added AUC function to provide a model free measure

BEC_AUC.m

@@ -0,0 +1,74 @@
+function [AUC] = BEC_AUC(~, P, ~, in)
+% function [AUC] = BEC_AUC(~, P, ~, in)
+%
+% This function returns the area under the discounting function.
+% The AUC (Area under the curve) is a model free measure of the discouting
+% behavior. See for example: DOI:10.1901/jeab.2001.76-235
+%
+% Author: Antonius Wiehler <antonius.wiehler@gmail.com>
+%
+% Original: 2021-03-29
+% Modified: 2021-04-03
+
+
+
+
+% on which range do we want to compute the AUC ?
+% ---------------------------------------------------------------------
+Cost = linspace(in.grid.costlimits(1), in.grid.costlimits(2), 10000);
+
+
+
+
+% Loop bins to get parameters for each bin (two parameters per bin)
+% ---------------------------------------------------------------------
+all_bias = zeros(in.grid.nbins,1);
+all_k = zeros(in.grid.nbins,1);
+
+for i_bin = 1 : in.grid.nbins
+
+    % Get this bin's indifference line's two parameters
+    % Weight on cost
+    k = exp(P(in.ind.bias + i_bin));
+    all_k(i_bin) = k;  % store k
+
+    %Choice bias
+    if i_bin == 1
+        bias = exp(P(in.ind.bias));
+    else
+        bias = 1 - k * C_i - R_i;
+    end
+
+    all_bias(i_bin) = bias;  % store bias
+
+    % Get the intersection point with the next bin
+    C_i = in.grid.binlimits(i_bin, 2); %Cost level of the bin edge
+    R_i = 1 - k * C_i - bias; %Indifference reward level
+
+end  % loop bins
+
+
+
+
+% Compute subjective values for each trial, based on the corresponding bin
+% function
+% ---------------------------------------------------------------------
+SV = zeros(1,length(Cost));
+
+for i_trl = 1:length(Cost)
+    bin = (Cost(i_trl) >= in.grid.binlimits(:, 1) & Cost(i_trl) <= in.grid.binlimits(:, 2));
+    SV(i_trl) = 1 - all_k(bin) .* Cost(i_trl);
+end
+
+
+
+% Ignore negative subjective values
+% ---------------------------------------------------------------------
+SV = max(SV, 0);
+
+
+% compute the area under the curve (AUC) aka the integral
+% ---------------------------------------------------------------------
+AUC = trapz(Cost, SV);
+
+end  % function