Parsing Heuristic and Forward Search in First‐Graders' Game‐Play Behavior

Seventy‐three children between 6 and 7 years of age were presented with a problem having ambiguous subgoal ordering. Performance in this task showed reliable fingerprints: (a) a non‐monotonic dependence of performance as a function of the distance between the beginning and the end‐states of the problem, (b) very high levels of performance when the first move was correct, and (c) states in which accuracy of the first move was significantly below chance. These features are consistent with a non‐Markov planning agent, with an inherently inertial decision process, and that uses heuristics and partial problem knowledge to plan its actions. We applied a statistical framework to fit and test the quality of a proposed planning model (Monte Carlo Tree Search). Our framework allows us to parse out independent contributions to problem‐solving based on the construction of the value function and on general mechanisms of the search process in the tree of solutions. We show that the latter are correlated with children's performance on an independent measure of planning, while the former is highly domain specific.     

Polytomous multilevel testlet models for testlet‐based assessments with complex sampling designs

A pplications of standard item response theory models assume local independence of items and persons. This paper presents polytomous multilevel testlet models for dual dependence due to item and person clustering in testlet‐based assessments with clustered samples. Simulation and survey data were analysed with a multilevel partial credit testlet model. This model was compared with three alternative models – a testlet partial credit model (PCM), multilevel PCM, and PCM – in terms of model parameter estimation. The results indicated that the deviance information criterion was the fit index that always correctly identified the true multilevel testlet model based on the quantified evidence in model selection, while the Akaike and Bayesian information criteria could not identify the true model. In general, the estimation model and the magnitude of item and person clustering impacted the estimation accuracy of ability parameters, while only the estimation model and the magnitude of item clustering affected the item parameter estimation accuracy. Furthermore, ignoring item clustering effects produced higher total errors in item parameter estimates but did not have much impact on the accuracy of ability parameter estimates, while ignoring person clustering effects yielded higher total errors in ability parameter estimates but did not have much effect on the accuracy of item parameter estimates. When both clustering effects were ignored in the PCM, item and ability parameter estimation accuracy was reduced.     

Estimation and visualization of confusability matrices from adaptive measurement data

We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes.     

Photic Stimulation of Young Rats

Zajonc, Harrison, and their colleagues have recently conducted a series of studies demonstrating a positive, monotonic relation between frequency of “mere” exposure and liking for stimuli. Other studies have found either the inverted-U relation or a decrease in liking. It was proposed that an emphasis upon mere exposure may be somewhat misleading, and that a concern with degree of stimulus familiarity might be more fruitful. Conflicting forms of the exposure-liking relation seem to be potentially reconcilable if consideration is given to factors that influence the rate at which stimuli become familiar, or capable of being anticipated and represented in memory.

Two experiments using stimuli and procedures taken from Zajonc (23) yielded a positive, monotonic relation between frequency and liking. A third experiment, designed to produce greater attention to the stimuli and thus hasten familiarization, yielded an inverted-U relation. A fourth experiment used simpler verbal stimuli than the first three. This was designed to result in even faster familiarization. As expected, there was a negative relation between liking and exposure frequency.

The “frequency group” of investigators has explained the monotonic exposure effect in terms of the response competition hypothesis. However, the latter is incapable of handling a nonmonotonic relation. A reasonable alternative seems to be the expectancy arousal hypothesis (5): viz., that liking is maximum for stimuli that arouse moderately strong expectancies of either a “molar” or a “molecular” nature. Previous research (5, 6, 7, 8) has supported this hypothesis, although some of the studies are also amenable to the response competition hypothesis. A further experiment was designed to distinguish between predictions from the response competition and the expectancy arousal hypotheses. The results supported the latter.     

Universality of the reversal transition in growth phenomena of molecular crystals

ABSTRACT

The fundamental origin of the reversal transition during crystal growth has been investigated by Monte Carlo simulations. Evidence is provided supporting the geometrical nature of the transition, arising from the broken translational invariance at the growth front and the interactions of multipoles of opposed parity. The range of interactions, the details of the force field and model are irrelevant to the occurrence and only determine the functional behaviour of the relevant physical quantities like the localisation of the critical point and the morphology of the phase diagram.     

