I wonder, if there is any possibilty to formulate multinomial logit models, where the utilities are defined by parametrized function as for example as follows:
V_1 = beta_1 _1* x1_1 + ln(beta_1_2 + beta_1_3 * x1_2) + gamma1 * s1
V_2 = alpha_2 + beta_2 _1* x2_2 + ln(beta_2_2 + beta_2_3 * x2_2) + gamma2 * s1
V_3 = alpha_3 + beta_3 _1* x3_2 + ln(beta_3_2 + beta_3_3 * x3_2) + gamma3 * s1
, where alpha, beta, and gamma are paramters to be estimated, and x's are attributes relating to the individual alternatives, s1 is a sociodemographic property of the respoindent, and U stands for the utilities of the individual alternatives.
V_1 = beta_1 _1* x1_1 + ln(beta_1_2 + beta_1_3 * x1_2) + gamma1 * s1
V_2 = alpha_2 + beta_2 _1* x2_2 + ln(beta_2_2 + beta_2_3 * x2_2) + gamma2 * s1
V_3 = alpha_3 + beta_3 _1* x3_2 + ln(beta_3_2 + beta_3_3 * x3_2) + gamma3 * s1
, where alpha, beta, and gamma are paramters to be estimated, and x's are attributes relating to the individual alternatives, s1 is a sociodemographic property of the respoindent, and U stands for the utilities of the individual alternatives.
