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function [alpha,beta,thresh92] = FitWeibAlphTAFC(inputs,nCorrect,nError,alpha0,beta0)
% [alpha,beta,thresh92] = FitWeibAlphTAFC(inputs,nCorrect,nError,alpha0,beta0)
%
% Maximum likelihood fit of a Weibull function to psychometric data,
% search only on alpha with fixed beta as passed.
%
% Requires the optimization toolbox.
%
% INPUTS:
% inputs: contains the input levels
% nCorrect: contains the number of yes responses at
% the corresponding input inputs
% nError: contains the number of no responses at
% the corresponding input inputs
% alpha0: Initial guess for alpha, empty for default [1].
% beta0: Value for beta
%
% OUTPUTS:
% alpha Weibull alpha parameter
% beta Weibull beta parameter
% thresh92 92% percent correct threshold
%
% See also: FitWeibTAFC, FitFitWeibYN, FitCumNormYN, FitLogitYN
%
% 8/25/94 dhb, ccc Cleaned comments, return 92% correct threshold.
% 2/8/97 dhb Added check for optimization toolbox.
% 4/26/97 dhb Change threshold to thresh92.
% 4/18/02 dhb Fix reference to undefined variable 'levels'.
% dhb Suppress warnings in calls to optimization toolbox.
% 3/5/05 dhb Update for optimization toolbox version 2.
% Initial parameters
if (isempty(alpha0))
x0(1) = mean(inputs);
else
x0(1) = alpha0;
end
% Check for needed optimization toolbox, and version.
if (exist('fminunc') == 2)
options = optimset;
options = optimset(options,'Display','off');
if ~IsOctave
options = optimset(options,'LargeScale','off');
end
x1 = fminunc(@WeibAlphTAFCFitFun,x0,options);
x = fminunc(@WeibAlphTAFCFitFun,x1,options);
elseif (exist('fminu') == 2)
options = foptions;
state = warning; warning('off');
x1 = fminu(@WeibAlphTAFCFitFun,x0,options);
x = fminu(@WeibAlphTAFCFitFun,x1,options);
warning(state);
else
error('FitWeibTAFCAlph requires the optional Matlab Optimization Toolbox from Mathworks');
end
% Extract parameters
alpha = x(1);
beta = beta0;
% Compute threshold from fit parameters
thresh92 = FindThreshWeibTAFC(0.92,alpha,beta);
function [f,g] = WeibAlphTAFCFitFun(x)
% [f,g] = WeibAlphTAFCFitFun(x,,beta0,inputs,nCorrect,nError)
%
% 8/26/94 dhb Wrote it.
% Unpack vector x
alpha = x(1);
% Force really big error if alpha or beta0 <= 0
if (alpha <= 0)
f = 1e25;
g = -1;
return;
end
% Compute Weibull function on input levels
pCorrect = ComputeWeibTAFC(inputs,alpha,beta0);
% Handle range problem, can't take log(0);
tol = 1e-4;
o_index = find(pCorrect == 1);
if (~isempty(o_index))
pCorrect(o_index) = (1-tol)*ones(length(o_index),1);
end
% Compute error function, which is -log(likelihood).
tmp = nCorrect.*log(pCorrect) + nError.*log(1 - pCorrect);
f = -sum(tmp);
g = -1;
end
end
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