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)))

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)))
   

1. If you want 200 copies of 5 categorical variables in random order, then do this

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.

set.seed(1)

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)))

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)))