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Herbert Hoijtink - One of the best experts on this subject based on the ideXlab platform.

  • market segmentation using brand strategy research bayesian inference with respect to mixtures of log linear models
    Journal of Classification, 2009
    Co-Authors: Pascal Van Hattum, Herbert Hoijtink
    Abstract:

    This paper presents a Bayesian model based clustering approach for Dichotomous Item responses that deals with issues often encountered in model based clustering like missing data, large data sets and within cluster dependencies. The approach proposed will be illustrated using an example concerning Brand Strategy Research.

  • the multidimensionality of self report schizotypy in a psychiatric population an analysis using multidimensional rasch models
    Schizophrenia Bulletin, 2000
    Co-Authors: Meinte G Vollema, Herbert Hoijtink
    Abstract:

    There is increasing empirical evidence from factor analytical studies that schizotypy is composed of three dimensions. All studies into the multidimensionality of schizotypy used common factor analysis of scales, either exploratory or confirmatory. We argue that for research into the multidimensionality of schizotypy with Dichotomous Item responses on questionnaires (as with the Schizotypal Personality Questionnaire [SPQ], Raine 1991) much can be learned using generalized multidimensional Rasch models (GMRMs). GMRMs require a priori postulated models of schizotypy, which can be tested in confirmatory analyses. We hypothesized four competing models of schizotypy, based on the literature and clinical impressions-two two-dimensional models and two three-dimensional models. We also hypothesized that Items differ in the degree they are indicative of a particular dimension of schizotypy. The sample was 418 psychiatric inpatients and outpatients, with moderate levels of psychopathology, who filled in the SPQ. Both three-dimensional models yielded a much better fit to the data than both two-dimensional models. Our revised three-dimensional model, a revision of that by Raine et al. (1994) and Gruzelier (1996), yielded the best fit. It consisted of positive schizotypy, disorganization, and negative schizotypy. The results strongly suggest that schizotypy, as measured with the SPQ, is a three-dimensional construct.

David Thissen - One of the best experts on this subject based on the ideXlab platform.

  • further investigation of the performance of s x2 an Item fit index for use with Dichotomous Item response theory models
    Applied Psychological Measurement, 2003
    Co-Authors: Maria Orlando, David Thissen
    Abstract:

    This study presents new findings on the utility of S - X2 as an Item fit index for Dichotomous Item response theory models. Results are based on a simulation study in which Item responses were generated and calibrated for 100 tests under each of 27 conditions. The Item fit indices S - X2 and Q1 - X2 were calculated for each Item. ROC curves were constructed based on the hit and false alarm rates of the two indices. Examination of these curves indicated that in general, the performance of S - X2 improved with test length and sample size. The performance of S - X2 was superior to that of Q1 - X2 under most but not all conditions. Results from this study imply that S - X2 may be a useful tool in detecting the misfit of one Item contained in an otherwise well-fitted test, lending additional support to the utility of the index for use with Dichotomous Item response theory models. Index Terms: Item response theory, S - X2, Q1 - X, model = data fit, Item fit index.

  • likelihood based Item fit indices for Dichotomous Item response theory models
    Applied Psychological Measurement, 2000
    Co-Authors: Maria Orlando, David Thissen
    Abstract:

    New goodness-of-fit indices are introduced for Dichotomous Item response theory (IRT) models. These indices are based on the likelihoods of number-correct scores derived from the IRT model, and they provide a direct comparison of the modeled and observed frequencies for correct and incorrect responses for each number-correct score. The behavior of Pearson’s X2 (S-X2) and the likelihood ratio G2 (S-G2) was assessed in a simulation study and compared with two fit indices similar to those currently in use (Q1-X2 and Q1-G2). The simulations included three conditions in which the simulating and fitting models were identical and three conditions involving model misspecification. S-X2 performed well, with Type I error rates close to the expected .05 and .01 levels. Performance of this index improved with increased test length. S-G2 tended to reject the null hypothesis too often, as did Q1-X2 and Q1-G2. The power of S-X2 appeared to be similar for all test lengths, but varied depending on the type of model misspe...

