# Sib-pair Command: mixture

 Class Analysis and data manipulation command Name mixture Arguments [ [normal|pooled_normal|exponential|poisson]]

Estimate mixing proportions, means and standard deviations for a 1..5 component mixture model describing the specified quantititative trait. The default is a mixture of Normal (Gaussian) distributions with different means and variances, but a common variance can alternatively be specified. Other distributions available are the exponential and Poisson. A line-printer type histogram is produced.

Example:

```# A mixture of two normals from:
#  Everitt B.S. and Hand D.J. (1981) Finite mixture distributions.
#  Chapman and Hall. p.46.
#
# means:       19.96   26.16
# variances:    4.6225  7.6176
# proportions:  0.65    0.35
#
>> macro mixexample
>>  if (index > %runtot and index <= (%runtot + %3)) then %1=%2
>>  eval (define runtot (+ runtot %3))
>> ;;;;
>>
>> set loc xvar
>> sim ped 1000 1 1
>> run
>> eval (define runtot 0)
>> mixexample xvar 15.5 10
>> mixexample xvar 16.5 21
>> mixexample xvar 17.5 56
>> mixexample xvar 18.5 79
>> mixexample xvar 19.5 114
>> mixexample xvar 20.5 122
>> mixexample xvar 21.5 110
>> mixexample xvar 22.5 85
>> mixexample xvar 23.5 85
>> mixexample xvar 24.5 61
>> mixexample xvar 25.5 47
>> mixexample xvar 26.5 49
>> mixexample xvar 27.5 47
>> mixexample xvar 28.5 44
>> mixexample xvar 29.5 31
>> mixexample xvar 30.5 20
>> mixexample xvar 31.5 11
>> mixexample xvar 32.5 4
>> mixexample xvar 33.5 4
>>
>> mix xvar 1
>> mix xvar 2

------------------------------------------------
Mixture distributions for trait "xval"
------------------------------------------------

Intvl Midpt  Count   Histogram
-------------------------------------------------------
15.5000     10   *
16.5000     21   **
17.5000     56   *****
18.5000     79   *******
19.5000    114 | ***********
20.5000    122 | ************
21.5000    110 + ***********
22.5000     85 | ********
23.5000     85 | ********
24.5000     61 | ******
25.5000     47 | ****
26.5000     49   ****
27.5000     47   ****
28.5000     44   ****
29.5000     31   ***
30.5000     20   **
31.5000     11   *
32.5000      4
33.0263      0
33.5000      4

Filliben correlation =        0.2732 (P=0.000)

Poissonness test Z   =    -2477.2956 (P=  NaN)
Median (IQR)         =       21.5000 (      19.5000 --       25.5000)
Symmetry test J(.02) =        0.3333 (P=0.000)

Distribution type    =   Normal
No. of distributions =        2
No. of observations  =     1000
No. of unique values =       19
-2*Loglikelihood     =     3536.9155

Dist       Mean      Standard Dev  Proportion
---------------------------------------------
1        20.4548        2.1459  0.6518
2        26.6588        2.7603  0.3482

>> lrt

Term         -2*LL NPar  P-value
------ ----------- ----  -------
Model0   3666.5179    2
Model1   3536.9155    4
LRTS      129.6024    2  0.0000

```

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