# dirichlet.simul: Simulation of a Dirichlet Distributed Vectors In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

 dirichlet.simul R Documentation

## Simulation of a Dirichlet Distributed Vectors

### Description

This function makes random draws from a Dirichlet distribution.

### Usage

dirichlet.simul(alpha)


### Arguments

 alpha A matrix with \bold{\alpha} parameters of the Dirichlet distribution

### Value

A data frame with Dirichlet distributed responses

### Examples

#############################################################################
# EXAMPLE 1: Simulation with two components
#############################################################################

set.seed(789)
N <- 2000
probs <- c(.7, .3)    # define (extremal) class probabilities

#*** alpha0=.2  -> nearly crisp latent classes
alpha0 <- .2
alpha <- alpha0*probs
alpha <- matrix( alpha, nrow=N, ncol=length(alpha), byrow=TRUE  )
x <- sirt::dirichlet.simul( alpha )
htitle <- expression(paste( alpha[0], "=.2, ", p[1], "=.7"   ) )
hist( x[,1], breaks=seq(0,1,len=20), main=htitle)

#*** alpha0=3 -> strong deviation from crisp membership
alpha0 <- 3
alpha <- alpha0*probs
alpha <- matrix( alpha, nrow=N, ncol=length(alpha), byrow=TRUE  )
x <- sirt::dirichlet.simul( alpha )
htitle <- expression(paste( alpha[0], "=3, ", p[1], "=.7"   ) )
hist( x[,1], breaks=seq(0,1,len=20), main=htitle)

## Not run:
#############################################################################
# EXAMPLE 2: Simulation with three components
#############################################################################

set.seed(986)
N <- 2000
probs <- c( .5, .35, .15 )

#*** alpha0=.2
alpha0 <- .2
alpha <- alpha0*probs
alpha <- matrix( alpha, nrow=N, ncol=length(alpha), byrow=TRUE  )
x <- sirt::dirichlet.simul( alpha )
htitle <- expression(paste( alpha[0], "=.2, ", p[1], "=.7"   ) )

#*** alpha0=3
alpha0 <- 3
alpha <- alpha0*probs
alpha <- matrix( alpha, nrow=N, ncol=length(alpha), byrow=TRUE  )
x <- sirt::dirichlet.simul( alpha )
htitle <- expression(paste( alpha[0], "=3, ", p[1], "=.7"   ) )