Browsing by Author "Muraki, Eiji"

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    Fitting a polytomous item response model to Likert-type data
    (1990) Muraki, Eiji
    This study examined the application of the MML-EM algorithm to the parameter estimation problems of the normal ogive and logistic polytomous response models for Likert-type items. A rating-scale model was developed based on Samejima’s (1969) graded response model. The graded response model includes a separate slope parameter for each item and an item response parameter. In the rating-scale model, the item response parameter is resolved into two parameters: the item location parameter, and the category threshold parameter characterizing the boundary between response categories. For a Likert-type questionnaire, where a single scale is employed to elicit different responses to the items, this item response model is expected to be more useful for analysis because the item parameters can be estimated separately from the threshold parameters associated with the points on a single Likert scale. The advantages of this type of model are shown by analyzing simulated data and data from the General Social Surveys. Index terms: EM algorithm, General Social Surveys, graded response model, item response model, Likert scale, marginal maximum likelihood, polytomous item response model, rating-scale model.
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    Full-information factor analysis for polytomous item responses
    (1995) Muraki, Eiji; Carlson, James E.
    A full-information item factor analysis model for multidimensional polytomously scored item response data is developed as an extension of previous work by several authors. The model is expressed both in factor-analytic and item response theory parameters. Reckase’s multidimensional parameters for the model also are discussed as well as the related geometry. An EM algorithm for estimation of the model parameters is presented and results of the analysis of item response data by a computer program incorporating this algorithm are presented. Index terms: EM algorithm, full-information item factor analysis, multidimensional item response theory, polytomous response data.
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    Full-information item factor analysis
    (1988) Bock, R. Darrell; Gibbons, Robert; Muraki, Eiji
    A method of item factor analysis based on Thurstone’s multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm is described. Statistical significance of successive factors added to the model is tested by the likelihood ratio criterion. Provisions for effects of guessing on multiple-choice items, and for omitted and not-reached items, are included. Bayes constraints on the factor loadings are found to be necessary to suppress Heywood cases. Numerous applications to simulated and real data are presented to substantiate the accuracy and practical utility of the method. Index terms: Armed Services Vocational Aptitude Battery, Beta prior, E M algorithm, Item factor analysis, TESTFACT, Tetrachoric correlation.
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    Full-information item factor analysis: Applications of EAP scores
    (1985) Muraki, Eiji; Engelhard, George, Jr.
    The full-information item factor analysis model proposed by Bock and Aitkin (1981) is described, and some of the characteristics of expected a posteriori (EAP) scores are illustrated. Three simulation studies were conducted to illustrate the model, and an application of full-information item factor analysis to a set of real data is described.
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    A generalized partial credit model: Application of an EM algorithm
    (1992) Muraki, Eiji
    The partial credit model (PCM) with a varying slope parameter is developed and called the generalized partial credit model (GPCM). The item step parameter of this model is decomposed to a location and a threshold parameter, following Andrich’s (1978) rating scale formulation. The EM algorithm for estimating the model parameters is derived. The performance of this generalized model is compared on both simulated and real data to a Rasch family of polytomous item response models. Simulated data were generated and then analyzed by the various polytomous item response models. The results demonstrate that the rating formulation of the GPCM is quite adaptable to the analysis of polytomous item responses. The real data used in this study consisted of the National Assessment of Educational Progress (Johnson & Allen, 1992) mathematics data that used both dichotomous and polytomous items. The PCM was applied to these data using both constant and varying slope parameters. The GPCM, which provides for varying slope parameters, yielded better fit to the data than did the PCM. Index terms: item response model, National Assessment of Educational Progress, nominal response model, partial credit model, polytomous response model, rating scale model.
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    Information functions of the generalized partial credit model
    (1993) Muraki, Eiji
    The concept of information functions developed for dichotomous item response models is adapted for the partial credit model. The information function is explained in terms of the model parameters and scoring functions. The relationship between the item information function and the item response function also is discussed. The information function then is used to investigate the effect of collapsing and recoding categories of polytomously-scored items of the National Assessment of Educational Progress (NAEP). The NAEP writing items were calibrated and the item and test information is used to discuss desirable properties of polytomous items. Index terms: information function, item response model, National Assessment of Educational Progress (NAEP), partial credit model, polytomous item response model.