# [R] Simulating Gaussian Mixture Models

Wensui Liu liuwensui at gmail.com
Mon Jun 23 03:36:04 CEST 2008

```Hi, Peng,
I had a piece of SAS code for 2-class gaussian mixture from my blog.
You might convert it to R code.

2-Class Gaussian Mixture Model in SAS
data d1;
do i = 1 to 100;
x = ranuni(1);
e = rannor(1);
y = 5 * x + e;
output;
end;
run;

data d2;
do i = 1 to 100;
x = ranuni(2);
e = rannor(2);
y = 15 + 10 * x - 5 * x ** 2 + e;
output;
end;
run;

data data;
set d1 d2;
run;

proc nlmixed data = data tech = quanew maxiter = 1000;
parms b10 = 0 b11 = 5 b12 = 0 b20 = 15 b21 = 10 b22 = -5
prior = 0.1 to 0.9 by 0.01 sigma = 1;

mu1 = b10 + b11 * x + b12 * x * x;
mu2 = b20 + b21 * x + b22 * x * x;
pi = constant('pi');

P1 = 1 / (((2 * pi) ** 0.5) * sigma) * exp(-0.5 * ((y - mu1) / sigma) ** 2);
P2 = 1 / (((2 * pi) ** 0.5) * sigma) * exp(-0.5 * ((y - mu2) / sigma) ** 2);

LH = P1 * prior + P2 * (1 - prior);
LL = log(LH);

model y ~ general(LL);
run;

/*
Parameter Estimates

Standard
Parameter  Estimate     Error    DF  t Value  Pr > |t|   Alpha
b10         -0.1744    0.3450   200    -0.51    0.6137    0.05
b11          5.3426    1.5040   200     3.55    0.0005    0.05
b12        -0.06454    1.4334   200    -0.05    0.9641    0.05
b20         15.3652    0.3099   200    49.57    <.0001    0.05
b21          9.6297    1.4970   200     6.43    <.0001    0.05
b22         -5.4795    1.4776   200    -3.71    0.0003    0.05
prior        0.5000   0.03536   200    14.14    <.0001    0.05
sigma        1.0049   0.05025   200    20.00    <.0001    0.05
*/
On 6/22/08, Peng Jiang <jp021 at sjtu.edu.cn> wrote:
>
>
>  Hi,
>   Is there any package that I can use to simulate the Gaussian Mixture Model
> , which is a mixture modeling method that is widely used in statistical
> learning theory.
>   I know there is a mclust, however, I think it is a little bit different
> from my problem.
>  Thanks very much..
>
>   regards.
>
>
>
>
>
>
>
>
>  --------------------------
>  Peng Jiang
>  江鹏
>  Ph.D. Candidate
>
>  Antai College of Economics & Management
>  安泰经济管理学院
>  Department of Mathematics
>  数学系
>  Shanghai Jiaotong University (Minhang Campus)
>  200240 Shanghai
>  P. R. China
>
>  ______________________________________________
>  R-help at r-project.org mailing list
>  https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
>  and provide commented, minimal, self-contained, reproducible code.
>

--
===============================
WenSui Liu
Acquisition Risk, Chase
Email : wensui.x.liu at chase.com
Blog   : statcompute.spaces.live.com
===============================
```