Newton Algorithms for Analytic Rotation: an Implicit Function Approach

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to m factors and p variables. The speed of the new algorithms is compared to that of existing algorithms and to that of Newton algorithms based on alternative parameterizations. Several rotation criteria were examined and the algorithms were evaluated over a range of values for m. Initial guesses for Newton algorithms were improved by subconvergence iterations of the gradient projection algorithm. Simulation results suggest that no one algorithm is fastest for minimizing all criteria for all values of m. Among competing algorithms, the gradient projection algorithm alone was faster than the implicit function algorithm for minimizing a quartic criterion over oblique rotation matrices when m is large. In all other conditions, however, the implicit function algorithms were competitive with or faster than the fastest existing algorithms. The new algorithms showed the greatest advantage over other algorithms when minimizing a nonquartic component loss criterion.     

项目反应理论中潜在心理特质“填补”的参数估计方法及其演变

在心理与教育测量中, 项目反应理论(Item Response Theory, IRT)模型的参数估计方法是理论研究与实践应用的基本工具。最近, 由于IRT模型的不断扩展与EM (expectation-maximization)算法自身的固有问题, 参数估计方法的改进与发展显得尤为重要。这里介绍了IRT模型中边际极大似然估计的发展, 提出了它的阶段性特征, 即联合极大似然估计阶段、确定性潜在心理特质“填补”阶段、随机潜在心理特质“填补”阶段, 重点阐述了它的潜在心理特质“填补” (data augmentation)思想。EM算法与Metropolis-Hastings Robbins-Monro (MH-RM)算法作为不同的潜在心理特质“填补”方法, 都是边际极大似然估计的思想跨越。目前, 潜在心理特质“填补”的参数估计方法仍在不断发展与完善。     

Locally dependent latent trait model for polytomous responses with application to inventory of hostility

Psychological tests often involve item clusters that are designed to solicit responses to behavioral stimuli. The dependency between individual responses within clusters beyond that which can be explained by the underlying trait sometimes reveals structures that are of substantive interest. The paper describes two general classes of models for this type of locally dependent responses. Specifically, the models include a generalized log-linear representation and a hybrid parameterization model for polytomous data. A compact matrix notation designed to succinctly represent the system of complex multivariate polytomous responses is presented. The matrix representation creates the necessary formulation for the locally dependent kernel for polytomous item responses. Using polytomous data from an inventory of hostility, we provide illustrations as to how the locally dependent models can be used in psychological measurement.     

Analysis of distractor difficulty in multiple-choice items

Two psychometric models are presented for evaluating the difficulty of the distractors in multiple-choice items. They are based on the criterion of rising distractor selection ratios, which facilitates interpretation of the subject and item parameters. Statistical inferential tools are developed in a Bayesian framework: modal a posteriori estimation by application of an EM algorithm and model evaluation by monitoring posterior predictive replications of the data matrix. An educational example with real data is included to exemplify the application of the models and compare them with the nominal categories model.This research was supported by the DGI grant BSO2002-01485.I would like to thank Eric Maris and Vicente Ponsoda for their advice, Juan Botella for providing the data for the empirical application, and three anonymous reviewers for their comments that were essential for improving the quality of the paper.     

Bootstrapping the lexicon: a computational model of infant speech segmentation

Prelinguistic infants must find a way to isolate meaningful chunks from the continuous streams of speech that they hear. BootLex, a new model which uses distributional cues to build a lexicon, demonstrates how much can be accomplished using this single source of information. This conceptually simple probabilistic algorithm achieves significant segmentation results on various kinds of language corpora - English, Japanese, and Spanish; child- and adult-directed speech, and written texts; and several variations in coding structure - and reveals which statistical characteristics of the input have an influence on segmentation performance. BootLex is then compared, quantitatively and qualitatively, with three other groups of computational models of the same infant segmentation process, paying particular attention to functional characteristics of the models and their similarity to human cognition. Commonalities and contrasts among the models are discussed, as well as their implications both for theories of the cognitive problem of segmentation itself, and for the general enterprise of computational cognitive modeling.     