Fritz Drasgow - One of the best experts on this subject based on the ideXlab platform.

Andries L Van Der Ark - One of the best experts on this subject based on the ideXlab platform.

  • a note on stochastic ordering of the latent trait using the sum of polytomous Item scores
    Psychometrika, 2010
    Co-Authors: Andries L Van Der Ark, Wicher Bergsma
    Abstract:

    In contrast to Dichotomous Item response theory (IRT) models, most well-known polytomous IRT models do not imply stochastic ordering of the latent trait by the total test score (SOL). This has been thought to make the ordering of respondents on the latent trait using the total test score questionable and throws doubt on the justifiability of using nonparametric polytomous IRT models for ordinal measurement. We show that a broad class of polytomous IRT models has a weaker form of SOL, denoted weak SOL, and argue that weak SOL justifies ordering respondents on the latent trait using the total test score and, therefore, the use of nonparametric polytomous IRT models for ordinal measurement.

  • stochastic ordering of the latent trait by the sum score under various polytomous irt models
    Psychometrika, 2005
    Co-Authors: Andries L Van Der Ark
    Abstract:

    The sum score is often used to order respondents on the latent trait measured by the test. Therefore, it is desirable that under the chosen model the sum score stochastically orders the latent trait. It is known that unlike Dichotomous Item response theory (IRT) models, most polytomous IRT models do not imply stochastic ordering. It is unknown, however, (1) whether stochastic ordering is often or rarely violated and (2) whether violations yield a serious problem for practical data analysis. These are the central issues of this paper. First, some unanswered questions that pertain to polytomous IRT models implying stochastic ordering were investigated. Second, simulation studies were conducted to evaluate stochastic ordering in practical situations. It was found that for most polytomous IRT models that do not imply stochastic ordering, the sum score can be used safely to order respondents on the latent trait.

Maria Orlando - One of the best experts on this subject based on the ideXlab platform.

  • further investigation of the performance of s x2 an Item fit index for use with Dichotomous Item response theory models
    Applied Psychological Measurement, 2003
    Co-Authors: Maria Orlando, David Thissen
    Abstract:

    This study presents new findings on the utility of S - X2 as an Item fit index for Dichotomous Item response theory models. Results are based on a simulation study in which Item responses were generated and calibrated for 100 tests under each of 27 conditions. The Item fit indices S - X2 and Q1 - X2 were calculated for each Item. ROC curves were constructed based on the hit and false alarm rates of the two indices. Examination of these curves indicated that in general, the performance of S - X2 improved with test length and sample size. The performance of S - X2 was superior to that of Q1 - X2 under most but not all conditions. Results from this study imply that S - X2 may be a useful tool in detecting the misfit of one Item contained in an otherwise well-fitted test, lending additional support to the utility of the index for use with Dichotomous Item response theory models. Index Terms: Item response theory, S - X2, Q1 - X, model = data fit, Item fit index.

  • likelihood based Item fit indices for Dichotomous Item response theory models
    Applied Psychological Measurement, 2000
    Co-Authors: Maria Orlando, David Thissen
    Abstract:

    New goodness-of-fit indices are introduced for Dichotomous Item response theory (IRT) models. These indices are based on the likelihoods of number-correct scores derived from the IRT model, and they provide a direct comparison of the modeled and observed frequencies for correct and incorrect responses for each number-correct score. The behavior of Pearson’s X2 (S-X2) and the likelihood ratio G2 (S-G2) was assessed in a simulation study and compared with two fit indices similar to those currently in use (Q1-X2 and Q1-G2). The simulations included three conditions in which the simulating and fitting models were identical and three conditions involving model misspecification. S-X2 performed well, with Type I error rates close to the expected .05 and .01 levels. Performance of this index improved with increased test length. S-G2 tended to reject the null hypothesis too often, as did Q1-X2 and Q1-G2. The power of S-X2 appeared to be similar for all test lengths, but varied depending on the type of model misspe...