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** Mx startup successful **
**Mx-OSX version 1.69**
!
! Maximum Likelihood Example
!
! Bernstein data on ABO blood-groups
! c.f. Edwards, AWF (1972) Likelihood. Cambridge Univ Press, pp. 39-41
!
#ngroups 2
The following MX script lines were read for group 1
#NGROUPS 2
Note: #NGroup set number of groups to 2
ABO single locus
Data NInput=1
Begin Matrices;
P Full 1 1 Free ! allele freq 1
Q Full 1 1 Free ! allele freq 2
R Full 1 1 Free ! allele freq 3
I Unit 1 1
D Full 1 1
O Full 4 1 ! observed data
End Matrices;
Matrix D 2
Matrix O 212 103 39 148
Bound 0 1 P 1 1 Q 1 1 R 1 1
Matrix P .6
Ma Q .3
Ma R .1
!Start .333 P 1 1 Q 1 1 R 1 1
Begin Algebra;
E = P*(P+D*R)_
Q*(Q+D*R)_
D*P*Q_
R*R;
F=\sum(O)@E;
End Algebra;
Compute -\sum(\ln(E).O);
Option User-Defined
End Group
The following MX script lines were read for group 2
Constraint Group
Constraint NI=1
Begin Matrices = (P1 Q1 R1 I1)
End Matrices;
Constraint I = P + Q + R;
Option RS
End Group
PARAMETER SPECIFICATIONS
GROUP NUMBER: 1
ABO single locus
MATRIX D
This is a FULL matrix of order 1 by 1
It has no free parameters specified
MATRIX E
This is a computed FULL matrix of order 4 by 1
It has no free parameters specified
MATRIX F
This is a computed FULL matrix of order 4 by 1
It has no free parameters specified
MATRIX I
This is a UNIT matrix of order 1 by 1
MATRIX O
This is a FULL matrix of order 4 by 1
It has no free parameters specified
MATRIX P
This is a FULL matrix of order 1 by 1
1
1 1
MATRIX Q
This is a FULL matrix of order 1 by 1
1
1 2
MATRIX R
This is a FULL matrix of order 1 by 1
1
1 3
GROUP NUMBER: 2
Constraint Group
MATRIX I
This is a UNIT matrix of order 1 by 1
MATRIX P
This is a FULL matrix of order 1 by 1
1
1 1
MATRIX Q
This is a FULL matrix of order 1 by 1
1
1 2
MATRIX R
This is a FULL matrix of order 1 by 1
1
1 3
Mx starting optimization; number of parameters = 3
*** WARNING! ***
I am not sure I have found a solution that satisfies
Kuhn-Tucker conditions for a minimum.
NAG's IFAIL parameter is 1
We probably have a minimum here, but you might consider trying different
starting values. You can randomize these with TH=n on the OU line, where
n is the number of times you wish to do this.
I STRONGLY recommend BOundaries to be set if you use TH
MX PARAMETER ESTIMATES
GROUP NUMBER: 1
ABO single locus
MATRIX D
This is a FULL matrix of order 1 by 1
1
1 2.0000
MATRIX E
This is a computed FULL matrix of order 4 by 1
[=P*(P+D*R)_Q*(Q+D*R)_D*P*Q_R*R]
1
1 0.4116
2 0.1936
3 0.0907
4 0.3042
MATRIX F
This is a computed FULL matrix of order 4 by 1
[=\SUM(O)@E]
1
1 206.6025
2 97.1783
3 45.5349
4 152.6842
MATRIX I
This is a UNIT matrix of order 1 by 1
MATRIX O
This is a FULL matrix of order 4 by 1
1
1 212.0000
2 103.0000
3 39.0000
4 148.0000
MATRIX P
This is a FULL matrix of order 1 by 1
1
1 0.2945
MATRIX Q
This is a FULL matrix of order 1 by 1
1
1 0.1540
MATRIX R
This is a FULL matrix of order 1 by 1
1
1 0.5515
GROUP NUMBER: 2
Constraint Group
MATRIX I
This is a UNIT matrix of order 1 by 1
MATRIX P
This is a FULL matrix of order 1 by 1
1
1 0.2945
MATRIX Q
This is a FULL matrix of order 1 by 1
1
1 0.1540
MATRIX R
This is a FULL matrix of order 1 by 1
1
1 0.5515
CONSTRAINT VALUES (should be near zero)
1
1 -3.6859E-14
*** WARNING! ***
Minimization may not be successful. See above
CODE GREEN - it probably was OK
Your model has 3 estimated parameters and 1 Observed statistics
Observed statistics include 1 constraints.
User defined function value = 627.104
'Degrees of freedom' >>>>>>>>>>>>>>>> -2
This problem used 0.0% of my workspace
Task Time elapsed (DD:HH:MM:SS)
Reading script & data 0: 0: 0: 0.00
Execution 0: 0: 0: 0.00
TOTAL 0: 0: 0: 0.00
Total number of warnings issued: 2
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