init1.2.jk.j: 2nd step of Initialization 1 for the \(\beta_{jk}\) (\(m=1\)) or \(\beta_{j}\) (\(m=2\)) parameterization.

Description

This function is the second step of the two-step small initialization procedure (Initialization 1), used for parameterizations \(m=1\) or \(m=2\). At first, init1.1.jk.j is called for each condition \(j=1,\ldots,J\). The values obtained from the first step are used for initializing the second step of the small EM algorithm for fitting the overall mixture \(\sum_{k=1}^{K}\pi_j\prod_{j=1}^{J}\prod_{\ell=1}^{L_j}f(y_{ij\ell})\). The selected values from the second step are the ones that initialize the EM algorithm (bjkmodel or bjmodel), when \(K=K_{min}\).

Usage

init1.2.jk.j(reference, response, L, K, m1, m2, t1, t2, model,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 \(J \times K \times T\) (if model = 1) or \(J \times T\) (if model = 2) containing the selected values of \(\beta_{jk\tau}^{(0)}\) (or \(\beta_{j\tau}^{(t)}\)), \(j=1,\ldots,J\), \(k=1,\ldots,K\), \(\tau=1,\ldots,T\), 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.
m1: positive integer denoting the number of iterations for each run of init1.1.jk.j.
m2: positive integer denoting the number of iterations for each run of init1.2.jk.j.
t1: positive integer denoting the number of different runs of init1.1.jk.j.
t2: positive integer denoting the number of different runs of init1.2.jk.j.
model: binary variable denoting the parameterization of the model: 1 for \(\beta_{jk}\) and 2 for \(\beta_{j}\) parameterization.
mnr: positive integer denoting the maximum number of Newton-Raphson iterations.

Author

Panagiotis Papastamoulis

Examples

Run this code

############################################################
#1.            Example with beta_jk (m=1) model            #
############################################################
## 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 overall small runs are t2 = 2
## each one consisting of m2 = 2 iterations of the EM.
## the number of the small runs for the first step small EM
## is t1 = 2, each one consisting of m1 = 2 iterations.
start2 <- init1.2.jk.j(reference=x, response=y, L=c(3,2,1), 
                       K=2, m1=2, m2=2, t1=2, t2=2, model=1,mnr = 3)
summary(start2)

############################################################
#2.            Example with beta_j (m=2) model             #
############################################################

## initialize the parameters for a 2 component mixture
## the number of the overall small runs are t2 = 3
## each one consisting of m2 = 2 iterations of the EM.
## the number of the small runs for the first step small EM
## is t1 = 2, each one consisting of m1 = 2 iterations.
start2 <- init1.2.jk.j(reference=x, response=y, L=c(3,2,1), 
                       K=2, m1=2, m2=2, t1=2, t2=3, model=2,mnr = 5)
summary(start2)