fitLogistic.m

function [bias, slope, lapseLow, lapseHigh] = fitLogistic(x,y)

% Code to fit the history-dependent drift diffusion models as described in
% Urai AE, de Gee JW, Tsetsos K, Donner TH (2019) Choice history biases subsequent evidence accumulation. eLife, in press.
%
% MIT License
% Copyright (c) Anne Urai, 2019
% anne.urai@gmail.com

% if there are NaNs, remove
x = x(~isnan(y));
y = y(~isnan(y));

% based on the range of X, decide starting point and range 
% for slope and bias
b = glmfit(x,y, 'binomial', 'link', 'logit');

% make gamma and lambda symmetrical
[pBest,~,exitflag,~] = fminsearchbnd(@(p) logistic_LL(p, ...
    x, y), [b(1) b(2) 0.02 0.02], [min(x) 0 0 0], [max(x) b(2)*10 1 1]);
assert(exitflag == 1); % check that this worked

bias        = pBest(1);
slope       = pBest(2);
lapseLow    = pBest(3);
lapseHigh   = pBest(4);

end

function err = logistic_LL(p, intensity, responses)
% see http://courses.washington.edu/matlab1/Lesson_5.html#1

% compute the vector of responses for each level of intensity
w   = logistic(p, intensity);

% negative loglikelihood, to be minimised
err = -sum(responses .*log(w) + (1-responses).*log(1-w));

end

function y = logistic(p, x)
% Parameters: p(1) bias
%             p(2) slope
%             p(3) lapse rate-low (guess rate)
%             p(4) lapse rate-high (lapse rate)
%             x   intensity values.

% include a lapse rate, see Wichmann and Hill parameterisation
y =  p(3)+(1-p(3)-p(4)) * (1./(1+exp(- ( p(1) + p(2).*x ))));

end