Further examinations of the category-recall function

Subjects were assigned to use either three or six categories and were given either 5 or 10 trials in a word-sorting task. Subsequent to sorting, they recalled as many words as they could. A measure of sorting consistency showed that the six-category sort was a more difficult task than was the three-category sort. Number of categories did not have a significant effect on recall performance regardless of whether 5 or 10 sorting trials were used. A correlational analysis raised questions about the relationship of the sorting tasks to recall performance and clustering.     

A New Zero-Inflated Negative Binomial Methodology for Latent Category Identification

We introduce a new statistical procedure for the identification of unobserved categories that vary between individuals and in which objects may span multiple categories. This procedure can be used to analyze data from a proposed sorting task in which individuals may simultaneously assign objects to multiple piles. The results of a synthetic example and a consumer psychology study involving categories of restaurant brands illustrate how the application of the proposed methodology to the new sorting task can account for a variety of categorization phenomena including multiple category memberships and for heterogeneity through individual differences in the saliency of latent category structures.     

Collecting paired-comparison data with a sorting algorithm

Monte Carlo techniques were used to evaluate the performance of an on-line paired-comparisons data collection procedure that makes use of a common computer sorting algorithm. The results revealed that the sorting method can reduce the number of trials per subject substantially even when a considerable amount of random error is present. While a complete paired-comparisons design requires N(N?1)/2 trials (where N is the number of objects), the sorting procedure requires a theoretical minimum of N(log₂N) trials. The savings in the number of trials consequently increases with N. Furthermore, the negative effect of random error on the final ordering of the data from the sorting method is small and decreases with the number of stimuli. The data from a small empirical study reinforces the Monte Carlo observations. It is recommended that the sorting method be used in place of the complete paired-comparisons procedure whenever a substantial number of stimuli are included in the design.     

Structure in the classification of stimuli differing on several continuous attrjbutes’

Subjects were requested to sort sets of multidimensional stimuli differing in tint or shade, size, shape, and orientation. Each S received either 64 triangles selected at random from a larger population or 16 selected at random from the sample of 64. On one sort he was allowed to select the number ofcategories to be used; otherwise, he was required to distribute the stimuli among four, five, and six categories, respectively. The predominant strategy proved to be simple abstraction, with incomplete generalization a frequent alternative. On all but a few of the sorts, the sorting principle involved the use of one or a pair of attributes. In addition, Ss displayed a marked tendency toward numerical balance in their sorts and, when allowed to select the number of categories to be used, to limit them to a relatively small number. Imai has previously reported numerical balance and the use of a limited number of categories also to characterize the sorting of stimuli differing on discontinuous attributes. Informational measures proved helpful in describing such aspects of classification behavior as response uncertainty, numerical balance, and efficiency in abstraction.     

Form characteristics of category-retrieval relationships in children and adults

Subjects from Grades 2, 4, 6, and college performed a sort-recall task with 24 noncategorized items, using two 12-item sorts, four 6-item sorts, or six 4-item sorts. Among the children, the effects of increasing unitization at study were uneven across the category size conditions used and did not resemble the linear patterns shown by adults. Second graders showed retrieval advantages only for the smallest categories used, whereas fourth and sixth graders benefited from the use of moderately sized sorting categories but failed to show additional improvements for smaller sorting categories. An examination of subjects' sorting explanations suggested that different category-retrieval patterns may reflect better and poorer item relations established in smaller and larger categories, respectively. Sort conditions affording the best recall at the different grade levels were those in which subjects established the greatest number of contextual and categorical (taxonomic) relations among sorted items.     

Does maintenance of colour categories rely on language? Evidence to the contrary from a case of semantic dementia

Recent neuropsychological evidence, supporting a strong version of Whorfian principles of linguistic relativity, has reinvigorated debate about the role of language in colour categorisation. This paper questions the methodology used in this research and uses a novel approach to examine the unique contribution of language to categorisation behaviour. Results of three investigations are reported. The first required development of objective measures of category coherence and consistency to clarify questions about healthy control performance on the freesorting colour categorisation task used in previous studies. Between-participant consistency was found to be only moderate and the number of colour categories generated was found to vary markedly between individuals. The second study involved longitudinal neuropsychological examination of a patient whose colour categorisation strategy was monitored in the context of a progressive decline in language due to semantic dementia. Performance on measures of category coherence and consistency was found to be relatively stable over time despite a profound decline in the patient's colour language. In a final investigation we demonstrated that, for both the patient and controls, between- and within-participant consistency were higher than expected by (a) random sorting and (b) sorting perceptually similar chips together. These findings indicate that the maintenance of colour categorisation need not depend on language.     

