inv_GMI: function to compute a vector of joint probabilities from a...
In hmmm: Hierarchical Multinomial Marginal Models

Description Usage Arguments Value See Also Examples

Given an hmmm model and the vector of its generalized interactions eta, the vector of joint probabilities p is computed by inverting eta=C*ln(M*p)

1	inv_GMI(etpar, mod, start = rep(0, prod(mod$modello$livelli)))

`etpar`	Vector of gmi
`mod`	hmmm model corresponding to etapar; an object of class `hmmmod` created by `hmmm.model`
`start`	Starting values for log-linear parameters in the non linear equations problem

Vector of joint probabilities

GMI, hmmm.model

# a joint distribution of 2 variables with 4 categories each

p4<-c(
0.0895, 0.0351 ,0.0004, 0.0003, 
0.0352, 0.2775, 0.0619, 0.0004, 
0.0004, 0.0620, 0.2775, 0.0351, 
0.0001, 0.0004, 0.0352, 0.089)

marg<-marg.list(c("l-m","m-l","l-l"), mflag="m") 
labelrisp<-c("R1","R2")
modello<-hmmm.model(marg=marg,lev=c(4,4),names=labelrisp)

etpar<-GMI(c(p4),c("l-m","m-l","l-l"),c(4,4),labelrisp,mflag="m")
etpar$gmi
p4rec<-inv_GMI(etpar$gmi,modello)
P<-cbind(p4rec,c(p4),c(p4)-p4rec)
colnames(P)<-c("prob","prob from eta","check")
P