Easy bayes estimation for rasch-type models

A Bayes estimation procedure is introduced that allows the nature and strength of prior beliefs to be easily specified and modal posterior estimates to be obtained as easily as maximum likelihood estimates. The procedure is based on constructing posterior distributions that are formally identical to likelihoods, but are based on sampled data as well as artificial data reflecting prior information. Improvements in performance of modal Bayes procedures relative to maximum likelihood estimation are illustrated for Rasch-type models. Improvements range from modest to dramatic, depending on the model and the number of items being considered.This research was supported by ORN Contact #00014-86-K0087. We wish to thank Sheng-Hui Chu and Dzung-Ji Lii for providing intelligent and energetic programming support for this article. We also thank one of the reviewers for pointing out several interesting and useful perspectives.     

Multidimensional scaling models for reaction times and same-different judgments

A method for joint analysis of reaction times and same-different judgments is discussed. A set of stimuli is assumed to have some parametric representation which uniquely defines dissimilarities between the stimuli. Those dissimilarities are then related to the observed reaction times and same-different judgments through a model of psychological processes. Three representation models of dissimilarities are considered, the Minkowski power distance model, the linear model, and Tversky's feature matching model. Maximum likelihood estimation procedures are developed and implemented in the form of a FORTRAN program. An example is given to illustrate the kind of analyses that can be performed by the proposed method.The work reported in this paper is supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada. Portions of this study have been presented at the Psychometric Society meeting in Chapel Hill, N.C., in May, 1981. We thank Tony Marley, Jim Ramsay and anonymous reviewers for their helpful comments. MAXRT, a computer program which performs the computations described in this paper may be obtained by writing to the first author.     

Goodness of fit tests for paired comparison models

A goodness of fit test presented by Andersen is shown to be incorrect. The correct test is described and a re-analysis of Andersen's data is provided.     

Solutions to some nonlinear equations from nonmetric data

A method is presented to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design. The analytic method, NOPE, is an iterative method in which monotone regression and the Gauss-Newton method of least squares are applied alternatively until a measure of stress is minimized. Examples of solutions from artificial data are presented together with examples of applications of the method to experimental results.This work was begun while the author was on sabbatical leave during 1970–71 at the Department of Mathematical Psychology, University of Nijmegen, the Netherlands, where discussions with E. E. Roskam on the problem were very helpful. Support was provided by Grant A0151 from the Natural Sciences and Engineering Council, Canada.     

概率估计的趋势效应及其对决策的影响机制——基于心理动量的视角

概率是反映风险与不确定性的重要指标, 概率估计具有趋势效应, 会对决策产生影响。文章描述了概率估计趋势效应的两种表现形式, 概率估计变化的趋势性(即不同时间点概率估计变化产生的趋势作用)与单边概率估计的趋势性(即高于或低于某个概率区间范畴的上界或下界的估计表述所产生的趋势作用), 揭示了概率估计趋势效应对于个体判断、决策行为和非理性决策偏差的影响; 基于心理动量的理论视角提出了一个整合模型, 阐述了概率估计趋势效应催生心理动量体验继而引发后续决策行为的内在机理。未来的研究可进一步关注：多方信息来源主体下概率估计的趋势效应; 动态趋势效应与静态概率估计的交互作用; 风险沟通中的概率估计变化趋势。     

Disappearing and appearing: Temporal binding effects are consistent across situations

Sense of agency refers to the feeling of control over actions and action outcomes. Previous studies were mostly confined to the situation of performing actions to make objects appear, while it remains unexplored whether we experience sense of agency when making objects disappear. Here, we examined the temporal binding effect, an implicit index of sense of agency, in performing actions to make objects disappear and compared the magnitude of this effect in the appearing and disappearing situations. Results showed that the temporal binding effect emerged when object’s disappearances served as action outcomes. Moreover, the temporal binding effects in the appearing and disappearing situations did not differ significantly. Our findings extend the temporal binding effect to the situation of voluntarily making objects disappear, suggesting a comparable level of implicit sense of agency when voluntarily making objects disappear and appear.     

Relating latent class membership to external variables: An overview

In this article we provide an overview of existing approaches for relating latent class membership to external variables of interest. We extend on the work of Nylund-Gibson et al. (Structural Equation Modeling: A Multidisciplinary Journal, 2019, 26, 967), who summarize models with distal outcomes by providing an overview of most recommended modeling options for models with covariates and larger models with multiple latent variables as well. We exemplify the modeling approaches using data from the General Social Survey for a model with a distal outcome where underlying model assumptions are violated, and a model with multiple latent variables. We discuss software availability and provide example syntax for the real data examples in Latent GOLD.     

Measurement bias and error correction in a two-stage estimation for multilevel IRT models

Among current state-of-the-art estimation methods for multilevel IRT models, the two-stage divide-and-conquer strategy has practical advantages, such as clearer definition of factors, convenience for secondary data analysis, convenience for model calibration and fit evaluation, and avoidance of improper solutions. However, various studies have shown that, under the two-stage framework, ignoring measurement error in the dependent variable in stage II leads to incorrect statistical inferences. To this end, we proposed a novel method to correct both measurement bias and measurement error of latent trait estimates from stage I in the stage II estimation. In this paper, the HO-IRT model is considered as the measurement model, and a linear mixed effects model on overall (i.e., higher-order) abilities is considered as the structural model. The performance of the proposed correction method is illustrated and compared via a simulation study and a real data example using the National Educational Longitudinal Survey data (NELS 88). Results indicate that structural parameters can be recovered better after correcting measurement biases and errors.     

A Gibbs sampler for the multidimensional four-parameter logistic item response model via a data augmentation scheme

The four-parameter logistic (4PL) item response model, which includes an upper asymptote for the correct response probability, has drawn increasing interest due to its suitability for many practical scenarios. This paper proposes a new Gibbs sampling algorithm for estimation of the multidimensional 4PL model based on an efficient data augmentation scheme (DAGS). With the introduction of three continuous latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. Simulation studies are conducted to evaluate the proposed method and several popular alternatives. An empirical data set was analysed using the 4PL model to show its improved performance over the three-parameter and two-parameter logistic models. The proposed estimation scheme is easily accessible to practitioners through the open-source IRTlogit package.     

An item response tree model with not-all-distinct end nodes for non-response modelling

The non-response model in Knott et al. (1991, Statistician, 40, 217) can be represented as a tree model with one branch for response/non-response and another branch for correct/incorrect response, and each branch probability is characterized by an item response theory model. In the model, it is assumed that there is only one source of non-responses. However, in questionnaires or educational tests, non-responses might come from different sources, such as test speededness, inability to answer, lack of motivation, and sensitive questions. To better accommodate such more realistic underlying mechanisms, we propose a a tree model with four end nodes, not all distinct, for non-response modelling. The Laplace-approximated maximum likelihood estimation for the proposed model is suggested. The validation of the proposed estimation procedure and the advantage of the proposed model over traditional methods are demonstrated in simulations. For illustration, the methodologies are applied to data from the 2012 Programme for International Student Assessment (PISA). The analysis shows that the proposed tree model has a better fit to PISA data than other existing models, providing a useful tool to distinguish the sources of non-responses.