min2LL_4pno(N, J, Y, as, bs, gs, ss, theta)int, which gives the number of observations. (> 0)int, which gives the number of items. (> 0)matrix of item responses.vector of item discrimination parameters.vector of item threshold parameters.vector of item lower asymptote parameters.vector of item upper asymptote parameters.vector of prior thetas.Gibbs_4PNO