Hi,

I’m working in some logits that shares parameters. By the utility function this model has non-identifiability problems that is solved fixing one of the element of the vector parameter beta (to one in this case) and a second element to be higher than the fixed one. I try to aplly that, but it seems don´t work fine for me.

Here the model specification:

`data { int<lower=1> NRUBROS; //number of independent variables int<lower=0> NCASOS; //number of observations int<lower=0,upper=1> y[NCASOS,NRUBROS]; //dependent variables vector[NRUBROS] x[NCASOS]; //covariates } transformed data{ vector[NCASOS] sumd; for (i in 1:NCASOS) { sumd[i] = fmax(sum(x[i]),1); //auxiliar data } } parameters { vector[NRUBROS-2] beta_free; //free parameters real<lower=1> beta_free_aux; //to constrain the second element } transformed parameters { vector[NRUBROS] beta; //to append vector of parameters beta = append_row(1,append_row(beta_free_aux,beta_free)); //create vector beta } model { vector[NRUBROS] utilidad[NCASOS]; //utility matrix vector[NRUBROS] probabilidad[NCASOS]; //probability matrix for (j in 1:NRUBROS){ for (i in 1:NCASOS){ utilidad[i, j] = fabs(beta[j] - dot_product(beta,x[i])/sumd[i]); //utility definition probabilidad[i, j] = inv_logit(utilidad[i, j]); } } { for(i in 1: NCASOS){ y[i] ~ bernoulli(probabilidad[i]); } } to_vector(beta_free) ~ normal(0,5); beta_free_aux ~ normal(0,5); }`

The problem is, for example for a 4 catogories simulation, with a real value of the parameter beta = (-1,-2,1,0) there is only one solution that respect the fixed and constrained parameters = (1,2,-1,0). But, looking the traceplot, you can see that three chains converge to the desired solution and the other one converge to a solution like (1,1,3,2) that looks very similiar to the plausible solution (1,0,3,2) with the diference that the second parameter is constrained to be higher than one. Then, i think the free parameters are be able to move in the space solution with the two first elements of beta don´t constrained and i don´t like that. Any idea to solve it?

Regards and like always sorry for my english!

simulation code: Simulation (MODELO 9B DM MEAN).R (1.7 KB)