forked from burakbayramli/books
-
Notifications
You must be signed in to change notification settings - Fork 0
/
mnprobit3.m
137 lines (116 loc) · 3.14 KB
/
mnprobit3.m
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
%generate data from a multinomial probit model
%with three choices (and thus work with
%two utility differences.
clear;
clc;
randn('seed',sum(100*clock));
%declare conditions for experimental design
nobs = 500;
beta0 = -.5; beta1 = 1;
beta_true = [beta0 beta1]';
nchoice = 2;
z = zeros(nchoice,2,nobs);
U_true = zeros(nchoice,nobs);
y = zeros(nobs,1);
rho = .4;
sigma2 = .5;
covmat = [sigma2 rho*sqrt(sigma2); rho*sqrt(sigma2) 1];
H = chol(covmat);
%generate the data
for i = 1:nobs;
z(:,:,i) = [1 randn(1,1); 1 randn(1,1)];
U_true(:,i) =z(:,:,i)*beta_true + H'*randn(2,1);
U_max = max(U_true(:,i));
location = findmin(-U_true(:,i));
if U_max <0
y(i,1) = 0;
else
y(i,1) = location;
end;
end;
%input prior hyperparameters
mu_beta = zeros(2,1);
V_beta = (20^2)*eye(2);
invV_beta = inv(V_beta);
rho = 3;
R = eye(2);
%set initial conditions
iter = 1000;
burn = 200;
Sigma = eye(2);
U_use = zeros(nchoice,nobs);
betas_final = zeros(2,iter-burn);
var_final = zeros(iter-burn,1);
corr_final = var_final;
%define some variables used when sampling the
%latent utility data
%dimensionalize a few matrices
A = zeros(2,2,3);
c = zeros(2,3);
d = zeros(2,3);
lc = zeros(2,3);
ld = zeros(2,3);
A(:,:,1) = eye(2);
A(:,:,2) = [1 0; 1 -1];
A(:,:,3) = [0 1; -1 1];
c(:,1) = [-999 -999]';
c(:,2) = [0 0]';
c(:,3) = [0 0]';
lc(:,1) = [1 1]';
lc(:,2) = [0 0]';
lc(:,3) = [0 0]';
d(:,1) = [0 0]';
d(:,2) = [999 999]';
d(:,3) = [999 999]';
ld(:,1) = [0 0]';
ld(:,2) = [1 1]';
ld(:,3) = [1 1]';
%Start the Gibbs sampler (Beta, Sigma, Latent Data)
clear i;
for i = 1:iter;
i
%-----------
%sample beta
%-----------
part1 = zeros(2,2);
part2 = zeros(2,1);
for j = 1:nobs;
temp1 = z(:,:,j)'*inv(Sigma)*z(:,:,j);
temp2 = z(:,:,j)'*inv(Sigma)*U_use(:,j);
part1 = part1 + temp1;
part2 = part2 + temp2;
end;
D_beta = inv(part1 + invV_beta);
d_beta = part2 + invV_beta*mu_beta;
HD_beta = chol(D_beta);
betas = D_beta*d_beta + HD_beta'*randn(2,1)
%----------------
%sample Sigma^{-1}
%-----------------
errors = zeros(nchoice,nobs);
for j = 1:nobs;
errors(:,j) = U_use(:,j) - z(:,:,j)*betas;
end;
error_part = errors*errors';
Sigma_inv = nobile_wishart(nobs+rho,(rho*R + error_part));
Sigma = inv(Sigma_inv);
%------------------
%sample latent data
%-------------------
for j = 1:nobs;
index_use = y(j) +1;
mean_use = z(:,:,j)*betas;
U_use(:,j) = tnorm_rnd(2,mean_use,Sigma,c(:,index_use),d(:,index_use),lc(:,index_use), ld(:,index_use),A(:,:,index_use),[1;2]);
end;
if i > burn;
betas_final(:,i-burn) = betas;
var_final(i-burn,1) = Sigma(1,1);
corr_final(i-burn,1) = Sigma(1,2)/sqrt(Sigma(1,1));
end;
end;
mean(betas_final')
std(betas_final')
mean(var_final)
std(var_final)
mean(corr_final)
std(corr_final)