Set Algorithm for Regularized Monotonic Regression

Burdakov

Sysoev

2017

J Optim Theory Appl

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Monotonic (isotonic) regression is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the monotonic regression, formulated as a least distance problem with monotonicity constraints. The resulting smoothed monotonic regression is a convex quadratic optimization problem. We focus on the case, where the set of observations is completely (linearly) ordered. Our smoothed pool-adjacent-violators algorithm is designed for solving the regularized problem. It belongs to the class of dual active-set algorithms. We prove that it converges to the optimal solution in a finite number of iterations that does not exceed the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of our algorithm grows quadratically with the problem size, we found its running time to grow almost linearly in our computational experiments.

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“…Such applications can be found in psychology, biology, signal processing, economics and many other disciplines [1,2,21,22]. Perhaps the most widely known approach which allows for extracting a monotonic dependence is monotonic regression (MR) [5,38].…”

Section: Introductionmentioning

confidence: 99%

A smoothed monotonic regression via L2 regularization

Sysoev

Burdakov

2018

Knowl Inf Syst

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Monotonic regression is a standard method for extracting a monotone function from non-monotonic data, and it is used in many applications. However, a known drawback of this method is that its fitted response is a piecewise constant function, while practical response functions are often required to be continuous. The method proposed in this paper achieves monotonicity and smoothness of the regression by introducing an L2 regularization term. In order to achieve a low computational complexity and at the same time to provide a high predictive power of the method, we introduce a probabilistically motivated approach for selecting the regularization parameters. In addition, we present a technique for correcting inconsistencies on the boundary. We show that the complexity of the proposed method is O(n 2 ). Our simulations demonstrate that when the data are large and the expected response is a complicated function (which is typical in machine learning applications) or when there is a change point in the response, the proposed method has a higher predictive power than many of the existing methods.

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A statistical test of the equality of latent orders

Cited by 34 publications

References 17 publications

A test of two processes: The effect of training on deductive and inductive reasoning

A test of two processes: The effect of training on deductive and inductive reasoning

A Dual Active-Set Algorithm for Regularized Monotonic Regression

A smoothed monotonic regression via L2 regularization

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