## 3 Method
\(\omega\) estimation: assume R = 10 for 3 variables and 100 observations: there would be a matrix with 10 columns and 3 rows, and 100 values: the values would be filled by \(\sum\limits_{i\ =\ 1}^{n\ =\ 3}(beta_{i}+\sigma_{i}\times\omega_{i})\), where \(\omega\) would be estimated based on pseudo-random numbers or Halton sequences, and \(\sigma_{i}\), or the SD of random parameters are values that would be estimated by maximum likelihood, and their initial values would be set by the investigator. Additionally, the initial value of beta would be set by investigator \(\rightarrow\ \big{(}\beta_{q}+\omega_{i}\big{)}\) 2. The multiplication of the above value by the vectors of observed coefficients would be saved as XR \(\rightarrow\ \big{(}\beta_{q}+\omega_{i}\big{)}x_{ij}\) 3. The resultant would be multiplied by response \(\rightarrow\ \sum\limits_{j\ =\ 1}^{J}y_{i,j}\big{(}\beta_{q}+\omega_{i} \big{)}x_{ij}\) 4. The exponential of the above values in c would be calculated and would be summed up across the number of J or classes \(\rightarrow\exp[\sum\limits_{j\ =\ 1}^{J}y_{i,j}\big{(}\beta_{q}+\omega_{i} \big{)}x_{ij}]\) 5. To have a probability based on the Multinomial logit model, the value in d would be divided by value in c. \(\rightarrow\ \frac{\exp[\sum\
olimits_{j\ =\ 1}^{J}y_{i,j}(\beta_{q}+\omega_{i} )x_{ij}]}{\sum\
olimits_{j\ =\ 1}^{J}\exp[(\beta_{q}+\omega_{i} )x_{ij}]}\) 6. There are 10 observations (draws), along with Q columns, related to classes. Thus, the means of each class would be estimated by reducing the dimension of the random draws (R): the average of all the draws over each observation. 9. Up to the above steps are related to \(\rightarrow\ \frac{1}{R}\sum\limits_{r\ =\ 1}^{R}\frac{\exp[\sum\
olimits_{j \ =\ 1}^{J}y_{i,j}(\beta_{q}+\omega_{i})x_{ij}]}{\sum\
olimits_{j\ =\ 1}^{J}\exp[(\beta_{q}+\omega_{i} )x_{ij}]}\). 2. For latent class parts, the steps would be taken as follows: 1. Create a vector of \(\gamma\): this constitutes the initial value of a constant or the heterogeneity point related to a covariate T, which the class allocation is based on. For the first class the value would be set as 0 based on the literature review for model identification. 2. Getting the exponential of T, times \(\gamma\), which discussed in the above, 3. The above would be transformed into a probability by dividing the values by the sum of all the components or classes. * The above are related to the \(\pi_{n,s}\) which is equal to \(\frac{\hat{e}^{\beta_{n}|x^{n}_{i}|}}{\sum_{k}\hat{e}^{\beta_{n}|x^{n}_{i}|}}\) part of the above equation. It should be noted that \(\pi_{n,s}\) acts as a constraint with \(\sum\limits_{s}\pi_{n,s}=1\), so the sum of the probability of each observation across classes would be added up to 1. * Now the resultants of item 1 and 2 would be multiplied. This would be the resultant of Equation (6). * In order to transform the probability of Equation (6) into a likelihood, the sum of the probability of the individuals would be calculated and set as the likelihood. * The log of 4 would be set as log likelihood and would be estimated by maximum likelihood. * Now to come up with ANA and ACMA, we put constraints on the means and the SDs of the parameters. For coming up with ANA, we impose restrictions on some attributes' means and for ACMA, we constrain two or more parameter means to be equal. * Maximum likelihood would be estimated by the finite-difference method and with the help of Hessian and Gradient. The standard practice in the use of the LC model is that they assume that all available information related to a choice, which is used by the respondent in making a decision. Additionally, they assume that the factors were assigned to be high importance by the respondents. Those mostly have been assumed in the modeling approach while some studies asked their respondents about whether they considered those characteristics or not [14]. It has been argued that their responses would not be reliable [15].