# Resilience Analysis Grid-Rasch Rating Scale Model for Measuring Organizational Resilience Potential
## 2 Materials and Methods
### The Rasch Model  
The Rasch model is a statistical approach that is primarily employed in the field of measurement theory, particularly for the examination of the data obtained from questionnaires, educational tests, or psychometric surveys [35]. It is an integral component of item response theory (IRT), yet it possesses distinctive characteristics that differentiate it from other models [36]. The Rasch measurement model, while primarily used in the fields of psychometrics and human sciences, has been effectively applied across various disciplines because of its versatility and robustness [35; 37]. In the field of psychological sciences, it is a fundamental tool for developing and validating assessment instruments as well as ensuring measurement precision and validity [37; 38; 39; 40; 41]. As a peculiar application case, it has been employed as a tool to develop a questionnaire for measuring videogaming engagement levels [42]. In marketing, the Rasch model has been used to analyze customer satisfaction surveys and brand perception [43] and to measure affective responses to products [44], while in the field of economics, it was employed to analyze the construct of poverty [45]. In health sciences, particularly in rheumatology, the Rasch model has been increasingly used over the past two decades to validate outcome measures and develop new scales [46]: a systematic review identified 114 relevant articles, with a focus on rheumatoid arthritis, osteoarthritis, and general musculoskeletal disorders. The Rasch model has been used in the field of rehabilitation to assess patient outcomes and comparing them over time [47]. An extensive use of Rasch analysis has emerged in diagnostic imaging [48; 49; 50]. It is noteworthy that within the domain of safety science, the Rasch model was utilized for evaluating the preparedness and awareness regarding the risk of flooding [51] and more specifically within the OHS domain to conduct a psychometric evaluation of the leading indicators suggested by organizational performance metrics [52]. The model, formulated by Danish mathematician [PERSON], is predicated on the fundamental premise that the probability of a respondent selecting a particular category for an item is a function of only two variables: the latent ability of the examinee to be high-scoring on an item of a test or questionnaire and the intrinsic difficulty of the item. The Rasch model postulates that each item can be characterized by an item difficulty parameter (\(\delta\)), while the response categories are defined by threshold parameters that are consistent across all items. The ability of each respondent is represented by a single person (ability) parameter (\(\theta\)) (see Equation (1)). \[ln\bigg{[}\frac{P_{n_{i}}(x=k)}{P_{n_{i}}(x=k-1)}\bigg{]}=\theta_{n}-\delta_{ i}-\tau_{k} \tag{1}\]  
The parameters are positioned on a uniform logit scale (log-odds), thereby ensuring direct comparability between groups and samples. The model predicts that as a respondent's ability level increases relative to an item's difficulty, the probability of selecting higher response categories increases. Conversely, as the item's difficulty exceeds the individual's ability, the probability of selecting lower response categories increases. The likelihood of choosing each response category given a person's ability level is plotted through the item characteristic curves (ICCs) to help evaluate the discriminative power of each item and the functioning of the response categories. The independent calibration of item difficulty and individual ability permits the application of the same questionnaire items in disparate populations, ensuring the consistency of difficulty measures irrespective of specific sample characteristics. In addition, the Rasch model estimates the extent of the match between empirically observed responses and modeled response patterns. Infit statistics are more sensitive to unexpected responses from individuals whose abilities are close to the item's difficulty level.