# Computational error for zeroinflated negative binomial regression model

I am trying to fit a zero-inflated neg. binomial model. I have many predictors for the count model, but only one for the zero model (Saturday).

#extract variable names for the glm model formula
n <- names(data_train)[-c(1:4)]
n <- n[! n %in% c("Saturday")]
fglm <- as.formula(paste("outcol ~", paste(n[!n %in% "outcol"], collapse = " + ")))

#identify which coefficients cannot be estimated and omit these
fm1 <- glm.nb(fglm, data = model.frame(data_train[,-c(1:4)]))
q <- as.data.frame(model.matrix(fm1))
q <- q[, !is.na(coef(fm1))]
q <- q[, -1]
q$$outcol<- data_train$$outcol
q$$Saturday <- data_train$$Saturday

#extract variable names for the model formula
n <- names(q)
n <- n[! n %in% c("Saturday")]
f <- as.formula(paste("outcol ~", paste(n[!n %in% "outcol"], collapse = " + "), paste("|",paste( "Saturday", sep = " + "))))

#fit zero-infl model only with coef. that can be estimated
fit <- zeroinfl(f, data=q, dist="negbin")


I followed Achim Zeileis's recommendation, on https://stat.ethz.ch/pipermail/r-help/2010-March/230576.html to first fit a neg. binomial model without zero-inflation and exclude the coefficients that cannot be estimated (i.e. that are NA), but I still get the error that the system is singular.

Error in solve.default(as.matrix(fit\$hessian)) :
system is computationally singular: reciprocal condition number = 2.14623e-23


It still persists even if I do not specifiy the zero model part (and hence the model should be the same as the one fitted with glm.nb), so I guess the problem has to be within the count model part. I just don't know how I can find the variables causing the error.