3.3.1. The multinomial logit model (MLM)

Multinomial model is easiest and straight forward in estimating choice modeling. Under this model, the probability of selecting option is formulated as a function of attributes and socio-economic variables of the respondents (Greene and Hensher, 2003).

In order to estimate choice probabilities using MLM it is assumed that

The random components are independently and identically distributed (IID)

The choice probability of the alternative depends only on the difference in the systematic utilities of different alternatives rather than actual values.

Based on the above assumption the probability of choosing alternative scenario multinomial model has the following expression

where, γ is the scale parameter, it is impossible to identify this parameter from the data. In addition, to this the model can be estimated by maximum likelihood estimation taking the log likelihood function.

Yij is an indicator variable that takes available of one if individual or respondent choose alternative n and 0 otherwise. To estimate the multinomial logit model, modeling constant known as Alternative Specific Constant (ASC) are included in the multinomial logit model.

where ASCi is an alternative specific constant which represents the role of the unobserved source of utility for option n, Him is the Mthattribute value of alternative n. the effect of attribute on the choice set are captured by Z variables.By interacting ASC with socioeconomic variable is one of the possible mechanisms of considering individuals or respondents Heterogeneity or detect “Hessian’’ singularities.

The model can be specified in the following form.

where St represents the socioeconomic or attitudinal variables for individual t, and ϒnt is the coefficient associated with the individual socioeconomic characteristic's interaction with the ASC.