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_D_i_f_f_u_s_i_o_n _M_o_d_e_l _f_o_r _C_o_n_f_l_i_c_t _T_a_s_k_s

_D_e_s_c_r_i_p_t_i_o_n:

     The DMC is a two-process evidence accumulation model for the study
     of conflict tasks. It sums together a controlled and an automatic
     process to generate a single accumulator for generating the
     likelihood function. This accumulator has the same parameters as
     the SDDM with the exception of the drift rate, given by

     v(x,t) = s*A*exp(-t/tau)*[e*t/(tau*(alpha-1))]^{alpha-1}*[(alpha-1)/t - 1/tau] + mu_c.
     
_U_s_a_g_e:

     dDMC(rt, resp, phi, x_res = "default", t_res = "default")
     
     pDMC(rt, resp, phi, x_res = "default", t_res = "default")
     
     rDMC(n, phi, dt = 1e-05)
     
_A_r_g_u_m_e_n_t_s:

      rt: vector of response times

    resp: vector of responses ("upper" and "lower")

     phi: parameter vector in the following order:

           1. Non-decision time (t_{nd}). Time for non-decision
              processes such as stimulus encoding and response
              execution. Total decision time t is the sum of the
              decision and non-decision times.

           2. Relative start (w). Sets the start point of accumulation
              as a ratio of the two decision thresholds. Related to the
              absolute start z point via equation z = b_l + w*(b_u -
              b_l).

           3. Coherence parameter (s). Sets stimulus coherence. If s =
              1, coherent condition; if s = 0, neutral condition; if s
              = -1, incoherent condition.

           4. Automatic process amplitude (A). Max value of automatic
              process.

           5. Scale parameter (tau). Contributes to time automatic
              process. Time to max t_{max} = (alpha – 1)*tau.

           6. Shape parameter (alpha). Indicates the shape of the
              automatic process. Must have value more than 1 (alpha >
              1).

           7. Drift rate of the controlled process (mu_c).

           8. Noise scale (sigma). Model noise scale parameter.

           9. Decision thresholds (b). Sets the location of each
              decision threshold. The upper threshold b_u is above 0
              and the lower threshold b_l is below 0 such that b_u =
              -b_l = b. The threshold separation a = 2b.

          10. Contamination (g). Sets the strength of the contamination
              process. Contamination process is a uniform distribution
              f_c(t) where f_c(t) = 1/(g_u-g_l) if g_l <= t <= g_u and
              f_c(t) = 0 if t < g_l or t > g_u. It is combined with PDF
              f_i(t) to give the final combined distribution f_{i,c}(t)
              = g*f_c(t) + (1-g)*f_i(t), which is then output by the
              program. If g = 0, it just outputs f_i(t).

          11. Lower bound of contamination distribution (g_l). See
              parameter g.

          12. Upper bound of contamination distribution (g_u). See
              parameter g.

   x_res: spatial/evidence resolution

   t_res: time resolution

       n: number of samples

      dt: step size of time. We recommend 0.00001 (1e-5)

_V_a_l_u_e:

     For the density a list of PDF values, log-PDF values, and the sum
     of the log-PDFs, for the distribution function a list of of CDF
     values, log-CDF values, and the sum of the log-CDFs, and for the
     random sampler a list of response times (rt) and response
     thresholds (resp).

_A_u_t_h_o_r(_s):

     Raphael Hartmann & Matthew Murrow

_R_e_f_e_r_e_n_c_e_s:

     Ulrich, R., Schröter, H., Leuthold, H., & Birngruber, T. (2015).
     Automatic and controlled stimulus processing in conflict tasks:
     Superimposed diffusion processes and delta functions. _Cognitive
     psychology, 78_, 148-174.

_E_x_a_m_p_l_e_s:

     # Probability density function
     dDMC(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
          phi = c(0.3, 0.5, -1.0, 0.2, 0.05, 2.5, 3.0, 1.0, 0.5, 0.0, 0.0, 1.0))
     
     # Cumulative distribution function
     pDMC(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
          phi = c(0.3, 0.5, -1.0, 0.2, 0.05, 2.5, 3.0, 1.0, 0.5, 0.0, 0.0, 1.0))
     
     # Random sampling
     rDMC(n = 100, phi = c(0.3, 0.5, -1.0, 0.2, 0.05, 2.5, 3.0, 1.0, 0.5, 0.0, 0.0, 1.0))