# Modeling Evacuees' Intended Responses to a Phased Hurricane Evacuation Order
## 4 Methodology  
Whether an individual will comply with the phased evacuation order is a binary choice. The probability of individual \(i\) choosing one alternative (\(Y=1\), i.e., COMPLY) instead of the other (\(Y=0\), i.e., NOT COMPLY) in a typical binary logit model is shown in Equation (1) [65]. While the typical binary logit model served as a starting point, compliance to the phased evacuation order was statistically estimated by other variants of binary choice models with theoretical needs (i.e., incorporating household perceptions into modeling) in mind. \[P_{i}(Y=1)=\frac{\exp(\beta^{\prime}\mathbf{x}_{i})}{1+\exp(\beta^{\prime}\mathbf{x}_ {i})} \tag{1}\]  
where, \(\mathbf{\beta}\) is the parameter vector to be estimated; \(\mathbf{x}_{i}\) is the vector of selected variables with values for individual \(i\). Latent class logit models use a discrete approximation to sort individuals (by their heterogeneity) into a certain number of classes [65]. The modeling approach is unlike random parameter logit models, which use continuous distributions to express individual heterogeneity. The discrete distribution is considered as making the latent class logit model less flexible than the random parameter logit model [66]. However, a benefit of using latent class models is saving the effort of specifying a distribution [66]. Both modeling approaches were tested during the model estimation process for statistical exploration purposes. However, in this study, the random parameter logit model was not found to be statistically superior to the latent class model in fitting the survey data by comparing their goodness-of-fit statistics, such as the pseudo \(R^{2}\) values. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**All Evacuees**} & \multicolumn{3}{c}{**In Final Model**} \\ \cline{2-7}
**Description** &
\begin{tabular}{c} **No. of** \\ **Observation** \\ \end{tabular} & **Range** & **Mean** & **Std. Dev.** & **Mean** & **Std. Dev.** \\ \hline Whether an evacuee has a household member who & 301 & [0, 1] & 0.40 & 0.49 & (na) & (na) \\ are over age 65 (1 = Yes) & 255 & [0, 1] & 0.32 & 0.47 & (na) & (na) \\ \hline Whether an evacuee has a pet (1 = Yes) & 288 & [0, 1] & 0.52 & 0.50 & (na) & (na) \\ \hline Whether an evacuee owns their residence (1 = Yes) & 301 & [0, 1] & 0.89 & 0.32 & (na) & (na) \\ \hline The number of cars in an evacuee’s household & 301 & [0, 4] & 2.11 & 0.85 & (na) & (na) \\ \hline The number of drivers in an evacuee’s household & 301 & [1, 4] & 1.99 & 0.76 & (na) & (na) \\ \hline \hline \end{tabular}  
* (Note: ‘na’ means not applicable. The number of observations varies for “All Evacuees” because the authors kept as many records as possible for each variable in describing the data. However, in the model estimation, only response records without any missing values for selected variables were used. See the last two columns for the statistics of variables included in the final model.)  
\end{table} 
Table 1: _Cont._Another reason for using the latent class logit model in this study was to address the concern of incorporating unobserved indicator variables as independent variables in explaining choice behavior. The latent class model's underlying theory states that individual choice behavior \"depends on observable attributes and on latent heterogeneity that varies with factors that are unobserved by the analyst\" [66]. Unobserved psychological characteristics of individuals (e.g., attitudes and perceptions) are one example. Incorporating psychological variables in latent class models is considered as the application of an intuitive market segmentation in modeling choice behavior [67; 68; 69]. The modeling approach has been applied not only in classic topics (e.g., estimating mode choice behavior) but also in emerging topics such as human-infrastructure interactions (e.g., incorporating cyclists' behavior in infrastructure design [70; 71]) and energy supply (e.g., considering consumers' security and sustainability perceptions in energy transition [72]).