# Resilience Analysis Grid-Rasch Rating Scale Model for Measuring Organizational Resilience Potential
## 2 Materials and Methods
### RAG-Rasch Analysis  
In the present study, we applied the Rasch rating scale model, also called the polytomous Rasch model (hence, RSM), to synthetically generate data for an ideal questionnaire based on [PERSON]'s general one to assess item functionality and to facilitate score inter pretation, following the foundational framework outlined by [PERSON] et al. [53]. The synthetic data generation and the analytical procedure were entirely carried out in the R environment for statistical computing mainly using the TAM package for Rasch analysis [54; 55]. Responses were encoded to ensure the lowest category was assigned a value of zero, adhering to the requirements of the TAM package. Although the synthetic nature of the data precluded missing values, in real data scenarios, missing responses would be imputed to maintain the integrity of the scale's analysis.  
Likert-scale instruments, commonly analyzed through the RSM, allow for the detection of item misfit and differential item functioning, which can reveal deviations from the original conceptual design of the instrument [56; 57; 58]. The RSM assumes that the structure of the response categories is consistent across all items, meaning that the category thresholds are the same for each item. Such assumption aligns well with the uniform scaling of our items. We modeled organizations' responses to account for the relationship between item responses and latent organizational resilience levels. To assess model fit, we first fitted the RSM to the response data and examined summary indices, inspecting the average of organization ability estimates, which reflects the average respondent level on the latent trait.  
We computed individual item fit statistics to verify item conformity to RSM expectations. Mean square (MNSQ) and standardized fit statistics (ZSTD) for both infit and outfit measures were calculated using Bond and Fox's guidelines for acceptable MNSQ ranges (0.6 to 1.4) and ZSTD values (\(\pm\)2) for Likert-scale items [35]. Items exhibiting ZSTD values above +2 were considered underfitting, indicating overly unpredictable response patterns, while ZSTD values below \(-\)2 suggested overfitting, indicating excessively predictable patterns. The infit and outfit MNSQ and ZSTD statistics for each organization were calculated, using the same criteria as for item fit to assess how well each organization's response pattern conformed to the model expectations.  
Next, we analyzed item difficulty estimates, which place each item on the latent trait continuum. The term _endorsement of an item_ indicates that a respondent selects one of the higher response categories that indicates agreement, approval, or affirmation of the item's statement. Note that higher item difficulty values indicate more challenging items for organizations to endorse. For example, in the case at hand for the anticipating resilience ability, the term endorsement indicates which aspects of the specific ability's resilience potential are more difficult to achieve.  
Finally, we estimated the organizational ability levels (person calibration), providing a measure of each organization's position on the latent trait continuum. Higher ability estimates indicate higher levels of the latent trait, allowing for the comparison of organizations based on their specific resilience potential. Furthermore, we generated item characteristic curves (ICCs) for each item to illustrate the likelihood of selecting each response category based on organization ability, thereby assessing the discriminative capacity of each item and the functionality of the response categories.  
The R syntaxes and datasets are available on the Open Science Framework (OSF), as Supplementary Materials, at the following link: [[https://osf.io/w56a2/?view_only=a4f343](https://osf.io/w56a2/?view_only=a4f343)]([https://osf.io/w56a2/?view_only=a4f343](https://osf.io/w56a2/?view_only=a4f343)) d5b82c4 fb99014 ce5f8c57f0 dd (accessed on 4 December 2024).