# Exploring the Role of Attitudinal Factors in Electric Vehicle Timeshare Rentals Adoption
## 2 Methodology
### Mixed Logit Model  
The utility of the first mode of travel for travelers \(u_{i}\) is as follows:  
\[u_{i}=a_{i}s+b_{i}z_{i}+c_{i}\eta_{i}+\epsilon_{i} \tag{1}\]  
where \(s\) is the vector of observable individual attributes of travelers; \(z_{i}\) is the vector of attributes of travel modes, including travel time and expenses; \(\eta\) is the vector of unobservable latent variables (i.e., perceived usefulness, perceived ease of use, attitudes, social pressures, perceived behavior control, and use willingness for EVTR); \(a_{i},b_{i},c_{i}\) are unknown parameter vectors to be estimated; and \(\epsilon_{i}\) is a random term.  
\[d=\begin{cases}1,&u=\max(u_{i})\\ 0,&other\end{cases} \tag{2}\]  
The structural equation that reflects the relationship between latent variables is defined as:  
\[\eta=\Gamma x+\zeta \tag{3}\]  
where \(\eta\) is the latent variable vector; \(x\) is the exogenous variable vector that affects the latent variable \(\eta\); \(\Gamma\) is the unknown parameter matrix to be estimated; and \(\zeta\) is the measurement error.  
\[y=\Lambda\eta+v \tag{4}\]  
where \(y\) is the observable indicator vector of the latent variable \(\eta\); \(\Lambda\) is the unknown parameter matrix to be estimated; and \(v\) is the error term.  
Equations (1) and (2) constitute a discrete selection model, while Equations (3) and (4) constitute a MIMIC model. Therefore, Equation (3) can also be written as follows:  
\[\eta_{i}=\alpha_{11}S_{gender}+\alpha_{12}S_{age}+\alpha_{13}S_{education}+ \alpha_{14}S_{income}+\alpha_{15}S_{car}+\alpha_{16}S_{marriage}+\cdots \tag{5}\]  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Latent Variable** & **Index** & **Description** \\ \hline Perceived comfort & \(\eta_{AC}\) & The respondents’ attitude towards the comfort of EVTRs \\ Perceived efficiency & \(\eta_{AQ}\) & The respondents’ attitude toward the efficiency of EVTRs \\ Subjective evaluation & \(\eta_{AW}\) & Investigators’ overall understanding and evaluation of EVTRs \\ Use preference & \(\eta_{AD}\) & The direct preference of respondents to travel using EVTRs \\ Station inconvenience & \(\eta_{RS}\) & Investigator perceived barriers to EVTR station \\ Station inconvenience & \(\eta_{BV}\) & Investigator perceived barriers to EVTR vehicle \\ Use inconvenience & \(\eta_{BU}\) & Investigator perceived barriers to the use of EVTRs \\ Personal inconvenience & \(\eta_{BI}\) & Investigators’ personal barriers to using EVTRs \\ Social pressure & \(\eta_{SN}\) & Social pressure sensed by investigators when using EVTRs \\ Use willingness & \(\eta_{CI}\) & Investigators’ willingness and possibility to use EVTRs \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of attitudinal variables.  
where \(\eta\) is an individual's latent attitudinal variables such as perceived usefulness, perceived availability, and subjective evaluations; and \(\alpha\) is an estimated parameter. It also shows that the potential preference of travelers for car sharing is influenced by the social demographic attributes such as gender, age, and monthly income of travelers.  
For the estimation of model parameters, the continuous two-stage estimation method can be used, which is mainly divided into two steps: Step 1, using the maximum likelihood method to estimate the latent variable model, that is, estimating the parameters of the MIMIC model; and Step 2, calculating the adaptation value of the latent variable according to the estimated value of the MIMIC model parameters, and substituting it as an exogenous variable into the discrete selection model for parameter calibration. This paper completes the above parameter estimation steps using AMOS v.24.0 and SPSS v.22.0 software. The conceptual diagram of the model is shown in Figure 2.