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#
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#        http://www.apache.org/licenses/LICENSE-2.0
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# -----------------------------------------------------------------------------
# Program: OneLocusLikelihood.R  
# Author: Michael Neale
# Date: 2009.11.23 
#
# ModelType: Locus Likelihood
# DataType: Frequencies
# Field: Human Behavior Genetics
#
# Purpose: 
#      One Locus Likelihood model to estimate allele frequencies
#      Bernstein data on ABO blood-groups
#      c.f. Edwards, AWF (1972)  Likelihood.  Cambridge Univ Press, pp. 39-41
#
# RevisionHistory:
#      Hermine Maes -- 2010.02.22 updated & reformatted
#      Ross Gore -- 2011.06.15 added Model, Data & Field
#      Hermine Maes -- 2014.11.02 piecewise specification
# -----------------------------------------------------------------------------

require(OpenMx)
# Load Library
# -----------------------------------------------------------------------------
    
# Matrices for allele frequencies, p, q and r
matP         <- mxMatrix( type="Full", nrow=1, ncol=1, 
                          free=TRUE, values=c(.3333), name="P")
matQ         <- mxMatrix( type="Full", nrow=1, ncol=1, 
                          free=TRUE, values=c(.3333), name="Q")
matR         <- mxMatrix( type="Full", nrow=1, ncol=1, 
                          free=TRUE, values=c(.3333), name="R")
# Matrix of observed data    
const        <- mxConstraint(P+Q+R == 1, name="EqualityConstraint")
obsFreq      <- mxMatrix( type="Full", nrow=4, ncol=1, 
                          values=c(211,104,39,148), name="ObservedFreqs")
# Algebra for predicted proportions
expFreq      <- mxAlgebra( expression=rbind(P*(P+2*R), Q*(Q+2*R), 2*P*Q, R*R), 
                          name="ExpectedFreqs")
# Algebra for -2logLikelihood
m2ll         <- mxAlgebra( expression=-(sum(log(ExpectedFreqs) 
                          * ObservedFreqs)), name="NegativeLogLikelihood")
# User-defined objective
funAl        <- mxFitFunctionAlgebra("NegativeLogLikelihood") 

OneLocusModel <- mxModel("OneLocus", 
                          matP, matQ, matR, const, obsFreq, expFreq, m2ll, funAl)

# Create an MxModel object
# -----------------------------------------------------------------------------

OneLocusFit <- mxRun(OneLocusModel)
OneLocusFit$matrices
OneLocusFit$algebras


estimates <- c(
    OneLocusFit$matrices$P$values, 
    OneLocusFit$matrices$Q$values, 
    OneLocusFit$matrices$R$values, 
    OneLocusFit$algebras$NegativeLogLikelihood$result)
Mx1Estimates<-c(0.2931,0.1552,0.5517,627.851)
omxCheckCloseEnough(estimates,Mx1Estimates,.01)
# Compare OpenMx estimates to original Mx's estimates
# -----------------------------------------------------------------------------