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fitPred=function(ai,vi,sd2A,sd2V,order,model=1,A,W){ # calculates predicted values up to a certain order for D diffusion and Q diffusion
nit=length(ai)
nq=length(A)
X=fitItems(nit,order)
N=fitCumChoose(nit,order)
ou=matrix(N,nit)
vi=matrix(vi)
ai=matrix(ai)
V=A
I=matrix(1,nq)
V=matrix(V*sqrt(sd2V))%x%I
A=I%x%matrix(A*sqrt(sd2A))
W=(matrix(W)%x%I) * (I%x% matrix(W))
if(model==1) dev=kronecker(V,t(vi),"-") #D diffusion
if(model==2) dev=kronecker(exp(V),exp(t(vi)),"/") #Q diffusion
amat=kronecker(exp(A),exp(t(ai)),"/")
dev2=amat*dev
p=1/(1+exp(-dev2))
ou=matrix(,nrow(X),1)
for(i in 1:nrow(X)) ou[i,1]=sum(W*apply(t(t(p)^(X[i,]))*t(t(1-p)^(1-X[i,])),1,prod))
return(ou)
}
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