% This code reproduces the analyses in the paper
% Urai AE, Braun A, Donner THD (2016) Pupil-linked arousal is driven
% by decision uncertainty and alters serial choice bias.
%
% Permission is hereby granted, free of charge, to any person obtaining a
% copy of this software and associated documentation files (the "Software"),
% to deal in the Software without restriction, including without limitation
% the rights to use, copy, modify, merge, publish, distribute, sublicense,
% and/or sell copies of the Software, and to permit persons to whom the
% Software is furnished to do so, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included
% in all copies or substantial portions of the Software.
% If you use the Software for your own research, cite the paper.
%
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
% OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
% DEALINGS IN THE SOFTWARE.
%
% Anne Urai, 2016
% anne.urai@gmail.com

function y = logistic(p, x)
% Parameters: p(1) bias
%             p(2) slope
%             p(3) lapse rate
%             x   intensity values.

% include a lapse rate, see Wichmann and Hill parameterisation
y =  p(3)+(1-p(3)-p(3)) * (1./(1+exp(- ( p(1) + p(2).*x ))));

end
