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#' @title Variance-covariance matrix of a CUB model with covariates for both uncertainty and feeling
#' @description Compute the variance-covariance matrix of parameter estimates of a CUB model with covariates for
#' both the uncertainty and the feeling components.
#' @aliases varcovcubpq
#' @usage varcovcubpq(m, ordinal, Y, W, bet, gama)
#' @param m Number of ordinal categories
#' @param ordinal Vector of ordinal responses
#' @param Y Matrix of covariates for explaining the uncertainty parameter
#' @param W Matrix of covariates for explaining the feeling parameter
#' @param bet Vector of parameters for the uncertainty component, with length equal to
#' NCOL(Y)+1 to account for an intercept term (first entry)
#' @param gama Vector of parameters for the feeling component, with length equal to
#' NCOL(W)+1 to account for an intercept term (first entry)
#' @details The function checks if the variance-covariance matrix is positive-definite: if not, it returns a warning
#' message and produces a matrix with NA entries.
#' @seealso \code{\link{probcubpq}}
#' @keywords internal
#' @references
#' Piccolo D. (2006), Observed Information Matrix for CUB Models, \emph{Quaderni di Statistica}, \bold{8}, 33--78
varcovcubpq <-
function(m,ordinal,Y,W,bet,gama){
Y<-as.matrix(Y);W<-as.matrix(W);
if (ncol(W)==1){
W<-as.numeric(W)
}
if (ncol(Y)==1){
Y<-as.numeric(Y)
}
qi<-1/(m*probcubpq(m,ordinal,Y,W,bet,gama))
ei<-logis(Y,bet)
eitilde<-ei*(1-ei)
qistar<-1-(1-ei)*qi
qitilde<-qistar*(1-qistar)
fi<-logis(W,gama)
fitilde<-fi*(1-fi)
ai<-(ordinal-1)-(m-1)*(1-fi)
ff<-eitilde-qitilde
gg<-ai*qitilde
hh<-(m-1)*qistar*fitilde-(ai^2)*qitilde
YY<-cbind(1,Y)
WW<-cbind(1,W)
i11<-t(YY)%*%(Hadprod(YY,ff)) ### i11<-t(YY)%*%(YY*ff);
i12<-t(YY)%*%(Hadprod(WW,gg)) ### i12<-t(YY)%*%(WW*gg);
i22<-t(WW)%*%(Hadprod(WW,hh)) ### i22<-t(WW)%*%;
## matinf<-rbind(cbind(i11,i12),cbind(t(i12),i22)) # Information matrix
nparam<-NCOL(Y)+NCOL(W)+2
npai<-NCOL(Y)+1
ncsi<-NCOL(W)+1
nparam<-npai+ncsi
matinf<-matrix(NA,nrow=nparam,ncol=nparam)
for (i in 1:npai){
matinf[i,]<-t(c(i11[i,],i12[i,]))
}
for (i in (npai+1):nparam){
matinf[i,]<-t(c(t(i12)[i-npai,],i22[i-npai,]))
}
if(any(is.na(matinf))==TRUE){
warning("ATTENTION: NAs produced")
varmat<-matrix(NA,nrow=nparam,ncol=nparam)
} else {
if(det(matinf)<=0){
warning("ATTENTION: Variance-covariance matrix NOT positive definite")
varmat<-matrix(NA,nrow=nparam,ncol=nparam)
} else {
varmat<-solve(matinf)
}
}
return(varmat)
}
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