## 4 Results  
The findings are presented in five models (A to E) in Table 2. The first and second models (standard LC and standard MM model) consider the full attributes attendance (FAA). It should be noted that normal distributions were assumed for all the considered random parameters. The number of classes was selected based on goodness of fit of Akaike information criterion (AIC). For model C, for instance, although fixed parameters are assumed for all the variables, they were allowed for ANA and ACMA. AIC value was used for determining the number of Q, and as a comparison across various models [10]. As can be seen from Table 2, the AIC is lowest for model E (log-likelihood of \(-3962\)). The following paragraphs elaborate on the considered models. While the first and second models, LC and MM, assume the full attributes attendance (FAA), the other model incorporates a combination of FAA, ANA, and ACMA. For instance, the third model sets constraints on variables such as sunny and day of a week for the first class and driver seat belt status vehicle registration for the second class. A choice of variables to be incorporated in ANA and ACMA were identified by evaluation attributes one at a time for ANA or ACMA. After identifying variables for both attribute processing rules, they were aggregated and considered in the included models. One of the challenges being observed was for the MM model, especially while considering for more than two classes, due to lack of convergence. Another point worthy of investigation is which variables to include for ACMA. In the literature review, most variables that belong to the similar category were considered to be incorporated in ACMA. Those include variables, for instance, related to cost or time. These variables mainly have consistent impacts (signs) on the response. Although various predictors were considered to be included for ACMA, they did not result in a model enhancement and were not justifiable to be used due to lack of interpretation, e.g., driver belt status and vehicle license registration. Two variables related to time (11:30-1:30 and 1:30-3:30) were found to be a better fit in models. However, as can be seen from all the included models in Table 2, these two variables have opposite signs/directions. Solutions could be proposed including changing the category coding of the variables, ignoring the differences across the signs, or constraining based on their opposite signs. Just to highlight the importance of constraining the variables with various signs, model D (for MM) and model E were proposed. First, it can be observed that a worst fit model could be observed for the LC model, with no extra layer of heterogeneity, and no ANA and ACMA. An improvement could be observed by including another layer with continuous distribution in the MM model (model B), 7959 for LC versus 7954. Moving to the models with attribute processing rules, ANA and ACMA consideration, although a small amount of improvement could be observed for standard latent class versus the latent class with ANA and ACMA (7959 for a standard latent class versus 7958 for the mixed-mixed model), a model is deteriorated moving from a standard MM to MM model with ANA and ACMA (with a wrong ACMA specification). However, as discussed, for the MM model in D, the parameters were assumed to have similar signs. Model E is presented in which the reverse signs were considered while constraining the parameters. That is a best fit model compared with the other considered models. Although the same approach for the latent class model is not presented in Table 2, it was observed that the AIC was improved for the latent class with reverse signs for ACMA (AIC = 7952), compared with the included model (AIC = 7958). It is also worth looking at the class membership across the considered models. Class memberships are only significant for ACMA with a wrong approach (models C and D).