#' Create the Z matrices based with sum contrasts
#'
#'@description Compute the z matrice for the random effects and reduced its rank and dimension with respect to the between effects.
#'
#'@param model_frame a model.frame object containint the facotors of interest
#'@param formula_f a formula of all the effects as fixed
#'@param formula_within a formula indicating the within effect
#'@param formula_id the formula indicating the sampling units
#'
#'@return a matrix with its contrasts as attributs.
#'@importFrom stats formula update.formula
mm_z = function(model_frame, formula_f, formula_within, formula_id){
tf = terms(formula_f)
tw = terms(formula_within)
tid = terms(formula_id)
term.labels_between = (attr(tf,"term.labels")[attr(tf,"order")==1])[
!(attr(tf,"term.labels")[attr(tf,"order")==1])%in%(attr(tw,"term.labels")[attr(tw,"order")==1])]
formula_between = formula(paste("~ 0",paste(term.labels_between, collapse = ":"),collapse = "+",sep="+"))
formula_id = update.formula(old = formula_id,new = ~ 0 + .)
mm0_id = model.matrix(formula_id,model_frame)
mm0_b = model.matrix(formula_between,model_frame)
#debug
# z = lapply(1:NCOL(mm0_b),function(i){
# which_row = which(mm0_b[,i] == 1)
# which_col = which(colSums(mm0_id[which_row,])!=0)
#
# z0i = mm0_id[which_row,which_col]%*%contr.sum(length(which_col))
# zi = matrix(0, ncol= NCOL(z0i),nrow= NROW(mm0_id))
# zi[which_row,] = z0i
# attr(zi,"contrasts") = contr.sum(length(which_col))
# zi
# })
#
# c = as.matrix(bdiag(lapply(z,function(zi)attr(zi,"contrasts"))))
# z = do.call("cbind",z)
# attr(z,"contrasts") = c
mm0_b<<-mm0_b
sq_i = seq_len(dim(mm0_b)[2])
if(length(sq_i)==0){sq_i=0}
z = lapply(sq_i,function(i){
if(i==0){which_row = 1:nrow(mm0_b)}else{which_row = which(mm0_b[,i] == 1)}
which_col = which(colSums(mm0_id[which_row,])!=0)
z0i = mm0_id[which_row,which_col]%*%contr.sum(length(which_col))
zi = matrix(0, ncol= NCOL(z0i),nrow= NROW(mm0_id))
zi[which_row,] = z0i
contr = matrix(0,nrow = ncol(mm0_id),ncol = length(which_col)-1)
contr[which_col,] = contr.sum(length(which_col))
attr(zi,"contrasts") = contr
zi
})
lapply(z,function(zi)attr(zi,"contrasts"))
c = do.call("cbind",lapply(z,function(zi)attr(zi,"contrasts")))
z = do.call("cbind",z)
attr(z,"contrasts") = c
attr(z,"label") = attr(terms(formula_id),"term.labels")
return(z)
}
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