Browsing by Author "Macready, George B."

Now showing 1 - 4 of 4
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    Comparing fit of nonsubsuming probability models
    (1985) Alvord, Gregory; Macready, George B.
    A "mixture" probability model that incorporates two component models defined by nonsubsuming sets of parameters is introduced, and a strategy for using this model in the selection of a preferred component model is developed. Example applications of the suggested strategy are considered for the special case in which the Rasch item response model and a Latent State Mastery model are the component models compared. Simulated data sets generated under each of these models were used to provide example applications of the proposed model selection strategy.
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    The nature and use of state mastery models
    (1980) Macready, George B.; Dayton, C. Mitchell
    This paper provides a review of a class of probabilistic models that has been developed for use in the assessment of trait or competency acquisition. Consideration is given to the relative merits and limitations of this class of state models, under which trait acquisition is conceived as being "all-ornone," as compared with those occurring under an alternative conceptual framework, in which trait acquisition is assumed to be gradual. In addition, some of the applications of these state models are presented, including the establishment of mastery classification decisions and the assessment of consistency with respect to items and classification. Finally, some extensions to the class of state models, which may be helpful in increasing the applicability of this class of models, are presented.
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    A simulation study of the difference chi-square statistic for comparing latent class models under violation of regularity conditions
    (1989) Holt, Judith A.; Macready, George B.
    This study explored the robustness of the likelihood ratio difference statistic to the violation of a regularity condition when used to assess differences in fit provided by pairs of latent class models. Under regularity conditions, the additive property of the likelihood ratio statistic can be used to assess the statistical difference between pairs of hierarchically related models (i.e., one model is a constrained form of the other). However, when one of the two models being compared is obtained by fixing parameters of the other model at boundary values (i.e., 0 or 1), a regularity condition is violated and the difference statistic is not necessarily distributed as x². The effects of three independent variables on the distribution of the difference statistics were studied for two generation models and a variety of subsuming models. Differential effects in terms of the direction and the extent of deviation were produced according to the types of model comparisons; these effects negate the application of a simple correction to the statistic to achieve a x² distribution. Recommendations are made regarding how this statistic might reasonably be used under violation of the regularity condition. Index terms: latent class model, likelihood ratio chi-square, mixture model, regularity conditions, tests of fit.
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    The use of generalizability theory for assessing relations among items within domains in diagnostic testing
    (1983) Macready, George B.
    The purpose of this study was to describe a procedure based on generalizability theory for assessing the adequacy of item groupings generated by means of a domain-referenced testing system. The procedure is based on an exploration of the extent to which items are grouped into homogeneous sets with similar levels of difficulty, when the sets are defined on the basis of a logical analysis of the perceived skills underlying the items. In addition, an example of the use of the developed analytic procedure is presented.