I am trying to generate fake data for exploratory purposes. Specifically, I am trying to produce data with a binary dependent variable (say, failure/success), and a categorical independent variable called 'picture' with 5 levels (pict1, pict2, etc.). I am following the answer provided [here][1], which allows me to successfully generate the data. However, I need each level of 'picture' to occur the same number of times (i.e. 11 repetitions of each level = 55 total observations per subject). 

Here is a reproducible example of what has worked to far (code from user: ocram):

    library(dummies)
    
    #------ parameters ------
    n <- 1000 
    beta0 <- 0.07
    betaB <- 0.1
    betaC <- -0.15
    betaD <- -0.03
    betaE <- 0.9
    #------------------------
    
    #------ initialisation ------
    beta0Hat <- rep(NA, 1000)
    betaBHat <- rep(NA, 1000)
    betaCHat <- rep(NA, 1000)
    betaDHat <- rep(NA, 1000)
    betaEHat <- rep(NA, 1000)
    #----------------------------
    
    #------ simulations ------
    for(i in 1:1000)
    {
      #data generation
      x <- sample(x=c("pict1","pict2", "pict3", "pict4", "pict5"), 
                  size=n, replace=TRUE, prob=rep(1/5, 5))  #(a)
      linpred <- cbind(1, dummy(x)[, -1]) %*% c(beta0, betaB, betaC, betaD, betaE)  #(b)
      pi <- exp(linpred) / (1 + exp(linpred))  #(c)
      y <- rbinom(n=n, size=1, prob=pi)  #(d)
      data <- data.frame(picture=x, choice=y)
      
      #fit the logistic model
      mod <- glm(choice ~ picture, family="binomial", data=data)
      
      #save the estimates
      beta0Hat[i] <- mod$coef[1]
      betaBHat[i] <- mod$coef[2]
      betaCHat[i] <- mod$coef[3]
      betaDHat[i] <- mod$coef[4]
      betaEHat[i] <- mod$coef[5]
    }

However, as you can see from the output, each level of the factor 'picture' does not occur the same number of times (i.e. 200 times each). 

    > summary(data)
    picture     choice     
    pict1:200   Min.   :0.000  
    pict2:207   1st Qu.:0.000  
    pict3:217   Median :1.000  
    pict4:163   Mean   :0.559  
    pict5:213   3rd Qu.:1.000  
                Max.   :1.000 

Moreover, it is not entirely clear to me how to manipulate the initial beta values as to determine the probability of success/failure for each level of 'picture'. I cannot comment the original question because I do not yet have the necessary reputation points. 

  [1]: http://stats.stackexchange.com/questions/49916/simulating-data-for-logistic-regression-with-a-categorical-variable