## 3 Data and Methods
### Methodology  
The generalized linear model (GLM) is an extension of traditional linear regression that allows response variables to follow distributions other than the normal distribution. GLMs are used for a wide range of data types, including binary outcomes (logistic regression), count data (Poisson regression), and more. The model is characterized by specifying a linear predictor and a link function that connects the linear predictor to the expected value of the response variable. The GLM framework introduced by [PERSON] and [PERSON] [51] extends linear regression by allowing the mean component \(\mu_{i}\) to be linked to a linear predictor via a nonlinear function, while the distribution of the stochastic component \(\epsilon_{i}\) can belong to any member of the linear exponential family. Specifically, a GLM specification includes:  
* a linear predictor or index \(\eta_{i}=X_{i}^{\prime}\beta+o_{i}\), unde oi is an optional offset term;
* a distribution for \(Y_{i}\) belonging to the linear exponential family;
* a smooth, invertible link function, \(g(\mu_{i})=\eta_{i}\), relating the mean \(\mu_{i}\) and the linear predictor \(\eta_{i}\)  
The GLM assumptions imply that the first two moments of \(Y_{i}\) may be written as functions of the linear predictor:  
\[\mu_{i}=g^{-1}(\eta_{i}) \tag{1}\]  
\[V_{i}=\left(\frac{\phi}{\omega_{i}}\right)V_{R}\left(g^{-1}(\eta_{i})\right) \tag{2}\]  
where \(V_{\mu}\) (\(\mu\)) is a distribution-specific variance function describing the mean-variance relationship, the dispersion constant \(\phi\) > 0 is a possibly known scale factor, and \(\omega_{i}\) > 0 is a known prior weight that corrects for unequal scaling between observations. In GLMs, the Newton-Raphson and Marquardt methods are used to iteratively estimate the model parameters by maximizing the log-likelihood function [52]. The Newton-Raphson algorithm is a root-finding algorithm used to solve equations by iteratively improving guesses. In the context of GLMs, it is employed to find the parameter estimates that maximize the likelihood function. The method converges quickly near the optimum if the initial guess is close enough to the true parameter values and requires computation of the Hessian matrix. The Marquardt method combines gradient descent and the Newton-Raphson algorithm to improve convergence, especially when the initial parameter estimates are far from the optimum. The method is less sensitive to poor initial guesses and can handle nonlinearities better [53]. The selection of GLM in this study is based on several key considerations related to the characteristics of the data and the research objectives. Traditional linear regression models operate under the assumption of normally distributed residuals, constant variance, and linear relationships between variables. However, environmental and economic data often \begin{table}
\begin{tabular}{c c c c c c} \hline  & **GHG** & **REN** & **AFFORD** & **INFR** & **USAD** \\ \hline Mean & \(1.44\times 10^{8}\) & 17.3528 & 28.1678 & 96.4807 & 72.6803 \\ Median & \(8.02\times 10^{7}\) & 15.9695 & 27.4550 & 99.8500 & 71.6600 \\ Maximum & \(3.82\times 10^{8}\) & 25.0320 & 43.6800 & 100.0000 & 107.6800 \\ Minimum & \(4.50\times 10^{7}\) & 9.2810 & 12.8600 & 61.2000 & 45.3400 \\ Std. Dev. & \(1.29\times 10^{8}\) & 4.7838 & 9.5904 & 8.5946 & 14.5435 \\ Skewness & 1.0793 & 0.2550 & 0.1901 & \(-\)2.9462 & 0.4775 \\ Kurtosis & 2.2909 & 1.7393 & 1.8656 & 10.7930 & 3.0700 \\ Jarque–Bera & 11.1866 & 4.0071 & 3.1014 & 206.8140 & 1.9873 \\ Probability & 0.0037 & 0.1348 & 0.2120 & 0.0000 & 0.3702 \\ \hline \end{tabular} Source: Own processing, 2024.  
\end{table} 
Table 2: Descriptive statistics of the variables. exhibit deviations from these assumptions due to inherent complexities, nonlinearity, and heteroskedasticity. GLM provides a more flexible modeling framework that accommodates a wider range of data distributions and relationships, making it particularly well-suited for analyzing the impact of digital transformation on environmental sustainability indicators.