# Public Perception of the Introduction of Autonomous Vehicles
## 2 Materials and Methods
### Model Approach  
An ordinal logistic regression (OLR) approach was applied to examine significant factors that could help in understanding the level of awareness of AVs in Saudi Arabia. We used the benefit perception of AVs as a dependent variable, and this is defined through the benefit responses seen from the transition to increased use of AVs. OLR is a widely used classification method with several key advantages. Firstly, OLR is useful when the dependent variable is classified into three or more ordered categories. For example, the benefits of adopting autonomous technology in this study, with a 5-point Likert scale, is a perfect context for the application of the OLR method. Secondly, the OLR method does not need to assume equal intervals between scoring categories, unlike other regression models. Thirdly, the OLR method includes the ranking information in the dependent variable when returning the information on the contribution of each independent variable based on the cumulative-odds principle. Note that the interpretation of an estimated regression slope for OLR is somewhat complex. It is considered to be one of the most respected methods in the field of data analytics. Before we fitted the ordinal logistic model, it was necessary to decide what outcomes to compare and what the most reasonable model was for the logit. In our case, we wanted to compare the lower probability with higher probability of public perception of benefits from the transition to increased use of AVs. Therefore, the proportional odds model was deemed to be suitable due to the following attractive characteristics: (a) instead of considering the probability of an individual event, it considers the probabilities of that event and all events that are ordered before the focal event in the ordered hierarchy, and compare it to the probability of a larger response; (b) it provides explainable and straightforward coefficients  
Figure 3: Percentage of people with the prior knowledge of Avs. of the regression due to the transformations used during the estimation and the log odds interpretation of the output. The coefficients and the intercept have different interpretations in the OLR model. Unlike simple linear regression, in the OLR model we obtain (_J-1_) intercepts, where \(J\) is the number of categories in the dependent variable. The intercepts can be interpreted as the expected odds in the listed categories, whereas the coefficients of the regression will be interpreted in terms of the increase in the log odds. Note that a lower cumulative odds value corresponds to fewer observations in the lower score categories, which results in a trend for higher scores. To understand more how to interpret the coefficients, let us first establish some notation and review the concepts involved in ordinal logistic regression. Let \(Y\) represent the response variable, in this case, \"perceptions of the benefits associated with the transition to increased use of AV\", on a scale with J-ordered levels of categories (i.e., 1 to 5; with 1 = no benefits at all and 5 = associated benefits of very high level). Then, we use \(P(Y\leq j)\) to denote the probability of \(Y\), falling at or below a particular level, with j taking values from 1 to J. In this context, Equation (1) expresses the odds of \(Y\) being less than or equal to a specific level. \[\frac{P(Y\leq j)}{P(Y>j)} \tag{1}\]  
Given that \(P(Y>j)\) is zero, and division by zero is impossible, the logarithmic function is introduced. Consequently, the log odds, often referred to as the logit, is defined by Equation (2). \[log\left[\frac{P(Y\leq j)}{P(Y>j)}\right]=logit\left[P(Y\leq j)\right] \tag{2}\]  
The partial proportional odds can be parametrized as given in Equation (3). \[logit\left[P(Y\leq j)\right]=\alpha_{j0}-\beta_{1}x_{1}-\cdots-\beta_{p}x_{p} \tag{3}\]  
where \(\alpha_{j0}\) is the model intercept and \(\beta_{1}\ldots\beta_{p}\) are model coefficient parameters representing the slopes with \(p\) independent variables for \(j=1,2\;\ldots,\;(j-1)\;\).