Browsing by Author "Andrich, David"

Now showing 1 - 7 of 7
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    Application of a psychometric rating model to ordered categories which are scored with successive integers
    (1978) Andrich, David
    A latent trait measurement model in which ordered response categories are both parameterized and scored with successive integers is investigated and applied to a summated rating or Likert questionnaire. In addition to each category, each item of the questionnaire and each subject are parameterized in the model; and maximum likelihood estimates for these parameters are derived. Among the features of the model which make it attractive for applications to Likert questionnaires is that the total score is a sufficient statistic for a subject’s attitude measure. Thus, the model provides a formalization of a familiar and practical procedure for measuring attitudes.
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    The application of an unfolding model of the PIRT type to the measurement of attitude
    (1988) Andrich, David
    Unfolding data for unidimensional variables constructed from direct responses (e.g., agreement or disagreement) are characterized by single peaked functions involving the locations of each person and each stimulus. A continuous discrirninal process, of the form postulated by Thurstone when he proposed his Law of Comparative Judgment, is suggested. This process is transformed to a qualitative dichotomous response in which the probability of endorsement is governed by the square of the distance between the locations of the person and the stimulus. Maximum likelihood estimates of the parameters are derived, and it is shown that the information associated with any response is a bimodal function of the difference between the person and stimulus locations. The feasibility of parameter estimation is demonstrated with a limited simulation study. The model is applied to a set of statements designed to measure attitudes toward capital punishment and scaled by the methods of Thurstone. The responses conformed to the unfolding mechanism, and the scale values of the statements are statistically equivalent to those obtained by Thurstone’s methods. Index terms: Attitude measurement, Developmental data, Discriminal process, Item response theory, Person response theory, Thurstone scaling, Unfolding data, Unidimensional scaling.
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    Distinctive and incompatible properties of two common classes of IRT models for graded responses
    (1995) Andrich, David
    Two classes of models for graded responses, the first based on the work of Thurstone and the second based on the work of Rasch, are juxtaposed and shown to satisfy important, but mutually incompatible, criteria and to reflect different response processes. Specifically, in the Thurstone models if adjacent categories are joined to form a new category, either before or after the data are collected, then the probability of a response in the new category is the sum of the probabilities of the responses in the original categories. However, the model does not have the explicit property that if the categories are so joined, then the estimate of the location of the entity or object being measured is invariant before and after the joining. For the Rasch models, if a pair of adjacent categories are joined and then the data are collected, the estimate of the location of the entity is the same before and after the joining, but the probability of a response in the new category is not the sum of the probabilities of the responses in the original categories. Furthermore, if data satisfy the model and the categories are joined after the data are collected, then they no longer satisfy the same Rasch model with the smaller number of categories. These differences imply that the choice between these two classes of models for graded responses is not simply a matter of preference; they also permit a better understanding of the choice of models for graded response data as a function of the underlying processes they are intended to represent. Index terms: graded responses, joining assumption, polytomous IRT models, Rasch model, Thurstone model.
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    A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses
    (1993) Andrich, David; Luo, Guanzhong
    Social-psychological variables are typically measured using either cumulative or unfolding response processes. In the former, the greater the location of a person relative to the location of a stimulus on the continuum, the greater the probability of a positive response; in the latter, the closer the location of the person to the location of the statement, irrespective of direction, the greater the probability of a positive response. Formal probability models for these processes are, respectively, monotonically increasing and single-peaked as a function of the location of the person relative to the location of the statement. In general, these models have been considered to be independent of each other. However, if statements constructed on the basis of a cumulative model have three ordered response categories, the response function within the statement for the middle category is in fact single-peaked. Using this observation, a unidimensional model for responses to statements that have an unfolding structure was constructed from the cumulative Rasch model for ordered response categories. A location and unit of measurement parameter exist for each statement. A joint maximum likelihood estimation procedure was investigated. Analysis of a small simulation study and a small real dataset showed that the model is readily applicable. Index terms: attitude measurement, item response theory, latent trait theory, latent trait theory, Rasch models, unfolding data, unidimensional scaling.
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    Hyperbolic cosine latent trait models for unfolding direct responses and pairwise preferences
    (1995) Andrich, David
    The hyperbolic cosine unfolding model for direct responses of persons to individual stimuli is elaborated in three ways. First, the parameter of the stimulus, which reflects a region within which people located there are more likely to respond positively than negatively, is shown to be a property of the data and not arbitrary as first supposed. Second, the model is used to construct a related model for pairwise preferences. This model, for which joint maximum likelihood estimates are derived, satisfies strong stochastic transitivity. Third, the role of substantive theory in evaluating the fit between the data and the models, in which unique solutions for the estimates are not guaranteed, is explored by analyzing responses of one group of persons to a single set of stimuli obtained both as direct responses and pairwise preferences. Index terms: direct responses, hyberbolic cosine model, item response theory, latent trait models, pair comparisons, pairwise preferences, unfolding models.
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    A probabilistic IRT model for unfolding preference data
    (1989) Andrich, David
    A probabilistic model is developed for the pair-comparison design in which the unfolding principle that governs the choice process uses a discriminal process analogous to Thurstone’s Law of Comparative Judgment. However, this process is governed by the square of the distance between the location of the person and the stimulus, rather than controlled by the location of the stimulus as in Thurstone’s formulation. A simulation study demonstrates the feasibility of estimation, and two examples use real data to show the implications of the unfolding models for psychological research. Index terms: choice data, item response theory, pair comparisons, preference data, unfolding.
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    Relationships between the Thurstone and Rasch approaches to item scaling
    (1978) Andrich, David
    When the logistic function is substituted for the normal, Thurstone’s Case V specialization of the law of comparative judgment for paired comparison responses gives an identical equation for the estimation of item scale values as does the Rasch formulation for direct responses. The law of comparative judgment must be modified to include a subject parameter; but this parameter, which is eliminated statistically with respect to the direct response design, is eliminated experimentally in the paired comparison design. Some comparisons and contrasts are made between the two approaches to item scaling, and it is shown that greater generalizability for item scaling is possible when the two approaches are juxtaposed appropriately.