# Digitalization of Public Services--An Input Output Logit Analysis
## 3 Materials and Methods
### Methodology  
IT was used as an independent variable. Satisfaction is a dependent variable. Another dependent variable, i.e., AD, was used in the data; it is a transformed binary variable for which satisfaction and IT are independent variables. We established a limit of 4 to convert outcomes (satisfaction) into a binary dependent variable AD of 1 (general agreement) and 0 (overall disagreement). It may be noted that our response data are ordinal on a five-point Likert scale, where 5 stands for strongly agreed, 4 agreed, 3 neutral, 2 disagreed, and 1 for strongly disagreed. To achieve this transformation, for all client responses \(\geq\) 4, we assigned a value of 1 to this additional variable, and for all responses \(<\) 4, we assigned 0. In this way, we assumed a careful and conservative approach in handling and analyzing the response data. First, we present a general analysis of the summary statistics generated from Stata. The summary statistics for all three variables are offered in both tabular and graphic form. Other than numerical and average estimates, we present estimates of the skewness, kurtosis, and coefficient of variation. Secondly, we calculated [PERSON]'s alpha to assess the reliability and internal consistency of the data's test items. Moreover, [PERSON]'s alpha was applied to test the strength and consistency of the data [20]. To calculate [PERSON]'s alpha, we correlated the score for each scale item with the total score \begin{table}
\begin{tabular}{c l c c} \hline \hline  & **Department/Ministry** & **No. of Questionnaires** & **No. of Questionnaires** \\  & **Collected from Employees (\(n1=200\))** & **Collected from Clients (\(n2=200\))** \\ \hline  & Department of & & \\
1. & Immigration \& & 10 \\  & Emigration & & \\
2. & Department of Register & & 10 \\  & of Persons & & 10 \\
3. & Department of Import & & 10 \\  & and Export & & \\
4. & Department of & & 10 \\  & Examination & & 10 \\
5. & Department of Customs & & 10 \\  & Department of Motor & & 10 \\
6. & Traffic & & 10 \\
7. & Department of Registrar & & 10 \\  & General & & 10 \\
8. & Department of Pension & & 10 \\
9. & Department of Fisheries & & 10 \\
10. & Department of Railway & & 10 \\
11. & Department of Labor & & 10 \\
12. & Ministry of Education & & 10 \\
13. & Ministry of Healthcare & & 10 \\
14. & Election Commission & & 10 \\
15. & Police Commission & & 10 \\
16. & Foreign Bureau & & 10 \\
17. & Electricity Board & & 10 \\
18. & Central Bank & & 10 \\
19. & National Transport & & 10 \\  & Commission & & \\
20. & Ministry of Foreign & & 10 \\  & Affairs & & \\ \hline  & & Total responses (\(n=400\)) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Departments and ministries surveyed. for each observation of our survey. Later, we compared that to the variance for all the individual item scores as per the following equation. \[\alpha=\left(\frac{j}{j-1}\right)\left(1-\frac{\sum_{i=1}^{k}\alpha_{y_{i}}^{2}} {\alpha_{x}^{2}}\right) \tag{1}\]  
Here, \(j\) refers to the number of scale items \(\alpha_{y_{i}}^{2}\) refers to the variance associated with item \(i\), and \(\alpha_{x}^{2}\) refers to the variance associated with the observed total scores. Furthermore, we present pairwise correlations and Spearman correlations to estimate the degree of interrelation among our three variables. We resorted to Spearman correlations due to the rank-order nature of the data. Additionally, we produced ordinal logistic (Ologit) regression results to deepen our understanding of the nature of the relationship that exists among various variables used in the analysis. The Ologit regression model is a generalization of a binary logistic regression model when the outcome variable has more than two ordinal levels, which in our case were five. Ologit estimates the probability of being at or below a specific outcome level, conditional on a collection of explanatory variables. The ordinal logistic regression model can be expressed as a latent variable model ([PERSON], 2006; [PERSON], 2002)[21; 22].