init1.k: Initialization 1 for the \(\beta_{k}\) parameterization (\(m=3\)).

Description

This function is the small initialization procedure (Initialization 1) for parameterization \(m=3\). The selected values are the ones that initialize the EM algorithm bkmodel.

Usage

init1.k(reference, response, L, K, t2, m2,mnr)

Value

alpha,: numeric array of dimension \(J \times K\) containing the selected values \(\alpha_{jk}^{(0)}\), \(j=1,\ldots,J\), \(k=1,\ldots,K\) that will be used to initialize main EM.
beta: numeric array of dimension \(K \times T\) containing the selected values of \(\beta_{k\tau}^{(0)}\), \(k=1,\ldots,K\), \(\tau=1,\ldots,T\), that will be used to initialize the main EM.
psim: numeric vector of length \(K\) containing the weights that will initialize the main EM.
ll: numeric, the value of the loglikelihood, computed according to the mylogLikePoisMix function.

Arguments

reference: a numeric array of dimension \(n\times V\) containing the \(V\) covariates for each of the \(n\) observations.
response: a numeric array of count data with dimension \(n\times d\) containing the \(d\) response variables for each of the \(n\) observations.
L: numeric vector of positive integers containing the partition of the \(d\) response variables into \(J\leq d\) blocks, with \(\sum_{j=1}^{J}L_j=d\).
K: positive integer denoting the number of mixture components.
t2: positive integer denoting the number of different runs.
m2: positive integer denoting the number of iterations for each run.
mnr: positive integer denoting the maximum number of Newton-Raphson iterations.

Author

Panagiotis Papastamoulis

Examples

Run this code

## load a simulated dataset according to the b_jk model
## number of observations: 500
## design: L=(3,2,1)
data("simulated_data_15_components_bjk")
x <- sim.data[,1]
x <- array(x,dim=c(length(x),1))
y <- sim.data[,-1]
## initialize the parameters for a 2 component mixture
## the number of the small runs are t2 = 3
## each one consisting of m2 = 5 iterations of the EM.
start1 <- init1.k(reference=x, response=y, L=c(3,2,1), 
                       K=2, m2=5, t2=3,mnr = 5)
summary(start1)