Additive Random Utility Models (ARUMs)

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Probit Class

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Class Definition

Definition:

 
class probit
{
    public:
        // build objects
        int nbX;
        int nbY;
        int nbParams;
        int aux_nbOptions;
        
        bool outsideOption;
        
        double rho;
        
        arma::cube Covar;
        
        // member functions
        ~probit(){};
         probit(){};
        explicit probit(int nbX_inp, int nbY_inp);
        explicit probit(int nbX_inp, int nbY_inp, bool outsideOption_inp);
        explicit probit(int nbX_inp, int nbY_inp, double rho_inp, bool outsideOption_inp);

        void build(int nbX_inp, int nbY_inp);
        void build(int nbX_inp, int nbY_inp, bool outsideOption_inp);
        void build(int nbX_inp, int nbY_inp, double rho_inp, bool outsideOption_inp);

        void unifCorrelCovMatrices();
        void unifCorrelCovMatrices(double rho_inp);

        empirical simul();
        empirical simul(int* nbDraws, int* seed);
        void simul(empirical& obj_out);
        void simul(empirical& obj_out, int* nbDraws, int* seed);
    
    private:
         void build_prv(int nbX_inp, int nbY_inp, double* rho_inp, bool outsideOption_inp);
};

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Member Objects

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Member Functions

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Notes

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Examples

Example:

arma::mat U(2,3);
    U  << 1.6 << 3.2 << 1.1 << arma::endr
       << 2.9 << 1.0 << 3.1 << arma::endr;
    
    arma::mat mu(2,3);
    mu << 1.0 << 3.0 << 1.0 << arma::endr
       << 2.0 << 1.0 << 3.0 << arma::endr;
    //
    int nbX = U.n_rows;
    int nbY = U.n_cols;
    
    arma::vec n = arma::sum(mu,1);
    
    trame::probit probits;
    probits.build(nbX,nbY,true);
    //
    // correlation matrices
    probits.rho = 0.5;
    
    probits.unifCorrelCovMatrices();
    //
    // empirical object:
    int sim_seed = 1777;
    int n_draws = 1000;

    trame::empirical emp_obj;
    
    probits.simul(emp_obj, &n_draws, &sim_seed);
    
    emp_obj.U = U;
    emp_obj.mu = mu;
    //
    // first compute optimal assignment (mu)
    double G_sim_val = emp_obj.G(n);
    
    arma::cout << "G-sim(U): \n" << G_sim_val << arma::endl;
    arma::cout << "G-sim -> mu: \n" << emp_obj.mu_sol << arma::endl;
    //
    // solution to dual problem U*
    arma::mat U_star_sim;
    double Gstar_sim_val = emp_obj.Gstar(n);
    //double Gstar_sim_val = emp_obj.Gstar(n,emp_obj.mu_sol,U_star_sim);
    
    arma::cout << "G*-sim(mu): \n" << Gstar_sim_val << arma::endl;
    arma::cout << "\\nabla G-sim*(\\nabla G-sim(U)): \n" << emp_obj.U_sol << arma::endl;
    //
    // Gbar
    arma::mat mu_bar(2,3);
    mu_bar.fill(2);
    
    arma::mat U_bar_temp, mu_bar_temp;

    double val_Gbar_sim = emp_obj.Gbar(emp_obj.U_sol, mu_bar, n, U_bar_temp, mu_bar_temp);
    
    arma::cout << "Gbar-sim val: \n" << val_Gbar_sim << arma::endl;

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