** 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 ______________________________________________________________________________ ______________________________________________________________________________