Feature selection and classification: A developmental study

Two hundred and thirteen children between the ages of 4 and 16 sorted 30 complex objects freely into groups. These were either schematic faces, schematic imaginary animals, or histoform patterns and were constructed from 9 independently and continuously varying features, each with 10 levels. The three sets were equivalent in terms of underlying numerical structure. A new method of analysis of the groups formed yielded the following direct measures of subjective organization in the sorting of each child: the number of features used in sorting, the accuracy of sorting, and the number of independent dimensions of classification. Both the material and the analysis of sorting were devised on the assumption that only some of the component features of complex objects are used for classification, while others are ignored. Sorting performance differed markedly both with age and with different types of material. The improvement in sorting ability with age, except for the youngest children, could be attributed to an increase in the number of features used rather than an improvement in the accuracy of use. In contrast, the poor sorting of histoform patterns as opposed to faces and animals was due to a low level of sorting accuracy. The basic results on the development of classification confirmed previous studies, and hence suggest that it is valid to consider feature selection as a basic component of classification.     

The effect of correlated linguistic dimensions on speeded classification of visually presented trigrams

The influence of two types of linguistic dimensions, word-nonword and consonant pronunciation, on classification speed of trigrams in card-sorting tasks of two levels of complexity was examined. In complex grouping tasks, which required the evaluation of more than one letter to classify each stimulus, sorting times were faster when the linguistic dimension was correlated with, rather than orthogonal to, the response categories. For tasks in which each stimulus could be classified on the basis of a single letter, no effect of the correlated vs orthogonal linguistic dimension was observed, even when performance was degraded by visual noise. These results provide further evidence that, while linguistic properties of visual stimuli may influence classification time in complex tasks, they are of little importance in the performance of tasks only requiring the discriminalion of a single visual feature.     

Free sorting with stimuli clustered in a multidlmensional attribute space

An experiment was conducted to determine whether Ss leam, without knowledge of results or prior familiarization with the prototypes, to sort histoform stimuli generated by three probablistic rules into categories consistent with these mies. Seven Ss were asked to sort 30 stimuli (10 from each schema population) on each trial. No constraints were placed on the number of categories to be used. A statistic was developed to measure consistency between schema-defined categories and subjeet-defined categories. Four of the seven Ss met the leaming criterion, and demonstrated increasing consistency with the schema-defined categories across trials. In general, more categories than necessary were used to classify the stimuli correctly. The results raise several questions about classification strategies used by Ss in perceptual learning tasks with stimuli generated by probabilistic rules, and indicate the need for further research conceming the variables that influence perceptual category formation.     

Abstract: Evaluation of Test Statistics for Robust Structural Equation Modeling With Nonnormal Missing Data

Traditional structural equation modeling (SEM) techniques have trouble dealing with incomplete and/or nonnormal data that are often encountered in practice. Yuan and Zhang (2011a) developed a two-stage procedure for SEM to handle nonnormal missing data and proposed four test statistics for overall model evaluation. Although these statistics have been shown to work well with complete data, their performance for incomplete data has not been investigated in the context of robust statistics.

Focusing on a linear growth curve model, a systematic simulation study is conducted to evaluate the accuracy of the parameter estimates and the performance of five test statistics including the naive statistic derived from normal distribution based maximum likelihood (ML), the Satorra-Bentler scaled chi-square statistic (RML), the mean- and variance-adjusted chi-square statistic (AML), Yuan-Bentler residual-based test statistic (CRADF), and Yuan-Bentler residual-based F statistic (RF). Data are generated and analyzed in R using the package rsem (Yuan & Zhang, 2011b).

Based on the simulation study, we can observe the following: (a) The traditional normal distribution-based method cannot yield accurate parameter estimates for nonnormal data, whereas the robust method obtains much more accurate model parameter estimates for nonnormal data and performs almost as well as the normal distribution based method for normal distributed data. (b) With the increase of sample size, or the decrease of missing rate or the number of outliers, the parameter estimates are less biased and the empirical distributions of test statistics are closer to their nominal distributions. (c) The ML test statistic does not work well for nonnormal or missing data. (d) For nonnormal complete data, CRADF and RF work relatively better than RML and AML. (e) For missing completely at random (MCAR) missing data, in almost all the cases, RML and AML work better than CRADF and RF. (f) For nonnormal missing at random (MAR) missing data, CRADF and RF work better than AML. (g) The performance of the robust method does not seem to be influenced by the symmetry of outliers.     

认知诊断测验中基于信息矩阵的多群组DIF检验

基于改进的Wald统计量,将适用于两群组的DIF检测方法拓展至多群组的项目功能差异（DIF）检验;改进的Wald统计量将分别通过计算观察信息矩阵（Obs）和经验交叉相乘信息矩阵（XPD）而得到。模拟研究探讨了此二者与传统计算方法在多个群组下的DIF检验情况,结果表明：（1）Obs和XPD的一类错误率明显低于传统方法,DINA模型估计下Obs和XPD的一类错误率接近理论水平;（2）样本量和DIF量较大时,Obs和XPD具有与传统Wald统计量大体相同的统计检验力。     

The development of the category-recall relationship in the sorting-recall task

The relationship between categorical organization and recall for children in grades two, four, and six (ages 8, 10 and 12 years, respectively), and for adults was investigated using the sorting-recall procedure. Subjects sorted unrelated words on individual cards into either two, four, or six categories prior to output, and recall performance improved significantly as a function of increased numbers of sorting categories. The category-recall relationship was shown to be independent of the effects of subject-determined item exposure time in sorting. This result was taken as evidence for a basic structural property of memory (“chunking”) that does not vary as a function of age. We further speculated that the slopes of the category-recall function obtained in this study suggest a limit on the size of organizational units in young children's memory.     

