## 3 Research Methodology
### Preparing the Survey Data  
This section describes the preparation of the survey data for integration into the CA method to assess the benefits and challenges of DTs and the integration of DTs with AI. Data preparation consists of coding and processing missing data. Coding the survey data using a five-point Likert scale is essential for data analysis. This involves assigning numerical values to the participants' responses to facilitate the quantitative analysis. The coded data were used to convert the linguistic variables (five-point Likert scale) to ordinal variables. The Likert scales of Very low, Low, Medium, High, and Very high were coded as 1, 2,3, 4, and 5, respectively. The missing data process is essential when dealing with questionnaire data because missing data can significantly impact the integrity and validity of research findings. Missing data can be attributed to the absence of responses or incomplete information in the collected survey. To ensure data completeness, it is crucial to address missing data effectively. Several common methods and techniques address missing questionnaire data. The participants' responses to the survey were complete, and there were no missing answers; therefore, no type of missing data processing was applied. Identification of Significant Benefits and Challenges of Applying the Correspondence Analysis Method  
The data were structured into a contingency table where the rows represent the responses and the columns represent the factors. Each cell represents the response using a Likert scale point. The computing of the contribution of factors using a five-point Likert scale through CA involves identifying the relative importance of factors by analyzing the relationships between the rows (respondents) and columns (factors). The process is outlined in the following steps, adapted from ([PERSON] et al., 2016). Correspondence analysis (CA) is performed to analyze the association between rows (respondents) and columns (factors). The total of all values in the table is first computed using Equation (2):  
\[N=\sum_{i=1}^{n}\sum_{j=1}^{m}a_{ij} \tag{2}\]  
where n represents the number of rows (respondents), and m represents the columns (factors). Then, the row totals and column totals are calculated using Equations (3) and (4), respectively:  
\[r_{i}=\sum_{j=1}^{m}a_{ij} \tag{3}\]  
\[c_{j}=\sum_{i=1}^{n}a_{ij} \tag{4}\]  
After that, each cell \(a_{ij}\) is divided by the grand N as in Equation (5) and \(P_{ij}\) isobtained:  
\[P_{ij}=\frac{a_{ij}}{N} \tag{5}\]  
Computing Row and Column Profiles  
The row profile (\(f_{ij}\)) and column profiles (\(g_{ij}\)) are computed using Equation (6) and Equation (7), respectively. \[f_{ij}=\frac{a_{ij}}{ri} \tag{6}\]  
\[g_{ij}=\frac{a_{ij}}{c_{j}} \tag{7}\]  
Then, the expected frequencies under independence (\(e_{ij}\)) can be computed using Equation (8):  
\[e_{ij}=\frac{r_{i}c_{j}}{N} \tag{8}\]  
The deviations from independence (\(d_{ij}\)) are shown in Equation (9):  
\[d_{ij}=\frac{P_{ij}-e_{ij}}{\sqrt{e_{ij}}} \tag{9}\]  
The total inertia measures the variance (or dispersion) in the data, which can be explained by the correspondence analysis. It is computed as:  
\[I=\sum_{i}\sum_{j}\frac{\left(a_{ij}-e_{ij}\right)^{2}}{e_{ij}} \tag{10}\]Singular value decomposition (SVD) is performed for the D matrix as in Equation (11):  
\[D=U\sum V^{T} \tag{11}\]  
where U is the left singular vectors (row coordinates), \(\Sigma\) is singular values (strength of association), and V is right singular vectors (column coordinates).