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

## Description

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)

## Usage

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

## Arguments

 `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

## Value

Vector of joint probabilities

`GMI`, `hmmm.model`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```# 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 ```