1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
|
function [alpha,beta,thresh92] = FitWeibTAFC(inputs,nCorrect,nError,alpha0,beta0)
% [alpha,beta,thresh92] = FitWeibTAFC(inputs,nCorrect,nError,[alpha0],[beta0])
%
% Maximum likelihood fit of a Weibull function to TAFC psychometric data.
%
% Requires the optimization toolbox. Doesn't work with Octave yet.
%
% 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 (optional)
% beta0: Initial guess for beta (optional)
%
% OUTPUTS:
%
% alpha Weibull alpha parameter
% beta Weibull beta parameter
% thresh92 92% percent correct threshold
%
% See also: FitWeibAlphTAFC, FitWeibYN, FitCumNormYN, FitLogitYN
%
% 8/25/94 dhb, ccc Cleaned comments, return 92% correct threshold
% 2/5/97 dhb Check if fminu is not available.
% Add slope test.
% 4/26/97 dhb Fix bug in threshold assignment
% 10/13/00 dhb Improve initial guess for alpha. Thanks to Duje Tadin
% for identifying the need for this.
% 4/18/02 dhb Suppress warnings in calls to optimization toolbox.
% 3/5/05 dhb Update for optimization toolbox version 2.
% Determine whether function is increasing or decreasing
lineParams = [inputs ones(size(inputs))]\(nCorrect ./ (nCorrect+nError) );
slope = lineParams(1);
% Initial parameters
if (nargin <= 3 || isempty(alpha0))
x0(1) = mean(inputs);
else
x0(1) = alpha0;
end
if (nargin <= 4)
if (slope > 0)
x0(2) = 3.5;
else
x0(2) = -3.5;
end
elseif (isempty(beta0) )
x0(2) = 3.5;
else
x0(2) = beta0;
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(@WeibTAFCFitFun,x0,options);
x = fminunc(@WeibTAFCFitFun,x1,options);
elseif (exist('fminu') == 2)
options = foptions;
state = warning; warning('off');
x1 = fminu(@WeibTAFCFitFun,x0,options);
x = fminu(@WeibTAFCFitFun,x1,options);
warning(state);
else
error('FitWeibTAFC requires the optional Matlab Optimization Toolbox from Mathworks');
end
% Extract parameters
alpha = x(1);
beta = x(2);
% Compute threshold from fit parameters
thresh92 = FindThreshWeibTAFC(0.92,alpha,beta);
function [f,g] = WeibTAFCFitFun(x)
% [f,g] = WeibTAFCFitFun(x,inputs,nCorrect,nError)
%
% 8/26/94 dhb, ccc Fix range checking bug left from YN conversion.
% Unpack vector x
alpha = x(1);
beta = x(2);
% Force really big error if alpha or beta <= 0
if (alpha <= 0 || beta <= 0)
f = 1e25;
g = -1;
return;
end
% Compute Weibull function on input levels
pCorrect = ComputeWeibTAFC(inputs,alpha,beta);
% 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
|
