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  • 1
    Electronic Resource
    Electronic Resource
    Some neglected problems in IRT (1995)
    Springer
    Psychometrika 60 (1995), S. 459-487 
    Details
    ISSN: 1860-0980
    Keywords: measurement ; IRT ; Rasch model ; measurement of change ; DIF ; Mantel-Haenszel statistic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract The paper addresses three neglected questions from IRT. In section 1, the properties of the “measurement” of ability or trait parameters and item difficulty parameters in the Rasch model are discussed. It is shown that the solution to this problem is rather complex and depends both on general assumptions about properties of the item response functions and on assumptions about the available item universe. Section 2 deals with the measurement of individual change or “modifiability” based on a Rasch test. A conditional likelihood approach is presented that yields (a) an ML estimator of modifiability for given item parameters, (b) allows one to test hypotheses about change by means of a Clopper-Pearson confidence interval for the modifiability parameter, or (c) to estimate modifiability jointly with the item parameters. Uniqueness results for all three methods are also presented. In section 3, the Mantel-Haenszel method for detecting DIF is discussed under a novel perspective: What is the most general framework within which the Mantel-Haenszel method correctly detects DIF of a studied item? The answer is that this is a 2PL model where, however, all discrimination parameters are known and the studied item has the same discrimination in both populations. Since these requirements would hardly be satisfied in practical applications, the case of constant discrimination parameters, that is, the Rasch model, is the only realistic framework. A simple Pearsonx 2 test for DIF of one studied item is proposed as an alternative to the Mantel-Haenszel test; moreover, this test is generalized to the case of two items simultaneously studied for DIF.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02294324
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Applying the principles of specific objectivity and of generalizability to the measurement of change (1987)
    Springer
    Psychometrika 52 (1987), S. 565-587 
    Details
    ISSN: 1860-0980
    Keywords: latent trait theory ; item response theory ; measurement of change ; logistic latent trait models ; specific objectivity ; conjoint measurement ; additivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract A formal framework for measuring change in sets of dichotomous data is developed and implications of the principle of specific objectivity of results within this framework are investigated. Building upon the concept of specific objectivity as introduced by G. Rasch, three equivalent formal definitions of that postulate are given, and it is shown that they lead to latent additivity of the parametric structure. If, in addition, the observations are assumed to be locally independent realizations of Bernoulli variables, a family of models follows necessarily which are isomorphic to a logistic model with additive parameters, determining an interval scale for latent trait measurement and a ratio scale for quantifying change. Adding the further assumption of generalizability over subsets of items from a given universe yields a logistic model which allows a multidimensional description of individual differences and a quantitative assessment of treatment effects; as a special case, a unidimensional parameterization is introduced also and a unidimensional latent trait model for change is derived. As a side result, the relationship between specific objectivity and additive conjoint measurement is clarified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02294820
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    An irt-based model for dichotomous longitudinal data (1989)
    Springer
    Psychometrika 54 (1989), S. 599-624 
    Details
    ISSN: 1860-0980
    Keywords: Rasch models ; logistic models ; measurement of change
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract The LLRA (linear logistic model with relaxed assumptions; Fischer, 1974, 1977a, 1977b, 1983a) was developed, within the framework of generalized Rasch models, for assessing change in dichotomous item score matrices between two points in time; it allows to quantify change on latent trait dimensions and to explain change in terms of treatment effects, treatment interactions, and a trend effect. A remarkable feature of the model is that unidimensionality of the item set is not required. The present paper extends this model to designs with any number of time points and even with different sets of items presented on different occasions, provided that one unidimensional subscale is available per latent trait. Thus unidimensionality assumptions within subscales are combined with multidimensionality of the item set. Conditional maximum likelihood methods for parameter estimation and hypothesis testing are developed, and a necessary and sufficient condition for unique identification of the model, given the data, is derived. Finally, a sample application is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02296399
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    An extension of the partial credit model with an application to the measurement of change (1994)
    Springer
    Psychometrika 59 (1994), S. 177-192 
    Details
    ISSN: 1860-0980
    Keywords: Partial credit model ; Rasch model ; item response theory ; measurement of change ; assessment of treatment effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract The partial credit model is considered under the assumption of a certain linear decomposition of the item × category parametersδ ih into “basic parameters”α j. This model is referred to as the “linear partial credit model”. A conditional maximum likelihood algorithm for estimation of theα j is presented, based on (a) recurrences for the combinatorial functions involved, and (b) using a “quasi-Newton” approach, the so-called Broyden-Fletcher-Goldfarb-Shanno (BFGS) method; (a) guarantees numerically stable results, (b) avoids the direct computation of the Hesse matrix, yet produces a sequence of certain positive definite matricesB k ,k=1, 2, ..., converging to the asymptotic variance-covariance matrix of the $$\hat \alpha _j $$ . The practicality of these numerical methods is demonstrated both by means of simulations and of an empirical application to the measurement of treatment effects in patients with psychosomatic disorders.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02295182
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    Paper (German National Licenses)
    Fulltext
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