Bayesian Factor Analysis as a Variable-Selection Problem: Alternative Priors and Consequences

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor-loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, Muthén & Asparouhov proposed a Bayesian structural equation modeling (BSEM) approach to explore the presence of cross loadings in CFA models. We show that the issue of determining factor-loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov's approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike-and-slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set is used to demonstrate our approach.     

The Impact of Item Misspecification and Dichotomization on Class and Parameter Recovery in LCA of Count Data

Mixture analysis of count data has become increasingly popular among researchers of substance use, behavioral analysis, and program evaluation. However, this increase in popularity seems to have occurred along with adoption of some conventions in model specification based on arbitrary heuristics that may impact the validity of results. Findings from a systematic review of recent drug and alcohol publications suggested count variables are often dichotomized or misspecified as continuous normal indicators in mixture analysis. Prior research suggests that misspecifying skewed distributions of continuous indicators in mixture analysis introduces bias, though the consequences of this practice when applied to count indicators has not been studied. The present work describes results from a simulation study examining bias in mixture recovery when count indicators are dichotomized (median split; presence vs. absence), ordinalized, or the distribution is misspecified (continuous normal; incorrect count distribution). All distributional misspecifications and methods of categorizing resulted in greater bias in parameter estimates and recovery of class membership relative to specifying the true distribution, though dichotomization appeared to improve class enumeration accuracy relative to all other specifications. Overall, results demonstrate the importance of accurately modeling count indicators in mixture analysis, as misspecification and categorizing data can distort study outcomes.     

Higher-order latent trait models for cognitive diagnosis

Higher-order latent traits are proposed for specifying the joint distribution of binary attributes in models for cognitive diagnosis. This approach results in a parsimonious model for the joint distribution of a high-dimensional attribute vector that is natural in many situations when specific cognitive information is sought but a less informative item response model would be a reasonable alternative. This approach stems from viewing the attributes as the specific knowledge required for examination performance, and modeling these attributes as arising from a broadly-defined latent trait resembling theϑ of item response models. In this way a relatively simple model for the joint distribution of the attributes results, which is based on a plausible model for the relationship between general aptitude and specific knowledge. Markov chain Monte Carlo algorithms for parameter estimation are given for selected response distributions, and simulation results are presented to examine the performance of the algorithm as well as the sensitivity of classification to model misspecification. An analysis of fraction subtraction data is provided as an example. This research was funded by National Institute of Health grant R01 CA81068. We would like to thank William Stout and Sarah Hartz for many useful discussions, three anonymous reviewers for helpful comments and suggestions, and Kikumi Tatsuoka and Curtis Tatsuoka for generously sharing data.     

计算机化自适应测验中原始题项目参数的估计

计算机化自适应测验(Computerized Adaptive Testing, 简称CAT)其安全性面临着新的挑战, 小题库的安全更受威胁。如何建设一个大型、优质的题库成为CAT研究中一个非常重要的课题。目前CAT题库的建设存在一些问题, 如成本高且保密性较差。尤其是等值技术较复杂且锚题重复使用容易造成泄露。如能在实施CAT过程中插入未经过参数估计的项目(原始题), 同时对原始题项目参数进行估计, 这对建设大型、优质的CAT题库来说其意义是不言而喻的。本文基于1PLM和2PLM对此进行研究, 提出了原始题在线估计的新方法以及推导出了求区分度参数a迭代初值的计算公式。研究结果表明：无论是模拟研究还是实证研究, 原始题被作答的次数对项目参数估计结果都会产生不同的影响, 并且原始题作答人数越多项目参数估计精度也越高。     

AN ANALYTIC FORM FOR THE INTERRESPONSE TIME ANALYSIS OF SHULL, GAYNOR, AND GRIMES WITH APPLICATIONS AND EXTENSIONS

Shull, Gaynor and Grimes advanced a model for interresponse time distribution using probabilistic cycling between a higher-rate and a lower-rate response process. Both response processes are assumed to be random in time with a constant rate. The cycling between the two processes is assumed to have a constant transition probability that is independent of bout length. This report develops an analytic form of the model which has a natural parametrization for a higher-rate within-bout responding and a lower-rate visit-initiation responding. The analytic form provides a convenient basis for both a nonlinear least-squares data reduction technique to estimate the model's parameters and Monte Carlo simulations of the model. In addition, the analytic formulation is extended to both a refractory period for the rats' behavior and, separately, the strongly-banded behavior seen with pigeons.