Update class allocation vector — update

This function updates the class allocation vector (independently for all observations) by drawing from its conditional distribution.

Usage

update_z(s, beta, b, Omega)

Arguments

s: The vector of class weights of length C. Set to NA if P_r = 0. For identifiability, the vector must be non-ascending.
beta: The matrix of the decision-maker specific coefficient vectors of dimension P_r x N. Set to NA if P_r = 0.
b: The matrix of class means as columns of dimension P_r x C. Set to NA if P_r = 0.
Omega: The matrix of class covariance matrices as columns of dimension P_r*P_r x C. Set to NA if P_r = 0.

Value

An updated class allocation vector.

Details

Let $z = (z_1,\dots,z_N)$ denote the class allocation vector of the observations (mixed coefficients) $\beta = (\beta_1,\dots,\beta_N)$. Independently for each $n$, the conditional probability $\Pr(z_n = c \mid s,\beta_n,b,\Omega)$ of having $\beta_n$ allocated to class $c$ for $c=1,\dots,C$ depends on the class allocation vector $s$, the class means $b=(b_c)_c$ and the class covariance matrices $Omega=(Omega_c)_c$ and is proportional to $$s_c \phi(\beta_n \mid b_c,Omega_c).$$

Examples

### class weights for C = 2 classes
s <- rdirichlet(c(1,1))
### coefficient vector for N = 1 decider and P_r = 2 random coefficients
beta <- matrix(c(1,1), ncol = 1)
### class means and covariances
b <- cbind(c(0,0),c(1,1))
Omega <- cbind(c(1,0,0,1),c(1,0,0,1))
### updated class allocation vector
update_z(s = s, beta = beta, b = b, Omega = Omega)
#>      [,1]
#> [1,]    1