A Two-Stage Model of Category Construction

The current consensus is that most natural categories are not organized around strict definitions (a list of singly necessary and jointly sufficient features) but rather according to a family resemblance (FR) principle: Objects belong to the same category because they are similar to each other and dissimilar to objects in contrast categories. A number of computational models of category construction have been developed to provide an account of how and why people create FR categories (Anderson, 1990; Fisher, 1987). Surprisingly, however, only a few experiments on category construction or free sorting have been run and they suggest that people do not sort examples by the FR principle. We report several new experiments and a two-stage model for category construction. This model is contrasted with a variety of other models with respect to their ability to account for when FR sorting will and will not occur. The experiments serve to identify one basis for FR sorting and to support the two-stage model. The distinctive property of the two-stage model is that it assumes that people impose more structure than the examples support in the first stage and that the second stage adjusts for this difference between preferred and perceived structure. We speculate that people do not simply assimilate probabilistic structures but rather organize them in terms of discrete structures plus noise.     

Use of relational and item-specific information in remembering by older and younger adults

The applicability to older adults of predictions from the integrated memory model, that optimal memory results from concurrent availability of relational and item-specific information, was assessed. In Experiment 1, older adults (M = 69 years) encoded related or unrelated words using rating, sorting, or both tasks. Using both tasks produced better recall than either separate task. Rating facilitated recall for related items, but sorting did not facilitate unrelated items. In Experiment 2, younger (M = 20) and older (M = 74) adults sorted or rated lists comprising categories of varying sizes. Young adults' free recall conformed to predictions, but older adults again showed facilitation mainly from rating larger categories. The stronger effects for younger adults imply that specific combinations of encoding and retrieval manipulations and materials must be considered in predicting older adults' performance.     

Retrieval processes in recognition

Retrieval processes in the long-term recognition of well organized material showed the expected organizational effects on “slow” recognition responses. Ss sorted 100 words into two to seven categories until a stable organization was achieved. The data showed the usual correlations between organization (number of categories used) and recall and recognition. Recognition tests a week after the sorting task revealed no differences between Ss using many or few categories for the “fast” recognition responses, defined as the faster 50% of each S’s latency distribution. The organizational effect was clearly evident for the “slow” 50% of the responses. The data support the retrieval check hypothesis in recognition under the assumption that retrieval operations take additional time during the recognition process.     

Induction and category coherence

In studies of category formation, subjects rarely construct family resemblance categories. Instead, they divide objects into categories using a single dimension. This is a puzzling result given the widely accepted view that natural categories are organized in terms of a family resemblance principle. The observation that natural categories support inductive inferences is used here to test the hypothesis that family resemblance categories would be constructed if stimuli were first used to generate inductive inferences. In two experiments, subjects answered either induction questions, which made interproperty relationships more salient, or frequency questions, which required information only about individual properties, before they performed a sorting task. Subjects were likely to produce family resemblance sorts if they had first answered induction questions but not if they had answered frequency questions.     

Sufficient statistics and latent trait models

For questionnaires with two answer categories, it has been proven in complete generality that if a minimal sufficient statistic exists for the individual parameter and if it is the same statistic for all values of the item parameters, then the raw score (or the number of correct answers) is the minimal sufficient statistic. It follows that the model must by of the Rasch type with logistic item characteristic curves and equal item-discriminating powers.This paper extends these results to multiple choice questionnaires. It is shown that the minimal sufficient statistic for the individual parameter is a function of the so-called score vector. It is also shown that the so-called equidistant scoring is the only scoring of a questionnaire that allows for a real valued sufficient statistic that is independent of the item parameters, if a certain ordering property for the sufficient statistic holds.     

Some Paradoxical Results for the Quadratically Weighted Kappa

The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories n it is shown that if one of the raters uses the same base rates for categories 1 and n, categories 2 and n−1, and so on, then the value of quadratically weighted kappa does not depend on the value of the center cell of the agreement table. Since the center cell reflects the exact agreement of the two raters on the middle category, this result questions the applicability of the quadratically weighted kappa to agreement studies. If one wants to report a single index of agreement for an ordinal scale, it is recommended that the linearly weighted kappa instead of the quadratically weighted kappa is used.     

Relational properties and memory-based category construction.

Although many experiments have investigated factors that constrain perceptual category construction, there have been no investigations of factors that constrain memory-based (MB) category construction. Six experiments examined the extent to which perceptual and MB sorting were influenced by correlated dimensions, family resemblance principles, and conceptual knowledge. Sensitivity to many types of relational information (e.g., correlated features, causal relations, interactive properties of objects, and family resemblance relations) was observed with perceptual sorting, but these properties were rarely used to organize information in MB sorting conditions. Instead, there was a clear preference to organize categories around single dimensions. Even when perfectly correlated features were causally related, Ss in memory conditions did not use correlations to construct categories. The strengths and limitations of MB analyses and categorizations are discussed.