Jürgen Rost

Rasch Models in Latent Classes: An Integration of Two Approaches to Item Analysis.

A model is proposed that combines the theoret ical strength of the Rasch model with the heuristic power of latent class analysis. It assumes that the Rasch model holds for all persons within a latent class, but it allows for different sets of item parameters between the latent classes. An estima tion algorithm is outlined that gives conditional maximum likelihood estimates of item parameters for each class. No a priori assumption about the item order in the latent classes or the class sizes is required. Application of the model is illustrated, both for simulated data and for real data.

Latent trait and latent class models

and Overview.- I Latent Trait Theory.- 1 Measurement Models for Ordered Response Categories.- 2 Testing a Latent Trait Model.- 3 Latent Trait Models with Indicators of Mixed Measurement Level.- II Latent Class Theory.- 4 New Developments in Latent Class Theory.- 5 Log-Linear Modeling, Latent Class Analysis, or Correspondence Analysis: Which Method Should Be Used for the Analysis of Categorical Data?.- 6 A Latent Class Covariate Model with Applications to Criterion-Referenced Testing.- III Comparative Views of Latent Traits and Latent Classes.- 7 Test Theory with Qualitative and Quantitative Latent Variables.- 8 Latent Class Models for Measuring.- Chaffer 9 Comparison of Latent Structure Models.- IV Application Studies.- 10 Latent Variable Techniques for Measuring Development.- 11 Item Bias and Test Multidimensionality.- 12 On a Rasch-Model-Based Test for Noncomputerized Adaptive Testing.- 13 Systematizing the Item Content in Test Design.

A Conditional Item-Fit Index for Rasch Models:

A new item-fit index is proposed that is both a descriptive measure of deviance of single items and an index for statistical inference. This index is based on the assumptions of the dichotomous and polytomous Rasch models for items with ordered categories and, in particular, is a standardization of the conditional likelihood of the item pattern that does not depend on the item parameters. This approach is compared with other methods for determining item fit. In contrast to many other item-fit indexes, this index is not based on response-score residuals. Results of a simulation study illustrating the performance of the index are provided. An asymptotically normally distributed Z statistic is derived and an empirical example demonstrates the sensitivity of the index with respect to item and person heterogeneity. Index terms: appropriateness measurement, item discrimination, item fit, partial credit model, Rasch model.

Polytomous Mixed Rasch Models

In this chapter, the discrete mixture distribution framework is developed for Rasch models for items with a polytomous ordered response format. Four of these models will be considered, based on different restrictions regarding the so-called threshold distances (Section 20.2). Since the concept of thresholds is basic for understanding this family of Rasch models, Section 20.1 elaborates the threshold concept in some detail. Section 20.3 focusses on parameter estimation, particularly describing some results on the computation of the γ-functions which correspond to the symmetric functions of the dichotomous Rasch model. Section 20.4 gives some references to applications of these models.

A Typology of Students' Interest in Physics and the Distribution of Gender and Age within Each Type.

This paper deals with the identification of qualitatively different types of interest in physics among students in the 12‐16 age range in Germany. Using the statistical tool of mixed‐Rasch analysis three groups of students with distinctly different interest patterns were identified. The three types are characterized in terms of preferred interest pattern, age and gender distribution, preferences over other subjects and physics‐related self‐concept. The consequences for physics education are discussed.

Mixture Distribution Rasch Models

This chapter deals with the generalization of the Rasch model to a discrete mixture distribution model. Its basic assumption is that the Rasch model holds within subpopulations of individuals, but with different parameter values in each subgroup. These subpopulations are not defined by manifest indicators, rather they have to be identified by applying the model. Model equations are derived by conditioning out the class-specific ability parameters and introducing class-specific score probabilities as model parameters. The model can be used to test the fit of the ordinary Rasch model. By means of an example it is illustrated that this goodness-of-fit test can be more powerful for detecting model violations than the conditional likelihood ratio test by Andersen.

Multidimensional Rasch Measurement via Item Component Models and Faceted Designs

A multidimensional Rasch model is presented here, which is a multidimensional extension of item component models. Relations to existing multidimensional item response theory models are discussed. Apart from other applications, it is also suitable for analyzing tests and questionnaires, which are designed according to two or more facets. An application to a 77-item questionnaire on students’ interest in physics with a two-facet structure demonstrates that the model parameters can even be estimated when 17 latent dimensions are to be measured simultaneously (by means of joint maximum likelihood methods).

RATING SCALE ANALYSIS WITH LATENT CLASS MODELS

A general approach for analyzing rating data with latent class models is described, which parallels rating models in the framework of latent trait theory. A general rating model as well as a two-parameter model with location and dispersion parameters, analogous to Andrichs Dislocmodel are derived, including parameter estimation via the EM-algorithm. Two examples illustrate the application of the models and their statisticalcontrol. Model restrictions through equality constrains are discussed and multiparameter generalizations are outlined.

19 Mixture Distribution Item Response Models

This chapter provides an overview of research on mixture distribution models for item response data. Mixture distribution models assume that the observed item response data are sampled from a composite population, that is, a population consisting of a number of components or sub-populations. In contrast to multi-group models, mixture distribution models do not assume a known partition of the population but use an un-observed grouping variable to model the item response data. Mixture distribution models do not typically assume that the mixing variable is observed, but offer ways to collect evidence about this variable by means of model assumptions and observed heterogeneity in the data. The components of a mixture distribution can be distinguished by the differences between the parameters of the assumed distribution model that governs the conditional distribution of the observed data. In the case of item response data, it may be assumed that either different parameter sets hold in different sub-populations or, in even more heterogeneous mixtures, different item response models hold in different sub-populations. Item response models such as the Rasch model, the 2-parameter and 3-parameter logistic model, and the generalized partial credit model have been extended to mixture distribution IRT models. This chapter introduces the derivation of mixture distribution models based on different origins and gives an overview of current fields of application in educational measurement, psychology, and other fields.

Naturwissenschaftliche Grundbildung: Testkonzeption und Ergebnisse

Die Leitfrage von PISA lautet, inwieweit die Jugendlichen auf die Herausforderungen der heutigen Wissensgesellschaft vorbereitet werden. Einen erheblichen Teil des gesellschaftlichen Wissens produzieren die Naturwissenschaften; der Zuwachs an Erkenntnissen erfolgt in diesen Disziplinen nach wie vor stark beschleunigt. Die Naturwissenschaften pragen die Wissensgesellschaft aber auch durch einen besonderen Umgang mit Wissen. Das naturwissenschaftliche Forschen und Argumentieren zeichnet sich durch systematische und rationale Verfahren aus, mit denen Wissen gewonnen, gepruft, mitgeteilt und diskutiert wird. Naturwissenschaftliche Erkenntnisse und ihre Anwendungen schaffen die Grundlage fur Innovationen, die weit uber die Wissenschaft hinaus weisen und alle Lebensbereiche beruhren. Die Naturwissenschaften sind auch ein entscheidender Wirt-schaftsfaktor. Sie stellen die Wissensbasis bereit fur Entscheidungen uber die Gestaltung unserer Lebensbedingungen. Damit besitzen die Naturwissenschaften eine Schlusselrolle fur den technologischen und gesellschaftlichen Wandel und fur die Sicherung der Lebensgrundlagen auf nationaler wie globaler Ebene. Alles weist darauf hin, dass die Naturwissenschaften und die mit ihnen verbundenen technischen Disziplinen in der absehbaren Zukunft noch mehr an Bedeutung gewinnen werden. Wer den Anschluss an diese sich dynamisch entwickelnden Gebiete verliert, hat wenig Chancen, ihn je wieder zu erlangen.