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
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
|
function [CI, Chi2, alpha2] = cond_indep_chisquare(X, Y, S, Data, test, alpha, ns)
% COND_INDEP_CHISQUARE Test if X indep Y given Z
% using either chisquare test or likelihood ratio test G2
%
% [CI Chi2 Prob_Chi2] = cond_indep_chisquare(X, Y, S, Data, test, alpha, node_sizes)
%
% Input :
% Data is the data matrix, N columns * NbVar rows
% X is the index of variable X in Data matrix
% Y is the index of variable Y in Data matrix
% S are the indexes of variables in set S
% alpha is the significance level (default: 0.05)
% test = 'pearson' for Pearson's chi2 test
% 'LRT' for G2 likelihood ratio test (default)
% node_sizes (default: max(Data'))
%
% Output :
% CI = test result (1=conditional independency, 0=no)
% Chi2 = chi2 value (-1 if not enough data to perform the test --> CI=0)
%
%
% V1.4 : 24 july 2003 (Ph. Leray - philippe.leray@univ-nantes.fr)
%
%
% Things to do :
% - do not use 'find' in nij computation (when S=empty set)
% - find a better way than 'warning off/on' in tmpij, tmpijk computation
%
if nargin < 5, test = 'LRT'; end
if nargin < 6, alpha = 0.05; end
if nargin < 7, ns = max(Data'); end
Data=Data';
N = size(Data,1);
qi=ns(S);
tmp=[1 cumprod(qi(1:end-1))];
qs=1+(qi-1)*tmp';
if isempty(qs),
nij=zeros(ns(X),ns(Y));
df=prod(ns([X Y])-1)*prod(ns(S));
else
% Commented by Mingyi
% nijk=zeros(ns(X),ns(Y),qs);
% tijk=zeros(ns(X),ns(Y),qs);
% Commention ends
% Added by Mingyi
nijk=zeros(ns(X),ns(Y),1);
tijk=zeros(ns(X),ns(Y),1);
% Addition ends
df=prod(ns([X Y])-1)*qs;
end
if (N<10*df)
% Not enough data to perform the test
Chi2=-1;
CI=0;
elseif isempty(S)
for i=1:ns(X),
for j=1:ns(Y),
nij(i,j)=length(find((Data(:,X)==i)&(Data(:,Y)==j))) ;
end
end
restr=find(sum(nij,1)==0);
if ~isempty(restr)
nij=nij(:,find(sum(nij,1)));
end
tij=sum(nij,2)*sum(nij,1)/N ;
switch test
case 'pearson',
tmpij=nij-tij;
[xi yj]=find(tij<10);
for i=1:length(xi),
tmpij(xi(i),yj(i))=abs(tmpij(xi(i),yj(i)))-0.5;
end
warning off;
tmp=(tmpij.^2)./tij;
warning on;
tmp(find(tmp==Inf))=0;
case 'LRT',
warning off;
tmp=nij./tij;
warning on;
tmp(find(tmp==Inf | tmp==0))=1;
tmp(find(tmp~=tmp))=1;
tmp=2*nij.*log(tmp);
otherwise,
error(['unrecognized test ' test]);
end
Chi2=sum(sum(tmp));
alpha2=1-chisquared_prob(Chi2,df);
CI=(alpha2>=alpha) ;
else
SizeofSSi=1;
for exemple=1:N,
i=Data(exemple,X);
j=Data(exemple,Y);
Si=Data(exemple,S)-1;
%Added by Mingyi
if exemple==1
SSi(SizeofSSi,:)=Si;
nijk(i,j,SizeofSSi)=1;
else
flag=0;
for iii=1:SizeofSSi
if isequal(SSi(iii,:),Si)
nijk(i,j,iii)=nijk(i,j,iii)+1;
flag=1;
end
end
if flag==0
SizeofSSi=SizeofSSi+1;
SSi(SizeofSSi,:)=Si;
nijk(i,j,SizeofSSi)=1;
end
end
%Addition ends
%Commented by Mingyi
% k=1+Si*tmp';
% nijk(i,j,k)=nijk(i,j,k)+1;
%Commention ends
end
nik=sum(nijk,2);
njk=sum(nijk,1);
N2=sum(njk);
% for k=1:qs, %Commented by Mingyi
for k=1:SizeofSSi %Added by Mingyi
if N2(:,:,k)==0
tijk(:,:,k)=0;
else
tijk(:,:,k)=nik(:,:,k)*njk(:,:,k)/N2(:,:,k);
end
end
switch test
case 'pearson',
tmpijk=nijk-tijk;
[xi yj]=find(tijk<10);
for i=1:length(xi),
tmpijk(xi(i),yj(i))=abs(tmpijk(xi(i),yj(i)))-0.5;
end
warning off;
tmp=(tmpijk.^2)./tijk;
warning on;
tmp(find(tmp==Inf))=0;
case 'LRT',
warning off;
tmp=nijk./tijk;
warning on;
tmp(find(tmp==Inf | tmp==0))=1;
tmp(find(tmp~=tmp))=1;
tmp=2*nijk.*log(tmp);
otherwise,
error(['unrecognized test ' test]);
end
Chi2=sum(sum(sum(tmp)));
alpha2=1-chisquared_prob(Chi2,df);
CI=(alpha2>=alpha) ;
end
clear tijk
clear nijk
clear nij
clear tij
clear tmpijk
|
