1. If you want 200 copies of each of 5 levels in a polytomous variable in random order, then do this instead

`x <- sample(rep(paste0('pict', 1:5), 200))`

2. If you want to control for overall prevalence of a specific outcome, then you must choose which `beta` you will fudge. I usually do `beta0`.

`MM <- model.matrix(~x)`

`betas <- rnorm(4)`

`prevTarget <- 0.3`

`prevDiff <- function(beta0)`
`  prevTarget - mean(binomial()$linkinv(MM%*%c(beta0, betas)))`

`beta0 <- uniroot(prevDiff, c(-100, 100))$root`

`mean(binomial()$linkinv(MM%*%c(beta0, betas)))`