V_BERK2PROB convert Berksons to probability Inputs: B(M,N) matrix containing Berkson values Outputs: P(M,N) Corresponding probability values D(M,N) Corresponding derivatives dP/dB Berksons, or log-odds, are a nonlinear scale for measuring probability defined by B = log2(P./(1-P)). When Berksons are used to measure probability, a logistic psychometric function becomes linear. The inverse function is v_berk2prob()

0001 function [p,d]=v_berk2prob(b) 0002 %V_BERK2PROB convert Berksons to probability 0003 % 0004 % Inputs: B(M,N) matrix containing Berkson values 0005 % 0006 % Outputs: P(M,N) Corresponding probability values 0007 % D(M,N) Corresponding derivatives dP/dB 0008 % 0009 % Berksons, or log-odds, are a nonlinear scale for measuring 0010 % probability defined by B = log2(P./(1-P)). 0011 % When Berksons are used to measure probability, a logistic 0012 % psychometric function becomes linear. 0013 % 0014 % The inverse function is v_berk2prob() 0015 0016 % Copyright (C) Mike Brookes 2014 0017 % Version: $Id: v_berk2prob.m 10865 2018-09-21 17:22:45Z dmb $ 0018 % 0019 % VOICEBOX is a MATLAB toolbox for speech processing. 0020 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0021 % 0022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0023 % This program is free software; you can redistribute it and/or modify 0024 % it under the terms of the GNU General Public License as published by 0025 % the Free Software Foundation; either version 2 of the License, or 0026 % (at your option) any later version. 0027 % 0028 % This program is distributed in the hope that it will be useful, 0029 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0030 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0031 % GNU General Public License for more details. 0032 % 0033 % You can obtain a copy of the GNU General Public License from 0034 % http://www.gnu.org/copyleft/gpl.html or by writing to 0035 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0037 p=1-1./(1+pow2(b)); 0038 if nargout>1 0039 d=log(2)*p.*(1-p); 0040 end

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