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Measurement and analysis of quality of life related to environmental hazards: the methodology illustrated by recent epidemiological studies
Published in Jiuping Xu, Syed Ejaz Ahmed, Zongmin Li, Big Data and Information Theory, 2022
In Section 2, some important measurement models used in HrQoL research are introduced. Within that section, we show how some important inequalities involving the Kullback–Leibler measure of association among conditionally independent variables can be very helpful in the process of validation. Then, the family of Rasch measurement models is introduced. The Rasch model can be considered as the standard of unidimensional measurement models. It must be used as a ‘docking’ target in building unidimensional scores. The statistical validation of health related quality-of-life measurement models is thoroughly considered in Section 3. First, we define the reliability of a measurement and we give its expression, and the expression for the reliability of the sum of item responses under a parallel model, which is estimated by Cronbach’s α-coefficient. Then the backward reliability curve is presented, and its connection with the notion of unidimensionality is explained, and consequently how it can be used to check empirically the unidimensionality of a set of variables. Cronbach’s α-coefficient is well known as a reliability or internal consistency coefficient, but is of little help in the process of validating questionnaires. On the other hand, the backward reliability curve can be very helpful in the assessment of unidimensionality, which is a crucial measurement property. We explain why, when such a curve is not increasing, the lack of unidimensionality of a set of questions is strongly suspected.
Improving mathematics diagnostic tests using item analysis
Published in International Journal of Mathematical Education in Science and Technology, 2023
The statistical analysis of results can be quite sophisticated. For instance, Rach and Ufer (2020) analysed students' scores on an entrance test, and its use as a predictor of success on a first analysis course. Their analysis was based on the Rasch model, which is one of a family of models in item response theory (DeMars, 2010). These models aim to establish a single scale on which to estimate both the difficulty of items on the test and the ability of individual students. This approach can help to reveal issues in a test: for example, Xie et al. (2019) used an item response theory model to evaluate a diagnostic test in computer science, and their analysis highlighted several questions that were too difficult for the group of students taking the test. We make use of item response theory in our analysis and give a detailed explanation in Section 4.5.
Beyond text comprehension: exploring items’ characteristics and their effect on foreign students’ disadvantage in mathematics
Published in International Journal of Mathematical Education in Science and Technology, 2022
Clelia Cascella, Chiara Giberti
The Rasch model is a logistic one that provides, for all items and subjects, an estimation of (item) difficulty and (person) ability used to scale both items and subjects according to the same latent trait. In fact, in the Rasch model, it is hypothesized that the probability of giving a correct answer depends on a student’s relative ability (i.e. his/her ability compared to item difficulty) exclusively: other variables (such as students’ personal features, like citizenship status or gender) should not affect the probability of answering an item successfully. The Rasch model is especially adequate for pursuing our paper’s goals because it has the property of measurement invariance. As stated by Rasch, ‘The comparison between two stimuli should be independent of which particular individuals were instrumental for the comparison. Symmetrically, a comparison between two individuals should be independent of which particular stimuli within the class considered were instrumental for comparison’ (1960, p. 332). Measurement invariance, a characteristic of the Rasch model and of this class of models specifically (Andrich & Marais, 2019, p. 329), thus allows groups the comparability that is the crux of our study.
Analysis of Mixed English Teaching Model based on Rasch Model and Construction of DE-FAHP-based Comprehensive Weight Quantization Model
Published in Applied Artificial Intelligence, 2023
The Rasch model is a useful tool for achieving objective detection and improving traditional measurement methods. It has been widely used in various research fields, including education and classroom teaching. In this section, we will focus on the application of the Rasch model in these areas.