The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

Analyzing sequential categorical data: Individual variation in markov chains

Markov chains are probabilistic models for sequences of categorical events, with applications throughout scientific psychology. This paper provides a method for anlayzing data consisting of event sequences and covariate observations. It is assumed that each sequence is a Markov process characterized by a distinct transition probability matrix. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. The elements of the transition probability matrices are written as functions of a vector of latent variables, with variation in the latent variables explained through a multivariate regression on the covariates. The regression is estimated using the EM algorithm, and requires the numerical calculation of a multivariate integral. An example using simulated cognitive developmental data is presented, which shows that the estimation of individual variation in the parameters of a probability model may have substantial theoretical importance, even when individual differences are not the focus of the investigator's concerns.Research contributing to this article was supported by B.R.S. Subgrant 5-35345 from the University of Virginia. I thank the DADA Group, Bill Fabricius, Don Hartmann, William Griffin, Jack McArdle, Ivo Molenaar, Ronald Schoenberg, Simon Tavaré, and several anonymous reviewers for their discussion of these points.     

On the sampling theory roundations of item response theory models

Item response theory (IT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the stochastic subject versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating versus estimating -predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.A presidential address can serve many different functions. This one is a report of investigations I started at least ten years ago to understand what IRT was all about. It is a decidedly one-sided view, but I hope it stimulates controversy and further research. I have profited from discussions of this material with many people including: Brian Junker, Charles Lewis, Nicholas Longford, Robert Mislevy, Ivo Molenaar, Donald Rock, Donald Rubin, Lynne Steinberg, Martha Stocking, William Stout, Dorothy Thayer, David Thissen, Wim van der Linden, Howard Wainer, and Marilyn Wingersky. Of course, none of them is responsible for any errors or misstatements in this paper. The research was supported in part by the Cognitive Science Program, Office of Naval Research under Contract No. Nooo14-87-K-0730 and by the Program Statistics Research Project of Educational Testing Service.     

Modeling item responses when different subjects employ different solution strategies

A model is presented for item responses when different subjects employ different strategies, but only responses, not choice of strategy, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of strategies, we model response probabilities in terms of item parameters for each strategy, proportions of subjects employing each strategy, and distributions of subject proficiency within strategies. The probabilities that an individual subject employed the various strategies can then be obtained, along with a conditional estimate of proficiency under each. A conceptual example discusses response strategies for spatial rotation tasks, and a numerican example resolves a population of subjects into subpopulations of valid responders and random guessers.The first author's work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. We are grateful to Murray Aitkin, Isaac Bejar, Neil Dorans, Frederiksen, and Marklyn Wingersky for their comments and suggestions, and to Alison Gooding, Maxine Kingston, Donna Lembeck, Joling Liang, and Kentaro Yamamoto for their assistance with Example 2.     

Continuous and discrete latent structure models for item response data

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.     

The use of the occupational stress indicator (OSI) in factory workers in China

The purpose of the study was to investigate occupational stress among Chinese factory workers (N=342), from three cities of South East China, using the shortened version of the Occupational Stress Indicator (OSI)-2. The results showed that the reliabilities and predictive validity of the OSI-2 subscales and other subscales used for the study were reasonably high. Quite a high percentage of workers perceived high work pressure. The main sources of stress were intrinsic to the job; and the coping strategies that were most frequently used to tackle stress were “control” methods. In addition, “satisfaction on environmental condition” seemed to be a common predictor for job satisfaction, and mental and physical well-being. The logical relationships between job satisfaction, mental well-being and physical well-being in Chinese workers have provided support to the findings obtained in Western countries.     

分时距认知特点的研究

本研究探讨了分时距估计的认知特点,检验了SS模型、PT模型和CS模型的预测效度,结果表明：分时距估计主要是在信息提取阶段采用分段推算策略对时间信息进行重建的过程,变化／分割和注意分配对分时距估计有显著影响;SS模型的预测效度最低,PT、CS模型的预测效度较高。