Preference for human or algorithmic forecasting advice does not predict if and how it is used

Past research has found that people treat advice differently depending on its source. In many cases, people seem to prefer human advice to algorithms, but in others, there is a reversal, and people seem to prefer algorithmic advice. Across two studies, we examine the persuasiveness of, and judges' preferences for, advice from different sources when forecasting geopolitical events. We find that judges report domain-specific preferences, preferring human advice in the domain of politics and algorithmic advice in the domain of economics. In Study 2, participants report a preference for hybrid advice, that combines human and algorithmic sources, to either one on it's own regardless of domain. More importantly, we find that these preferences did not affect persuasiveness of advice from these different sources, regardless of domain. Judges were primarily sensitive to quantitative features pertaining to the similarity between their initial beliefs and the advice they were offered, such as the distance between them and the relative advisor confidence, when deciding whether to revise their initial beliefs in light of advice, rather than the source that generated the advice.     

A latent class distance association model for cross‐classified data with a categorical response variable

In this paper we propose a latent class distance association model for clustering in the predictor space of large contingency tables with a categorical response variable. The rows of such a table are characterized as profiles of a set of explanatory variables, while the columns represent a single outcome variable. In many cases such tables are sparse, with many zero entries, which makes traditional models problematic. By clustering the row profiles into a few specific classes and representing these together with the categories of the response variable in a low‐dimensional Euclidean space using a distance association model, a parsimonious prediction model can be obtained. A generalized EM algorithm is proposed to estimate the model parameters and the adjusted Bayesian information criterion statistic is employed to test the number of mixture components and the dimensionality of the representation. An empirical example highlighting the advantages of the new approach and comparing it with traditional approaches is presented.     

Research and application of virtual user context information security strategy based on group intelligent computing

This article first introduced the current technology of the privacy protection model, and analyzed their characteristics and deficiencies. Afterwards, from the point of view of revenue, the shortcomings of the traditional privacy protection model have analyzed through the group intelligent computing method. Based on this, this paper proposes a research and application of virtual user information of security strategy based on group intelligent computing, through the collection of visitor's private information historical access data, intelligent calculation of the strategy group between the visitor and the interviewee. The setting of the threshold of the visited person can protect the privacy information of the user more effectively. In this paper, the implementation flow, algorithm implementation process, and specific architecture design of the proposed virtual user of privacy protection model based on group intelligent computing are introduced respectively. The specific algorithms include PCA, BP neural network, and genetic algorithm. Finally, the proposed privacy has verified through experiments. Protection model can protect user privacy more effectively than traditional privacy protection model. In the future, we will further expand and improve the privacy protection model of virtual users based on group intelligent computing, including considering the dynamic and inconsistency of access to the privacy information, that is, accessing different private information will produce different overlay effects and parallelism. We will also study how to apply this model to actual systems such as shopping websites and social platforms, and use commercial data to evaluate the performance of the model and further improve it.     

Dynamic analysis of multivariate panel data with non-linear transformations

Many models for multivariate data analysis can be seen as special cases of the linear dynamic or state space model. Contrary to the classical approach to linear dynamic systems analysis, in which high-dimensional exact solutions are sought, the model presented here is developed from a social science framework where low-dimensional approximate solutions are preferred. Borrowing concepts from the theory on mixture distributions, the linear dynamic model can be viewed as a multi-layered regression model, in which the output variables are imprecise manifestations of an unobserved continuous process. An additional layer of mixing makes it possible to incorporate non-normal as well as ordinal variables.Using the EM-algorithm, we find estimates of the unknown model parameters, simultaneously providing stability estimates. The model is very general and cannot be well estimated by other estimation methods. We illustrate the applicability of the obtained procedure through an example with generated data.     

Bluffing and betting behavior in a simplified poker game

A pure‐strategy, simplified poker (PSP) game is proposed, where two players draw from a small and discrete number of hands. Equilibrium strategies of the game are described and an experiment is conducted where 120 subjects played the PSP against a computer, which was programmed to play either the equilibrium solution or a fictitious play (FP) learning algorithm designed to take advantage of poor play. The results show that players did not adopt the cutoff‐type strategies predicted by the equilibrium solution; rather they made considerable “errors” by: Betting when they should have checked, checking when they should have bet, and calling when they should have folded. There is no evidence that aggregate performance improved over time in either condition although considerable individual differences were observed among subjects. Behavioral learning theory (BLT) cannot easily explain these individual differences and cognitive learning theory (CLT) is introduced to explain the apparent anomalies. Copyright © 2009 John Wiley & Sons, Ltd.